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Xerox University Microfilms 300 North Zeeb Road Ann Arbor, Michigan 481 OS i i 75-14,732 FISKE, Paul Raymond, 1938A REGIONAL ANALYSIS OF RECREATIONAL BOATING PARTICIPATION IN THE STATE OF MICHIGAN. Michigan State University, Ph.D., 1974 Economics, general Xerox University Microfilms , Ann Arbor, M ichigan 48106 4 A REGIONAL ANALYSIS OF RECREATIONAL BOATING PARTICIPATION IN THE STATE OF MICHIGAN By Paul Raymond Fiske A DISSERTATION Submitted to Michigan State U n iversity in p a r t ia l f u l f i l l m e n t o f the requirements f o r the degree o f DOCTOR OF PHILOSOPHY Department o f Resource Development 1974 ABSTRACT A REGIONAL ANALYSIS OF RECREATIONAL BOATING PARTICIPATION IN THE STATE OF MICHIGAN By Paul Raymond Fiske This study was designed to in v e s tig a te regional v a ria tio n in recreatio n al boating p a r tic ip a tio n rates in f i v e regions w ith in the State o f Michigan. Each study region consisted o f m ulti-county u n its , delineated as Michigan Planning and Development Regions, or re c re ­ ation sub-planning regions. Two o f the regions u t i l i z e d consisted of Standard M etropolitan S t a t i s t i c a l Areas (SMSA's): D e t r o it , Lansing, and the Monroe County portion o f the Toledo, Ohio SMSA. Two o f the study regions were m ulti-cou nty units located in the northern portion of Michigan's Lower Peninsula; and the f in a l region (M arquette-Iron Mountain) is located in the Upper Peninsula. A d e ta ile d questionnaire was prepared and mailed to a sample of 21,764 Michigan re g is tere d boat owners. This questionnaire was designed to c o lle c t inform ation in six p rin c ip a l categories: (1 ) i n f o r ­ mation concerning sampled w a te rc r a ft ( e . g . , len g th , horsepower); (2) place of storage o f w a te rc r a ft during the boating season; (3) tra n s­ portation of w a te rc ra ft during the study year; (4) use of recrea tio n al w a te rc ra ft during the study year (calendar 1968); (5 ) number o f Paul Raymond F iske (registered and unregistered) w ate rcraft owned by respondents; and (6) socio-economic c h a ra c te ris tic s o f sampled w a te rc ra ft owners. Individual v a ria tio n in boating p a rtic ip a tio n was analyzed by estimating a lea st squares equation fo r each o f the f iv e independent study regions, and fo r the to ta l (State o f Michigan) sample. Regional v a ria tio n in population p a rtic ip a tio n in boating a c t i v i t i e s was analyzed by an aggregate p a rtic ip a tio n model. Considerable v a ria tio n in the ra te o f recreational boating p a rtic ip a tio n was found to e x is t among sampled registered w ate rcraft owners in the State o f Michigan. The estimated number o f to ta l boating a c t i v i t y occasions varied considerably among counties. The highest rates of boating p a rtic ip a tio n were found to e x is t in non-metropolitan areas o f the State. Among socio-economic variables analyzed in th is study, fam ily size , occupation of fam ily head, and age o f family head were s i g n i f i ­ cantly correlated with individual boating p a rtic ip a tio n in one or more study regions. Boating p a rtic ip a tio n increased p o s itiv e ly with family size in two of the study regions delineated. A s ig n ific a n t (and p o s itive ) co rrela tio n was also noted fo r the statewide equation. This finding indicates that boating tends to be a fam ily a c t i v i t y ; and th at the highest rates of boating p a rtic ip a tio n tend to e x is t among larger fam ilies who own registered w ate rc ra ft. S ig n ific a n t relationships were found to e x is t between registered boat owner's occupational class and boating p a rtic ip a tio n rate in four of the fiv e study regions examined. In Region l - - D e t r o i t , the pro­ fessional occupation had a s ig n ific a n t (but negative) e ff e c t upon Paul Raymond F iske boating p a rtic ip a tio n . In Region 6— Lansing, none o f the occupational classes used were s ig n if ic a n t ly correlated with boating p a rtic ip a tio n . In Region 7C— Saginaw Bay, boat owners employed as service workers had a s ig n ific a n t (and p o s itiv e ) e f f e c t upon boating p a rtic ip a tio n . Other factory workers was the only occupational class which had a s ig n ific a n t re latio n sh ip with boating p a rtic ip a tio n ra te in Region 12A— MarquetteIron Mountain. This occupational class had a p o s itiv e e f f e c t on the dependent va ria b le. Age o f fam ily head was s ig n ific a n t ly correlated with boating p a rtic ip a tio n in three o f the f iv e study regions examined: Region 1 -- D e tr o it, Region 10— Traverse Bay, and Region 12A— Marquette-Iron Mountain. In Region 10, age of fam ily head was p o s itiv e ly correlated with boating p a rtic ip a tio n . However, there was a negative c o rre la tio n between age and boating p a rtic ip a tio n in both the D e tro it and MarquetteIron Mountain Regions. While s ig n ific a n t co rrelatio ns existed between family income of respondents and boating p a r tic ip a tio n , these findings should be regarded as inconclusive since the data collected on family income was inadequate to provide a basis fo r a rigorous te s t o f th is re latio n sh ip . In addition to (independent) variables re la tin g to socio­ economic ch a ra c te ris tic s of sampled w ate rcraft owners (or th e ir immediate f a m ilie s ) , the modified u s e r-c h a ra c te ris tic model contained variables concerning the sp ecification s of sampled w a te rc ra ft. Place- of-storage o f w ate rcraft (during the boating season) was found to be s ig n if ic a n t ly correlated with boating p a rtic ip a tio n in three of the fiv e study regions u t i l i z e d , as well as in the to ta l (statewide) Paul Raymond F is k e automobile d riv in g distance from a county seat to the closest point of boating access on a Great Lake increases, boating p a r t ic ip a tio n by the population o f th a t county would decrease. Surface water acreage was p o s itiv e ly co rrelated w ith boating p a r tic ip a tio n in the "bottom t h i r t y " counties o f o r i g i n , i . e . , among the bottom t h i r t y counties of o r i g i n , the aggregate boating p a r t i c i ­ pation ra te would be expected to increase d i r e c t l y with the r e l a t i v e a v a i l a b i l i t y o f boatable surface water acreage. A p o s itiv e r e l a t i o n ­ ship was also found to e x is t between a county's boating p a r tic ip a tio n rate and the number o f public boat-launching s ite s w ith in the county. Supply variables are thus found to be important as explanatory v a ria b le s , and represent p o lic y tools which are a v a ila b le to public adm inistrators. ACKNOWLEDGMENTS I wish to express my appreciation to Dr. M ilton H. S tein m u eller, my academic advisor and d is s e rta tio n chairman, fo r his endless patience, encouragement and guidance during a l l stages o f th is study. Special thanks also go to Dr. Daniel Chappelle and Dr. Michael Chubb fo r t h e i r many h elpfu l ideas, suggestions, and c r itic is m s during th is study, and throughout my graduate program. I also wish to thank Drs. Roleigh Barlowe and Michael Chubb fo r making a v a ila b le the necessary computer time f o r analyzing the data collected in th is study. Special thanks are also extended to the s t a f f o f the Recreation Research and Planning U n it, Department o f Parks and Recreation Resources, Michigan State U n iv e rs ity , fo r assistance rendered in preparation and d is t r ib u t io n o f the boater survey questionnaire, and in data processing and coding. Appreciation is also expressed to Mr. Keith Wilson, D ire c to r, Waterways D iv is io n , Michigan Department o f Natural Resources, fo r sponsoring th is study, and f o r making a v a ila b le s t a f f assistance in d is t r ib u t io n and r e t r i e v a l o f the survey questionnaire. F in a l l y , I wish to g r a t e f u l l y acknowledge the assistance o f my w ife , Jan. Without her assistance and u n tirin g support, i t would not have been possible fo r me to complete th is study. My two sons, Scott and Steven, also demonstrated much patience and understanding over an extended period o f time, when they did not receive the usual amount o f a tte n tio n and guidance from t h e i r fa th e r . TABLE OF CONTENTS Page ACKNOWLEDGMENTS ii LIST OF A P P E N D IC E S ............................................................................................... v1 LIST OF TABLES................................................................................................................... v i i LIST OF F I G U R E S ...................................................................................................... x Chapter I. II. III. ............................................................... 1 Introduction .......................................................................................... The Problem S ettin g ............................................................................. Study O b j e c t i v e s ................................................................................... Assumptions and L im itations .......................................................... Study H y p o t h e s e s ................................................................................... M ethodology................................................................................................ Background o f This Study and Data S o u r c e s ................................ 1 2 12 12 15 16 17 INTRODUCTION AND BACKGROUND THE NATURE OF THE DEMAND FOR OUTDOOR RECREATION . . . . 18 The Theory o f Consumer Demand .......................................................... Growth in Outdoor Recreation Demand ............................................. The Outdoor Recreation Commodity ................................................... Public, P riv ate and Mixed Goods ................................................... Problems o f Measuring Demand .......................................................... Recreational Boating--A Case Study ............................................. 18 26 40 49 53 63 DATA COLLECTION PROCEDURES............................................................... 68 The Study A r e a .......................................................................................... The Sample D e s i g n ................................................................................... The Sample U n i v e r s e ...................................................................... The Sample U n i t ................................................................................... The Sample F r a m e ............................................................................ Drawing o f S a m p l e ............................................................................ The Mail Q u e s t i o n n a i r e ....................................................................... M ailing Procedures ............................................................................. Response to the Q u e s t i o n n a i r e ................................................... Non-Respondent Interviews .......................................................... Data Processing and C o d in g ................................................................ 68 82 82 83 84 84 86 88 89 89 93 ■ ■ j m C hapter IV. Page RESULTS OF THE INVESTIGATION................................................................. 95 Geographical D is tr ib u tio n o f Boating P a rtic ip a tio n . . . 95 A n a ly tic a l Procedures ....................................................................... 102 Modified U s er-C h ara cte ristics Model ............................. 102 Model S p e c i f i c a t i o n .......................................................................103 Computational Procedures .......................................................... 112 .................................................... 116 Aggregate P a rtic ip a tio n Model Model S p e c i f i c a t i o n .............................................................................. 117 Computational Procedures .......................................................... 130 Data Analysis— R e s u l t s .......................................................................130 Modified User C h a ra c te ris tic s Model .......................................... 131 Region 1— D e t r o i t .......................................................................132 139 Region 6— L a n s i n g ................................................................ ...... Region 7C— Saginaw B a y ................................................................ 145 Region 10— Traverse B a y .......................................................... 153 Region 12A--M arquette-Iron Mountain ................................ 159 The S tate o f Michigan ................................................................ 164 Aggregate P a rtic ip a tio n Model .................................................... 172 The State of M i c h i g a n ................................................................ 174 Top 30 O rigin C o u n t ie s ........................................................................177 Bottom 30 Counties o f O r i g i n ....................................................180 O u t-o f-S ta te Boating ............................................................................. 184 V. SUMMARY, CONCLUSIONS, LIMITATIONS, AND RECOMMENDATIONS FOR FURTHER RESEARCH .............................................................................................. 187 S u m m a ry .............................................................................................................. 187 .......................................... 187 Modified User C h a ra c te ris tic s Model Family Income ................................................................................... 188 Family S i z e ................................................................................... 188 Occupation o f Household H e a d ....................................................189 Age o f Family H e a d .......................................................................189 Educational Level o f Household Head ................................ 190 Place o f Storage o f W a t e r c r a f t .....................................................191 Number o f W atercraft Owned ................................................... 192 Length o f Sampled W atercraft .................................................... 192 Horsepower Rating o f W atercraft Motor ................................ 193 Type o f Power System o f W a t e r c r a f t .......................................193 Transportation o f Sampled W atercraft ................................ 194 Aggregate P a rtic ip a tio n Model .................................................... 195 Travel Distance ............................................................................. 196 Aggregate Disposable Income .................................................... 196 Percent of Households w ith Incomes under $3,000 . . 197 Percent o f Households w ith Incomes over $10,000 . . 197 Population Density ....................................................................... 198 Distance from a Great L a k e ....................................................198 Proportion o f M in o rity Races in Population . . . . 199 Distance from an SMSA— S i z e - D i s t a n c e ................................ 199 1v Chapter Page Number o f Commercial and Public Campgrounds . . . . 200 Surface Water Acreage o f County ................................................ 201 Public Boat-Launching Sites ...................................................... 201 Number o f Hotels, Hotels, Tou rist Courts, and Camps . 202 Number o f Amusement and Recreation Service Firms . . 202 Number o f Registered W atercraft per County . . . . 203 Occupations o f County Residents ................................................ 203 Conclusions..................................................................................................... 204 L i m i t a t i o n s ..................................................................................................... 213 Recommendations fo r Further Research .......................................... 217 APPENDICES........................................................................................................................ 220 BIBLIOGRAPHY ........................................................................................................... v 324 LIST OF APPENDICES Appendix Page A. Mail Survey Q u e s tio n n a ire ............................................................................. 221 B. Code Numbers fo r Michigan Counties, Total Number o f Registered W atercraft, Number o f Questionnaire Responses used in Analysis, and Expansion Factors Calculated fo r use in Estimating Total Boating A c t iv ity Occasions, by Michigan O rigin County. . . . 229 C. Optical Scan Sheets used in Coding Mail Survey R e s p o n s e s ..................................................................................................... 234 D. O rig in -D is tin a tio n Matrix and Table Showing Procedure Followed in Calculating the One-Way Travel Distance, by Michigan Origin County ............................................................... 240 E. Correlation Matrices 301 F. S ta t is tic s from I n i t i a l Regression Equations ............................................................................ vi .......................... 305 LIST OF TABLES T ab le 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. Page Numbers o f Registered W atercraft in Michigan, by Size Class, fo r Selected Y e a r s .................................................................................. 64 Expenditures fo r the Michigan Waterways Commission Marina Construction Program, 1964-1970 65 Population o f Regional Study Areas and the State o f Michigan, and Percentage Change: 1960-1970 75 Median Family Income, and Per Cent o f Families in Selected Income Classes, fo r Regional Study Areas and the State o f Michigan: 1960-1970 76 Percentage D is trib u tio n o f Population by Residence Class fo r Regional Areas and the State o f Michigan, 1960 and 1970 78 Selected Employment C h aracteristics o f Employed Persons fo r Regional Study Areas and the State o f Michigan, 1960 and 1970 80 Number o f Questionnaires Mailed, and Number o f Responses Retained f o r S t a t i s t i c a l Analysis, by Boat-Length Class . 90 Questionnaires Mailed and Returned, and Percentage Response f o r Survey Control Counties ............................................................... 91 Estimated Population, Boat Days, Sample S ize, and Calculated Boat-Use Periods Per 1,000 Population, by Michigan Origin County, 1968 97 Income Class D is trib u tio n o f Sampled W atercraft Owners from Region 1, 1968 . . . . 133 Frequency o f Boating on Great Lakes by Number and Per­ centage of Respondents in Selected Income Classes, Region 1, 1968 134 Frequency o f Boating on Inland Lakes and Streams by Number o f Respondents in Selected Income Classes, Region 1, 1968 . 135 S t a t is tic s from the Final Regression Equation fo r Region 1, D e t r o i t .........................................................................................137 v ii T ab le 14. 15. 16. Page Income Class D is trib u tio n o f Sampled W atercraft Owners, Region 6, 1968 140 Frequency o f Boating on Great Lakes by Number and Per­ centage o f Respondents in Selected Income Classes, Region 6, 1968 141 Frequency o f Boating on Inland Lakes and Streams, by Number and Percentage o f Respondents in Selected Income Classes, Region 6, 1968 142 17. S t a t is tic s from the Final Regression Equation fo r Region 6, L a n s i n g ............................................................................................................144 18. Income Class D is trib u tio n o f Sampled W atercraft Owners from Region 7C, 1968 ........................................................................................ 146 Frequency of Boating on Great Lakes by Numbers o f Respondents in Selected Income Classes, Region 7C, 1968 149 Frequency o f Boating on Inland Lakes and Streams by Number o f Respondents in Selected Income Classes, Region 7C, 1968 150 19. 20. 21. S t a t is t ic s from the Final Regression Equation fo r Region 7C, Saginaw B a y ..................................................................................................... 152 22. Income Class D is trib u tio n o f Sampled Watercraft Owners, Region 10, 1968 ........................................................................................ 154 Frequency o f Boating on Great Lakes by Number and Percentage of Respondents in Selected Income Classes, Region 10, 1968 155 Frequency o f Boating on Inland Lakes and Streams by Number and Percentage o f Respondents in Selected Income Classes, Region 10, 1968 ........................................................................................ 156 23. 24. 25. S t a t is tic s from the Final Regression Equation fo r Region 10, Traverse B a y ..................................................................................................... 158 26. Income Class D is trib u tio n o f Sampled W atercraft Owners, Region 12A, 1968 160 Frequency o f Boating on Great Lakes by Number and Per­ centage o f Respondents in Selected Income Classes, Region 12A, 1968 161 Frequency o f Boating on Inland Lakes and Streams by Number and Percentage o f Respondents in Selected Income Classes, Region 12A, 1968 162 27. 28. v iii i T a b le 29. Page S t a t i s t i c s from the Final Regression Equation f o r Region ............................................................. 12A, M arquette-Iron Mountain 30. Income Class D is tr ib u tio n o f Sampled W atercraft Owners, S tate o f Michigan, 1968 31. A Comparison o f Median Family Income o f Respondents, by Study Region, 1968 ....................................................................................... 32. Frequency o f Boating on Great Lakes by Number o f Respondents in Selected Income Classes, S tate o f Michigan, 1968 . . . 163 166 167 33. Frequency o f Boating on Inland Lakes and Streams by Number o f Respondents in Selected Income Classes, S tate of Michigan, 1968 34. S t a t i s t i c s from the Final Regression Equation f o r the State o f M i c h i g a n ....................................................................................................... 169 35. S t a t i s t i c s from the Final Regression Equation, State o f M i c h i g a n .............................................................................................................. 175 36. S t a t i s t i c s from the Final Regression Equation, Top 30 Michigan Counties o f O rigin .................................................................... 37. 179 S t a t is t ic s from Final Regression Equation, Bottom 30 Countries o f O r i g i n .................................................................................... 182 ix LIST OF FIGURES F ig u re 1. Page Michigan Planning and Development and Recreation Sub-Plan Regions U t iliz e d as Study Areas .................................................... x 72 CHAPTER I INTRODUCTION AND BACKGROUND Introduction When we e le c t to watch the play o f human motives th a t are o r d i­ nary— that are sometimes mean and dismal and ignoble— our impulse is not the philosopher's impulse, knowledge fo r the sake o f know­ ledge, but rather the p hysiologist's knowledge f o r the healing th at knowledge may help to bring. Wonder . . . is the beginning o f philosophy. I t is not wonder, but rather the social enthusi­ asm which revolts from the sordidness of mean streets and the joylessness o f withered liv e s , th at is the beginning o f economic science. Here, i f in no other f i e l d , Comte’ s great phrase holds good: " I t is f o r the heart to suggest our problems; i t is fo r the i n t e l l e c t to solve them. . . . ' Outdoor recreation constitutes an area o f increasing importance in public resource policy. A m ajority o f Americans cu rren tly p a r t i c i ­ pate in some form o f outdoor recreation a t public or p riv a te f a c i l i t i e s . V is ita tio n rates a t national parks and fo re s ts , and a t s ta te , county, and local f a c i l i t i e s have climbed ste ad ily fo r decades. Extensive recreation f a c i l i t i e s have been provided by the various levels of government (fe d e r a l, s ta te , and l o c a l ) , and by the private sector. In response to increasing levels o f use of av ailab le f a c i l i t i e s by campers, swimming enthusiasts, boaters, and other re c re a tio n is ts , public agencies have embarked upon extensive land acquisition programs in order to "keep ahead" of increased p a rtic ip a tio n . ^Cf. A. C. Pigou, The Economics o f Welfare (4th ed.; New York: St. M artin 's Press, 1962), pp. 4-5. 1 2 In the United States, most people do. p a rtic ip a te in some form o f outdoor recreatio n . In 1960, fo r example, i t was estimated th a t Americans engaged in one or more outdoor recreation a c t i v i t i e s on 4.4 b i l l i o n separate occasions; and fu rth e r, th a t 90 per cent o f a l l Americans p a rtic ip ate d one or more tim es J A 1968 study places the aggregate level o f consumer spending on outdoor recreation a t $83 b il l io n in the United States. I t was fu rth e r estimated in the same study th a t the average annual rate o f increase in consumer spending on recreation equipment between 1964 and 1368 was about $6 b i l l i o n per year. Outdoor recreation has, indeed, become big business. The Problem Setting V ir t u a l l y every re p o rt, paper, or a r t i c l e w ritte n on the topic of outdoor recreation during the past several years speaks o f everincreasing demand. For many years, Americans have been expanding t h e ir level o f p a rtic ip a tio n . absolute sense. This has been true in both a r e l a t i v e and While many improvements are needed in the s t a t is t i c a l information re la tin g to the rate and level o f demand, the a v a ila b le Outdoor Recreation Resources Review Commission, Outdoor Recreation For America (Washington: U.S. Government P rin tin g O ffic e , 1962), pp. 4-5; As used h e re a fte r, ORRRC refers to the U. S ., Outdoor Recreation Resources Review Commission, created by Congressional Act o f June 28, 1958 (Public Law 85-470, 72 S tat. 238). The Commission was established to determine (1) . . the recreation wants and needs of the American People now and . . . in the years 1976 and 2000;” (2) ". the recreation resources o f the Nation a v a ila b le to f i l l those needs;” and (3 ) "What p o licies and programs should be recommended to insure th at the needs o f the present and fu tu re are adequately and e f f i c i e n t l y met?" o Expenditure categories included camper t r a i l e r s , boats, camping equipment, fis h in g , hunting, vacation t r i p s , and "other amusements." See, "$80 B illio n For Leisure," U. S. News and World Report, Vol. 70, No. 13 (September 15, 1969), pp. 58-61. 3 information a t hand appears c le a r: a large m ajority o f Americans, when afforded the physical opportunity, and given fre e choice, are w il lin g to devote ce rtain portions o f t h e i r time and incomes to outdoor recre­ ation a c t i v i t i e s . Mass p a rtic ip a tio n in recreation {as a le is u re time a c t i v i t y ) is , fo r the most p a rt, a uniquely American phenomenon. In past times, and even today in many parts o f the world, very few countries have experienced le is u re on a scale such as is enjoyed by the people o f the United States. History reveals th a t most people down through the ages have had to labor so hard during t h e i r lif e t im e in order to produce the bear necessities o f l i f e - - f o o d , c lo th in g , and s h e lt e r - - t h a t l i t t l e i time was ever l e f t over fo r spare time ( le is u r e ) a c t i v i t i e s . Under these circumstances, only the most wealthy or priviledged classes ever had much le is u re . In the United States, a number o f social and economic (as well as p o l i t i c a l ) conditions have changed in order to make recreation a c t i v i t i e s a more a tta in a b le goal fo r the average American. Most scholars agree th at the princip al factors contributing to widespread p a rtic ip a tio n in outdoor recreation consist o f: (1) higher population lev els; (2) increased p ro d u ctivity per man hour o f labor, (3) changes in the amount and timing o f a v a ila b le le is u re , e . g . , shorter work weeks, more paid holidays, longer paid vacations; (4) increased ^There is , o f course, room fo r genuine debate concerning the actual extent o f le is u re time a v a ila b le to most people. Some re ­ searchers have advanced convincing arguments th at most Americans are r e a lly without much discretion ary le is u re or "choosing" time. More w il l be said about th is fa c to r in Chapter I I . 4 concentration o f population in c i t i e s and urban areas, coupled w ith urban expansion and sprawl; (5 ) widespread ownership o f automobiles; (6) improved a ll-w e a th e r highways, and the a v a i l a b i l i t y o f cheaper a i r t r a v e l; {7) increasing consumers' real incomes; (8) changed a t t i ­ tudes towards le is u re and re c re a tio n ; and (9) mass a d v e rtiz in g and marketing promotion practices.^ Much o f the current in te r e s t in outdoor recreatio n can a c tu a lly be traced, in large measure, to very e a rly land p o lic ie s during the n ation 's form ative years. Even in co lo n ial times, in te r e s t was shown in conserving c e rta in land and water resources f o r public b e n e fit. One o f the e a r l i e s t public in terven tio ns having im plications f o r outdoor recreation was the Great Ponds A ct, Passed by the Massachusetts Bay Colony in 1641. This act reserved about two thousand bodies o f w ater, exceeding ten acres in s iz e , and t o t a l l i n g some 90,000 acres, decreeing that they " . . . were to remain as a public resource fo re v e r open to the public fo r 'fis h in g and f o w l i n g . " 1 The common or "Green," so ty p ic a l o f many New England Towns even today, had i t s o rig in in the e a rly co lo n ial period. One of the e a r l i e s t and most noteworthy o f these municipal areas was the Boston Common, established in 1634. This area has been reserved f o r public use by Boston c itiz e n s f o r more than three hundred years. Another milestone in the h is to ry o f municipal parks occurred in 1853 when the ^See, f o r example, Marion Clawson, Methods o f Measuring the Demand For and Value o f Outdoor R ecreation, Reprint No. 10 (Washington: Resources fo r the Future, I n c . , 1959), p. 1; a ls o , Raleigh Barlowe and M ilton H. Steinm ueller, "Trends in Outdoor Recreation," A Place to Live; 1963 Yearbook o f A g ric u ltu re (Washington: U. S. Department o f A g ric u ltu re , 1963), pp. 299-301. 5 C ity of New York began acquiring land fo r Central P a rk --th e f i r s t area acquired by a m u n ic ip a lity e x c lu s iv e ly fo r public re c re a tio n . The Congress o f the United States established an important preccedent e a rly in the 19th Century when i t passed an act in 1832, reserving four sections o f land in the Quachita Mountains o f Arkansas . f o r the fu tu re disposal o f the United S ta te s ." This reservation was made to preserve the hot mineral springs o f the area from ". descriminate e x p lo ita tio n and abuse by p riv a te in t e r e s t s ." th is i n i t i a l . . in - Following step, Congress established the Yosemite Grant in 1864. The Yosemite V a lle y , and the nearby grove o f "Mariposa Big Trees" were reserved from the public domain and entrusted to the State o f C a li ­ fo rn ia " . . . upon the express conditions th a t the premises shall be held fo r public use, re s o rt and re c re a tio n ; shall be in a lie n a b le fo r a l l time. . . . " L ater (in 1872), Congress established Yellowstone National Park— the f i r s t national park in the world. I t should also be noted th a t commercial recreatio n assumed some importance q u ite e a rly in the 19th Century. As e a rly as 1820, hotels and accommodations fo r to u r is ts were a v a ila b le a t Franconia Notch in the White Mountains o f New Hampshire. By 1825, a hotel and resort area was also well established in the C a ts k ills o f New York State as w e l l . 1 For the most p a r t , however, outdoor re c re a tio n has la rg e ly remained a public m atter in the United States. As Clawson notes: ^The preceeding h is to r ic a l n a rr a tiv e is based upon several references: Frank E. Smith, The P o lit ic s o f Conservation (New York: Pantheon Books, 1966); C. Frank Brockman, Recreational Use o f Wild Lands (New York: McGraw-Hill Book Company, I n c . . 1959); John Is e . Our National Park Policy; A C r i t i c a l History (Baltim ore: The Johns Hopkins Press, 1961). 6 Most outdoor recreatio n in the United States takes place on p u b lic ly owned and provided areas, including water bodies open to the p ub lic. Some in d ivid u als own t h e i r own outdoor recreation places, but in most instances these people also use public areas. Hunting, fis h in g , camping, p ic n ic in g , h ik in g , and other extensive land use a c t i v i t i e s are la r g e ly upon public lands and waters. There are several reasons f o r the dominance o f the p u b lic ly owned areas. For one th in g , the minimum adequate area f o r most outdoor recreatio n a c t i v i t i e s is simply too large and too expen­ sive f o r any but the ric h e s t people to have as t h e i r own; fo r another, such areas normally have ample capacity fo r f a r more people than the members o f a single fa m ily . I t is not only the costs o f owning such areas, but also the costs o f minimum up­ keep and serv ice, th a t may be d ec is iv e. For many kinds o f o u t­ door a c t i v i t i e s , supervision or in s tru c tio n is also needed, and t h i s , too, can usually be provided most economically on a la rg e r scale than the single fam ily . At any r a t e , public provision o f outdoor recreatio n areas is a w idely accepted aspect o f American l i f e . The ro le o f p riv a te lands and waters may be la rg e r in the fu tu re . . . but outdoor recreation seems l i k e l y to continue to be ca rrie d out la r g e ly on p u b lic ly provided a r e a s .1 In addition to e a rly reservations o f land fo r municipal and national parks, large acreages were withdrawn from the public domain around the end o f the 19th Century. Withdrawals were made fo r fo re s t reserves, water power and re s e rv o ir s i t e s , national monuments, m i l it a r y reservations, b ird and game sanctuaries, and a host o f other uses. While much of the land (and w ater) area reserved was not withdrawn ^Marion Clawson, Land and Water For Recreation (Chicago: Rand-McNally and Company, 1963), pp. 10-11. 2 The public domain is here defined to include a l l lands th a t were a t any time owned by the United States and subject to sale or other tra n s fe r o f ownership under the laws o f the federal government. The national domain consists o f the to t a l area o f land and water under the ju r is d ic t io n o f the United States. The federal government has, or has had, both ownership in and ju r is d i c t io n over the public domain, while i t exercises only ju r is d ic t io n over the national domain. See, E. Louise P e ffe r, The Closing o f the Public Domain (Stanford, C a li ­ fo rn ia : The Stanford U n ive rsity Press, 1951), pp. 8-31. 7 ex clu sive ly fo r outdoor recreation uses, much o f the acreage has, over the ye ars, come to have tremendous s ig n ific a n c e as a physical supply base f o r re crea tio n al a c t i v i t i e s . National Forest reserves were a c tu a lly authorized as e a rly as 1817-J however, the power vested in the President o f the United States by Congress was never o f f i c i a l l y invoked u n t il the Hot Springs Reservation in 1832. More e x p l i c i t au th o riza tio n was to come much l a t e r in a Congressional act in 1891. There is strong evidence to suggest th a t the Congress did not recognize the f u l l s ig n ific a n c e o f the l e g is la t io n passed, however. The portion o f the b i l l dealing with fo re s t reserves was included in the le g is la t io n a t the l a s t minute as an obscure " r id e r ." For the most p a rt, the b i l l d e a lt with ro u tin e land m atters; however, the attached r id e r sp ecified th at: The President o f the United States . . . may set ap art and reserve any p art o f the public lands wholly or in p art covered with timber . . . as public reservation s.^ Several presidents made use o f th is a u th o rity . During 1897, President Cleveland created th irte e n new fo re s t reserves, t o t a l l i n g about 21.4 m illio n acres. This acreage, when added to previously 3 established reserves, made a t o ta l o f nearly 39 m illio n acres. In itia l V h e United States C onstitution places control over p u b lic ly owned lands in the hands of Congress. However, in 1817 Congress began the p ractice o f delegating to the President the a u th o rity " . . . from time to tim e, to withdraw c e rta in lands from entry to serve p a r t ic u la r functions." P e ffe r, 0 £. c i t . , pp. 14-15. 2 Cf. Outdoor Recreation Resources Review Commission, Federal Agencies and Outdoor Recreation, ORRRC Study Report 13 (Washington: U.S. Government P rin tin g O ffic e , 1962), p. 20. 3P e ffe r, 0£ . c i t . , p. 17. 8 withdrawals were made by President Harrison beginning in 1891. How­ ever, by f a r the most impressive acreage was reserved by President Theodore Roosevelt a f t e r the turn o f the century: in two years (1905 and 1906) he withdrew more than 63 m illio n acres o f public land; and alto g e th e r, created more than 148 m illio n acres o f fo re s t reserves. The Congress, f i n a l l y aware o f the f u l l sig nificance o f the powers which i t had granted, took s w ift action to s t r ip the president of these prerogatives. According to two scholars: These withdrawals aroused so much opposition th at an act was passed p ro h ib itin g additional withdrawals in many states without sp e cific congressional approval. Roosevelt signed the b i l l , but f i r s t — rumor says on the same day— he established twenty-one additional f o r e s t s .1 By 1923, there were about 161.3 m illio n acres o f land which had been withdrawn as fo re s t reserves (which by th is time were known as National Forests). In ad d itio n , power s it e reserves to ta lle d nearly 2.5 m illio n acres; national parks reserves amounted to about 7.2 m illio n acres; national monuments about 1.1 m illio n acres; m ilit a r y reservations 1.5 m illio n acres; and bird and game sanctuaries about 0.4 m illio n acres. 2 As of 1960, i t was estimated th at about 12 per cent o f the to ta l land area of the United States was contained in 25,000 designated ^Marion Clawson and Burnell Held, The Federal Lands, Their Use and Management (Baltimore: The Johns Hopkins Press, 1957), p. 167. 7 2 Including a l l other reserve categories, about 272.3 m illio n acres (more than a f i f t h o f the o rig in a l public domain) had been reserved by 1923, By way of comparison, the o rig in a l public domain was estimated to to ta l about 1.4 b i l l i o n acres. The present land area of the United States (excluding Alaska) is placed a t roughly 1.9 b il l io n acres. See, E. Louise P e ffe r, o j j . c i t . , p. 8 ; Benjamin A. Hibbard, A History o f the Public Land P o licies (New York: The MacMillan Company, 1924), pp. 529-537; and "Marion Clawson, Burnell Held, and Charles H. Stoddard, Land For the Future (Baltimore: The Johns Hopkins Press, I9 6 0 ), p. 43. public recreation areas. Most o f th is acreage, and a m a jo rity o f the recreation areas, is located w ith in the f o r ty - e ig h t contiguous states. Outdoor recreation is also premitted on much o f the remaining public domain land--873 m illio n acres administered by the Bureau o f Land Management.1 At the time of the ORRRC inventory in 1960, over f o u r - f i f t h s o f the designated land area fo r outdoor recreation was fe d e r a lly owned and managed. Most o f the acreage was administered by the so-called land-managing agencies: the National Park Service, the Forest Service, and the Bureau o f Sport Fisheries and W il d l i f e . Another group of federal agencies f a l l under the category of water management: the Corps o f Engineers, the Bureau o f Reclamation, the Tennessee Valley Authority, and the Federal Power Commission. A large number o f other agencies, bureaus, and departments play less d ir e c t or p e rife ra l roles in administering outdoor recreation programs and/or f a c i l i t i e s , e . g . , the Soil Conservation Service, the Bureau o f Indian A f f a ir s , the Depart­ ment of Housing and Urban Development, the U. S. Coast Guard, etc . One of the major recommendations o f the Outdoor Recreation Resources Review Commission, following i t s national study, was th a t a Bureau o f Outdoor Recreation be established a t the federal l e v e l , w ith in the U. S. Department o f In t e r io r . A Bureau of Outdoor Recreation was established in 1964, and i t is now charged with overall re s p o n s ib ility fo r coordinating various Outdoor Recreation Resources Review Commission, Public Outdoor Recreation Areas--Acreage, Use, P o te n tia l, ORRRC Study Report 1 "(Washington: U.S. Government P rin tin g O ffic e , 1962), p. 1. 10 programs o f the federal agencies. In a d d itio n , the Bureau has responsi­ b i l i t y fo r providing assistance to other lev els o f government ( s t a te , county, l o c a l) . In addition to providing public programs, land, and f a c i l i t i e s fo r use by the recreating public, the Federal Government has i n i t i a t e d financial assistance to p riva te landowners in order to encourage the establishment of corrmercial recreation f a c i l i t i e s . The U. S. Depart­ ment o f A griculture has been assigned r e s p o n s ib ilitie s fo r assisting in the development o f resources presently in a g ric u ltu ra l uses, and in rural areas. authority.^ The Food and A griculture Act o f 1962 provides th is Several agencies w ithin the Department o f A griculture have been given re s p o n s ib ilitie s fo r implementing the provisions of this le g is la tio n . The Soil Conservation Service has been designated as the c h ie f planning agency o f the department. The Farmers' Home Administration and the Federal Land Bank have been authorized to grant loans to rural land owners fo r the department o f recreation f a c i l i t i e s in ce rtain instances, i . e . , when design and construction standards, among other things, appear adequate. The A g ric u ltu ra l S ta b iliz a tio n and Conservation Service (ASCS) also has been given a u th o rity to make incentive payments to p riv a te land owners in order to encourage the transfer o f ce rtain lands out of a g ric u ltu re and into recreation uses. At the federal le v e l, agency e ffo r ts in administering programs and f a c i l i t i e s demanded by the recreating public have often been U. S ., Congress, Food and A g ricu lture Act o f 1962, Public Law 87-703, 87th Congress, H.R. 12391, September 27, 1962, pp. 1-2 . 11 fru strated by a lack o f uniform standards, p o lic ie s , and c r i t e r i a . Commenting on th is problem, the ORRRC observed that: In 1960 there were some 425 to 450 m illio n recreational v i s i t s to government managed, financed, or licensed f a c i l i t i e s , but no agency o f the Federal Government was established to provide recre­ ation fo r the public. The U. S. Army Corps o f Engineers was con­ cerned with aids to navigation and flood co n tro l—y e t i t en ter­ tained 106 m illio n v is ito rs in 1960. The Forest Service was estab­ lished to conserve the fo re s ts , but i t played host to 92.5 m illio n v is ito r s . Even the national park service was not formed to provide recreation in the usual sense, but to preserve unique or exceptional scenic areas. Recreation has been an in c id e n ta l, and almost a c c i­ den tal, byproduct o f the "primary" purposes o f federal agencies. Lack o f anything resembling a national recreation policy is th ere­ fore a t the root o f most o f the recreation problems o f the federal , government. But the re c re a tio n is ts e x is t even i f a policy does not. In addition to federal f a c i l i t i e s , s ta te , county, and municipal governments have acquired and developed s ig n ific a n t land areas fo r out­ door recreation. In 1960, i t was estimated th a t sta te agencies owned and administered 20,429 individual recreation areas, t o t a l li n g about 32.1 m illio n acres. County and other local units of government operated an estimated 2,560 park and recreation areas, comprising a to ta l land area o f 3.5 m illio n acres. 2 Much has been learned about the magnitude o f p a rtic ip a tio n in outdoor recreation. While a v a ila b le l i t e r a t u r e has succeeded in focusing a tte n tio n on outdoor re crea tio n , there is a general lack of q u a n tita tiv e research in the f i e l d . Although most studies have docu­ mented the fa c t th at recreation p a rtic ip a tio n has been generally in ­ creasing fo r a number of years, they generally do not attempt to analyze precisely the underlying factors thought to be re la te d to ^ORRRC Study Report 13, ojk c i t . , p. 1. ^ORRRC Study Report 1, 0 £. c i t . , pp. 8-9 . 12 levels o f p a rtic ip a tio n in p a r tic u la r recreation a c t i v i t i e s . The present study w i l l concern i t s e l f with p a rtic ip a tio n in a s p e c ific outdoor recreation a c t i v i t y — recreational boating. I t w il l be designed to id e n tify sp e cific variables believed to be associated with i n d i­ vidual and aggregate p a rtic ip a tio n in boating in the state o f Michigan, and to measure the influence o f these factors upon p a rtic ip a tio n ra tes . Study Objectives (1) The f i r s t o bjective is to obtain an estimate of the to ta l level o f recreational boating undertaken in Michigan during 1968; i t s d is trib u tio n in various geographic regions in the s ta te , and among various segments of the population. parts, dealing with This o bjective w ill involve two (a) boating a c t i v i t i e s in Michigan by residents of other states or (Canadian) Provinces, and ( b) recreational boating undertaken in other states or (Canadian) Provinces by Michigan residents. (2) The second o bjective is to id e n tify sp ecific socio-economic, demographic, and environmental factors believed to be associated with recreational boating a c t i v i t i e s ; to is o la te these factors and measure the extent o f th e ir influence upon individual and aggregate levels of boating a c t i v i t y during a given time period. A m ultiple-regression model w il l be u t il i z e d fo r s t a t is t i c a l analysis. (3) The f in a l objective is to suggest policy guidelines which w ill be relevant to the problems o f administering public and private boating f a c i l i t i e s in the State o f Michigan. Assumptions and Lim itations (1) The f i r s t major assumption is th a t the household is the decision-making u nit concerned with consumption goods and services 13 such as a recreational boating t r i p . As such, i t is faced with the problem o f a llo c a tin g i t s f i n i t e income between recreational boating trip s and other goods and services in a way th at maximizes to ta l sa tisfac tio n s. (2) I t is assumed th at households which have purchased powered w ate rcraft, and have registered them with the Michigan Secretary o f State, co n stitute the major recreational boating population o f the state. (3) I t is assumed th at a mail questionnaire mailed to a sample o f the registered w ate rcraft owners in the State of Michigan w i l l be representative of the to ta l universe o f recreational w atercraft users in the s ta te . (4) This study assumes th at w ate rcraft owners can adequately recall the magnitude and location (Michigan County) o f recreational boating a c t i v i t y undertaken during the previous boating season when asked to complete a mail questionnaire a t the conclusion o f the boating season (one calendar y e a r). (5) Each recreational boating t r i p taken presents the consumer with a set of time and money costs. This study assumes, however, that fixed costs are unimportant in the decision to make a boating t r i p as the study is lim ited to a population which has already purchased recreational boating equipment. Further, fo r purposes o f the analysis, variable travel and o n -s ite costs (made up o f such items as gasoline, food, highway t o l l s , user fees, lodging) are held constant. However, distance tra v e lle d and travel time w i l l be e x p l i c i t l y introduced in the s t a t is t i c a l analysis. 14 (6) W atercraft owners w i l l vary in the to ta l amount o f re c re ­ ational boating a c t i v i t y undertaken during any given year. household w i l l be affe c te d by Each (a ) lo c atio n w ith respect to boating opportunities (supply); (b) tastes and preferences; (c) personal circumstances such as h e a lth , fam ily income, and le is u re time a v a i l ­ able; (d) the amount o f money, time, and bother associated with going boating; (e) a lt e r n a t iv e o u tle ts fo r time and money budgets. (7) Recreational boat owners are i n d i f f e r e n t as between d i f f e r ­ ent boating a c t i v i t i e s undertaken ( e . g . , fis h in g , cruising fo r p le as u re). That i s , i t is assumed fo r the purpose o f th is study th a t the marginal ra te o f s u b s titu tio n between, say, a day spent fis h in g and a day o f waterskiing is u n ity . (8) The q u a lity o f the recreation experience is important in determining where one goes boating. That is to say, boaters are able to d i f f e r e n t i a t e the "product" produced a t a p a r tic u la r la k e , stream, or pond from th a t obtainable a t an a lt e r n a t iv e s i t e , and these per­ ceptions are important in boaters' decisions. (9) I t is assumed th a t e ith e r zero or nominal^ prices are charged fo r the use o f public boating marinas, public launching s it e s , and other re creatio n al boating f a c i l i t i e s in Michigan which are maintained and operated by the various le v e ls o f government ( s t a t e , federal and l o c a l ) . Further, i t is assumed th a t prices charged fo r comparable f a c i l i t i e s and services a t commercial boating marinas nominal p rice is d efined, in th is instance, as one which is not s u f f i c i e n t to cover construction, o peration, maintenance, and depreciation costs o f the f a c i l i t y over i t s useful economic l i f e . 15 are not s ig n ific a n t ly d if f e r e n t from those charged a t public f a c i l i ­ t ie s . Study Hypotheses (1) The level o f p a rtic ip a tio n in recreational boating by a household is not s ig n ific a n tly influenced by: (a) Family income (b) Family size (c) Occupation o f household head (d) Age o f household head (e) Educational level o f household head ( f ) Place o f storage of w a te rc ra ft (during boating season) (g) Number o f w atercraft owned (h) Length of sampled w a te rc ra ft ( i ) Horsepower rating o f w a te rc ra ft motor ( j ) Type of power system o f w ate rcraft (k) Transportation o f w ate rcraft (2) The ra te o f p a rtic ip a tio n in recreational boating by a regional (county) population is not s ig n if ic a n tly influenced by: (a) Travel distance (b) Aggregate disposable income (c) Per cent o f households with incomes under $3,000 (d) Per cent o f households with incomes over $10,000 (e) Population density ( f ) Distance from a Great Lake (g) Per cent o f population composed o f m inority races (h) Location with respect to an SMSA 16 ( i ) Number o f commercial and public campgrounds in county ( j ) Surface water acreage o f county (k) Number o f public boat launching s ite s in county (1) Number o f h otels, motels, to u r is t courts, and camps in county (m) Number of amusement and recreation service firms in county (n) Number of registered recreational w a te rc ra ft in county (o) Occupations o f county residents Methodol og.y This study is designed to estimate regional v a ria tio n in i n d i ­ vidual and aggregate p a rtic ip a tio n rates in recreational boating in the State o f Michigan. Least squares techniques w il l be used to estimate a lin e a r equation fo r f i v e Michigan Planning and Development Regions, as well as fo r the statewide sample. In a d d itio n , a second model w il l be used to in vestig ate factors associated with aggregate boating p a rtic ip a tio n rates o f regional (county) populations. The investig atio n w il l also focus upon estimating the to ta l amount of recreational boating undertaken in Michigan during calendar year 1968; i t s d is trib u tio n in various geographic regions in the s ta te , and among various segments o f the population. A sample o f 21,764 registered w a te rc ra ft owners was drawn from boat re g is tra tio n records maintained by the Michigan Department of S tate, Vehicle and W atercraft Registration D ivisio n . Approximately 10 per cent o f a l l registered Michigan w a te rc ra ft greater than 20 fe e t in 17 length were selected from each county; and 5 per cent o f the registered w ate rcraft 20 fe e t or less in length were selected in a systematic sampling procedure. A d e ta ile d questionnaire was mailed to the 21,764 boat owners selected in the f in a l sampleJ Follow-up post card reminders were mailed to survey non-respondents in three control counties: Grand Traverse, and Leelanau. Ingham, In a d d itio n , personal interviews were conducted among survey non-respondents in these three control counties. Background o f This Study and Data Sources The data used in th is study were collected in a survey o f Michigan registered boat owners by the Recreation Research and Planning U nit, Department o f Parks and Recreation Resources, Michigan State Uni­ v e rs ity . The data were collected o r ig in a lly by the Recreation Research and Planning Unit under a contract grant from the Waterways D ivis io n , Michigan Department o f Natural Resources, in order to investig ate problems of: { ! ) inventorying and analyzing current rates o f water­ c r a f t use on a statewide basis; and (2) with developing q u a n tita tiv e projection techniques f o r forecasting fu tu re levels of recreational boating in various geographic regions o f the s ta te . ^The survey questionnaire is exhibited in Appendix A. CHAPTER I I THE NATURE OF THE DEMAND FOR OUTDOOR RECREATION The prelim in ary chapter was la r g e ly devoted to a discussion o f the h is t o r ic a l roots o f outdoor recreatio n in the United S tates. Two underlying themes were woven in to (o r implied in ) the n a rr a tiv e : (1) Aggregate le v e ls o f p a r tic ip a t io n in outdoor recreatio n a c t i v i t i e s — such as camping, p ic n ic kin g , b ik in g , swimming, hunting, f is h in g , boating, e t c . — have been increasing over time; and (2 ) much o f the required supply base fo r extensive a c t i v i t i e s such as re crea tio n have been provided by means o f public action through the p o l i t i c a l process. In the present chapter, the focus w i l l s h i f t . Emphasis w i l l be given to the fac to rs which help to explain the nature and s i g n i f i ­ cance o f demand; and which are associated with consumer behavior. The Theory o f Consumer Demand Consumer behavior is concerned w ith the purchasing decisions o f households. Thus a study o f consumer demand attempts to is o la t e those va ria b les which help to explain household consumption o f goods and services. In th is respect, p a r tic ip a tio n in an outdoor recreatio n a c t i v i t y (say, boating) is not viewed as being d if f e r e n t from any other economic choice problem facing the consumer to a llo c a te c e rta in portions o f his income i f he wishes to p a r t ic ip a t e . 18 Thus, the 19 household is viewed as the major decision u n it which decides how much outdoor re crea tio n to buy a t a l t e r n a t iv e p ric e s , given the level o f household income, the prices o f a lt e r n a t iv e goods and services, e tc . There appear to be three conditions which force the individual consuming u n it (the household) to make choices concerning the various q u a n titie s o f goods and services which i t consumes: (1 ) each consuming u n it has a lim ite d ( f i n i t e ) income; (2 ) each consuming u n it has varied and unlim ited ( i n f i n i t e ) wants to be s a t i s f i e d ; and (3 ) each good or service to be consumed to s a t is f y a want may be acquired only a t a (nonzero) p r i c e d Given these three conditions, i t becomes c le a r th a t the household cannot purchase unlim ited q u a n titie s o f goods and services. I t must, th e re fo re , se lec t c e rta in combinations from among a l l o f those a v a ila b le (a t nonzero p r ic e s ). F u rth e r, i t is assumed t h a t , on the basis o f a v a ila b le knowledge, most households w il l attempt to purchase a combination o f goods and services which maximizes the t o ta l s a t is ­ fac tio n s o f the members o f th a t household group. Within the mainstream o f economic theory, there ex is ts a body o f generalized propositions r e la tin g to consumer behavior; the actions o f in d ivid u als and households in t h e i r e ff o r ts to maximize s a tis fa c tio n s (u tility ). One o f the e a r l i e s t theories advanced to explain why con­ sumers demand c e rta in goods and services was th a t o f A lfre d M arshall: I f a person has a thing which he can put to several uses, he w i l l d is t r ib u t e i t among these uses in such a way th a t i t has the same marginal u t i l i t y in a l l . For i f i t had a g reater ^W illard W. Cochrane and Carolyn S. B e ll , The Economics of Consumption (New York: McGraw-Hill Book Company, 1956), p. 79. 20 marginal u t i l i t y in one use than another, he would gain by taking away some o f i t from the second use and applying i t to the f i r s t . But when commodities have become very numerous and h ig hly s p e c ia l­ ize d , there is an urgent need fo r the fre e use o f money, or general purchasing power; fo r th a t alone can be applied e a s ily in an unlim ited v a r ie ty o f purchases. And in a money-economy, good management is shown by so ad justin g the margins o f suspense on each l i n e o f expenditure th a t the marginal u t i l i t y o f a s h illin g s worth o f goods on each l i n e sh a ll be the same. And t h is r e s u lt each one w i l l a t t a in by constantly watching to see whether there is anything on which he is spending so much th a t he would gain by taking a l i t t l e away from th a t l in e o f expenditure and putting i t on some other 1i n e . 1 This concept o f demand, i t should be noted, assumes th a t the ra tio n a l consumer w i l l seek to maximize u t i l i t i e s . As a number o f l a t e r th e o ris ts have pointed o u t, M arshall— together w ith a group o f e a r l i e r economists such as Jevons (1871) and Walras (1874)— assumed th a t u t i l i t i e s were independent, were a measurable q u a lity o f any cormtodity, and were a d d itiv e . A l a t e r economist, building upon e a r l i e r work by Pareto and Edgeworth, challenged M arsh all's assumptions con­ cerning cardinal measurement o f u t i l i t y : M arsh all's argument, th e re fo r e , proceeds from the notion of maximizing to ta l u t i l i t y , by way o f the law o f diminishing marginal u t i l i t y , to the conclusion th a t the marginal u t i l i t i e s o f com­ modities bought must be proportional to t h e i r prices. But now what is th is " u t i l i t y " which the consumer maximizes? And what is the exact basis fo r the law o f diminishing marginal u t i l i t y ? Marshall leaves one uncomfortable on these s u b je c ts .2 V ilfr e d o Pareto is credited with o rig in a tin g the underlying foundation o f the modern theory o f consumer demand. Pareto departed A lfre d M arshall, P rin cip le s of Economics (8th e d .; London MacMillan and Co., Lim ited, 1947), pp. 117-118. 2John R. Hicks, Value and Capital (2nd ed .; Oxford: Clarendon Press, 1946), p. 12. The 21 from the tr a d itio n a l subjective value theory, and did away with the assumptions o f independent and ad d itive u t i l i t y . Further, he removed the major obstacle— the assumption o f c a rd in a lly measurable u t i l i t y . Pareto's contribution was to show th a t consumer tastes and preferences could be analyzed by means o f in d iffe re n c e curves which require only ordinal measurement— the rank ordering o f budgets.^ An in d iffe re n c e curve is a locus of points, or combination o f goods each of which yie ld s the same level of to ta l s a tis fa c tio n s , and toward which the consumer is in d iffe r e n t . choice problem facing the consumer, i . e . , I t e f f e c t iv e ly portrays the i t forces the consumer to "give up" ce rtain q uantities o f one good in order to obtain additional units o f other goods, given a fixed budget constraint. 2 In order to construct an ind ifference curve, a l l th at is required is to have the consumer rank order the various combinations (q u a n titie s ) o f two goods which he would be w illin g to purchase under a given budget le v e l. The rank ordering o f combinations o f two goods (say x and y) can now be used to establish the boundaries o f an in d iffe re n c e curve. An in d iffe re n c e curve usually slopes downward to the rig h t. That th is is most often the case, can be i ll u s t r a t e d by considering an example. Consider again the case o f two goods (x and y ) , with units of good y on the v e rtic a l axis and units o f good x on the horizontal ^C. E. Ferguson, Microeconomic Theory (3rd ed.; Homewood, I l l i n o i s : Richard D. Irw in , In c ., 1972), p. 24. 2 This p rin c ip le serves as a basis fo r the concept of the marginal rate o f su b stitution o f one good fo r another. The marginal rate o f su b stitution o f , say, good x fo r good y (MRSxy) is defined as the amount o f y the consumer is ju s t w illin g to give up in order to get an additional u nit o f x. 22 axis. An in d ifference curve is provided which shows the various combinations o f the two goods which would be purchased under p rev ailin g market prices and the individual consumers budget. I f the in d iffe re n c e curve in such a diagram were p e rfe c tly h o riz o n ta l, th is would mean th at the consumer was in d iff e r e n t between combinations o f the two goods (x and y ) , both o f which contain the same amount o f y , but one o f which contains more units o f good x. In order fo r th is to occur, the consumer would have to be receiving enough units o f good x to be saturated with it. The same re la tio n s h ip would hold true (in reverse) i f the i n d i f f e r ­ ence curve were p e rfe c tly v e rtic a l in the diagram, i . e . , the consumer would have to be receiving enough units o f good y to be saturated with it. The usual case, then, is one in which the in d iffe re n c e curve slopes downward to the r ig h t . In th is s itu a tio n , the consumer must give up units o f one commodity, and th is loss is compensated fo r by taking additional units of the other commodity in order f o r him to maintain constant s a tis fa c tio n s .^ In d ifferen ce curves also are usually convex to the o rig in of the in d iffe re n c e map. 2 11bid. , pp. 41-45. o The curvature o f an in d iffe re n c e curve is closely re lated to the degree o f complementarity and s u b s t it u t a b ilit y between two com­ modities. The in d iffe re n c e curves f o r p erfect su b stitu te s, fo r example, would be downward-sloping s tr a ig h t lin e s . In d ifferen ce curves fo r two goods which are good complements, on the other hand, tend to approximate rig h t-a n g le axes, with the o rig in o f the two axes, showing a narrow range o f s u b s t it u t a b ilit y between the two goods. Perfect substitutes may be regarded as the same commodity fo r a l l p ractical purposes. Complementarity and s u b s t it u t a b ilit y have considerable significance regarding consumer purchasing decisions. John R. Hicks, op. c i t . , pp. 42-51. For a more recent treatm ent, see J. R. Hicks, A Revision o f Demand Theory (Oxford: The Clarendon Press, 1956). 23 In d ifferen ce curves are important tools in economic analysis. They may be u t il i z e d to obtain an individual consumer's demand curve fo r a p a rtic u la r good, and the consumer's income-consumption curve. An income-consumption curve shows the re la tio n s h ip between the equilibrium combinations o f two goods purchased a t varying levels o f money income with prices held constant. As a consumer's level o f money income increases, his budget line^ s h i f t s , to points o f tangency on successively higher in d iffe re n c e curves, defining new equilibrium combinations of goods. A l in e drawn connecting these equilibrium points is called an income-consumption curve. The income-consumption curve slopes upward to the r ig h t (p o s itiv e ly ) with "normal" goods. Engel Curves may be constructed d ir e c t ly from income-consumption curves, and are highly important in the study o f household expenditure patterns. Such curves re la te the amount o f any good purchased to the consumer's level o f income. The income e l a s t i c i t y o f demand 2 may be re lated to the slope or curvature of an Engel curve. The budget lin e is simply the individual consumer's budget r e s t r a in t . In the two goods case (x and y ) , a consumer's oppor­ tu n ity factors consist o f his level o f income a t a point in time, and the prices of goods x and y a t a fixe d point in time. The to ta l units o f good x which can be purchased a t any one time is obtained by d ivid ing the consumer's income ( I . ) by the u n it price o f good x (P x .). Likewise, the maximum number o f units o f good y which the consumer can purchase is I . / P y . The budget lin e join s these two extreme points. In d ifferen ce curves show the consumers preferences fo r various combinations o f the two goods, while the budget lin e shows the consumers "opportunity fa c to r ," i . e . , i t shows what i t is possible fo r him to do. See, Richard H. Leftwich, The Price System and Resource A llocation {3rd ed .; New York: H o lt, Rinehart and Winston, 1966), pp. 72-75. ? The income e l a s t i c i t y o f demand is " . . . the proportional change in the consumption o f a commodity, divided by the proportional change in income." Ferguson, o£. c i t . , p. 47. 24 Engel's Law was formulated in nineteenth-century Belgium in an empirical study o f the re la tio n s h ip between household incomes and expenditures on food. The law states th a t the proportion o f the fam ily income spent on food declines as income ris e s . Later re ­ searchers, expanding upon many implied relationships exhibited in the data collected by Engel, generally have a ttrib u te d to him four basic propositions; namely, "As income increases: 1. The percentage o f the income spent fo r food decreases. 2. The percentage o f income spent fo r re n t, f u e l , and l ig h t remains the same. 3. The percentage o f the income spent f o r clothing remains about the same. 4. The percentage o f the income spent fo r sundries (items such as education, care of h ea lth , comfort, and recreation) increased r a p i d ly . ' Over the years, many empirical studies have been made which have, in general, tended to support Engel's laws. Studies made in the 1950's, however, resulted in some m odification in the four propo­ sitio n s stated above. A reformulation of these generalizations was made in order to r e f le c t more current study re s u lts : As the income of fam ilies increases, the DOLLARS they spend fo r each important category o f expenditure also ris e s , but the PERCENTAGES o f to ta l income spent fo r the various categories change in the following ways: 1. The percentage spent fo r food decreases. 2. The percentage spent fo r housing and household operation remains about constant. ^Charles S. Wyand, The Economics o f Consumption (New York: The Macmillan Company, 1938), pp. 220-21. 25 3. The percentage spent f o r c lo th in g , tra n s p o rta tio n , re c re a tio n , health and education increases, as does the percentage saved.' Most studies based upon the propositions o f Engel's laws have been o f the " s ta tic " v a r ie t y , u t i l i z i n g cross-section income d i s t r i ­ butions, and have assumed constant ta s te s . be useful in p re d ic tio n , however, In order f o r the laws to . '. they must also apply to changes in income from one time period to another." 2 A national study of le is u re spending patterns o f consumers was undertaken in 1963 by 3 Dr. George Fisk o f the U n iv e rs ity o f Pennsylvania. Using tim eseries data, Fisk traced the re la tio n s h ip between national le is u re spending behavior and aggregate disposable personal income. For the period 1929-60, i t was found th a t to ta l measured le is u re expenditures of consumers increased a t approximately the same ra te as aggregate disposable personal income, and s l i g h t l y more ra p id ly than personal consumption expenditures. According to F isk, "The impression conveyed by marketing p erio d ic als th a t expenditures f o r le is u re are r is in g 'e x p lo s iv e ly ' stems from the r e d is tr ib u t io n o f to ta l measured le is u r e , which has produced rapid expenditures f o r items such as fo reig n t r a v e l , boats, toys, TV sets, and b o o k s . F i s k ' s contention is th a t changes in tastes and preferences over tim e, re s u ltin g in expenditure ^Benjamin S. Loeb, "The use o f Engel's Laws as A Basis fo r Predicting Consumer Expenditures," Journal o f Marketing, Vol. 20, No. 1 (J u ly , 1955), p. 21. 2Ib id . 3 George F isk, Leisure Spending Behavior (P h ila d e lp h ia : v e rs ity o f Pennsylvania Press, 1963). ^ I b i d . , p. 80. Uni­ 26 re d is trib u tio n to other le is u re goods and services, have usually been mistaken fo r changes in the to ta l (aggregate) level of le is u re spending as a whole. Within the expenditure categories included under to ta l measured leisu re ,^ computed per capita time series income e l a s t i c i t i e s indicated th at foreign t r a v e l, pleasure boats, sporting goods, and durable and non-durable toys captured . . an increasing share o f per capita expenditure increases r e la t iv e to per capita increases in income." Expenditures fo r le is u re (TML) projected to 1965 (in 1958 d o lla rs ) also indicated th at average propensities to consume w ill remain r e l a ­ t i v e ly unchanged a t about 8 or 9 per cent o f per capita disposable personal income. Engel's law is o f considerable in te re s t in th is present study. The relationship between fam ily income and level o f p a rtic ip a tio n in recreational boating w il l be explored fu rth e r as a sub-hypothesis of the d is s e rta tio n . Growth in Outdoor Recreation Demand In order to explore what is meant by the demand f o r outdoor recreation, i t w il l be helpful a t th is point to return once again to indifference curves as a beginning point. I t was noted, previously, that ind ifference curves may be used to determine an individual consumer's income-consumption curve, which allow construction o f Engel 1Total measured le is u re (TML) spending was the sum o f the outlays fo r re crea tio n , reading, alcoholic beverages, and foreign travel (when a v a ila b le ). I b i d . , p. 7. 27 Curves. In d iffe re n c e curves may be u t i l i z e d , w ith in a m ic ro -s ta tic framework, to derive an individual consumer's demand curve f o r a s p e c ific commodity. Whereas income-consumption curves tra c e out the changes in purchasing behavior o f consumers when money income varies ( r e l a t i v e prices of goods remaining constant); the consumer demand curve fo r a s p e c ific commodity re la te s q u a n titie s o f th a t good purchased to market p rice (money income and prices o f a l l other goods held constant). The demand curve can be derived from a price-consumption c u rv e d By p lo ttin g a l l points from the price-consumption curve ( e . g . , the number o f units of a good purchased a t observed market p ric e s , where market p rice is given by the slope o f the budget l i n e ) , a demand curve can be traced out. The shape o f the demand curve so constructed indicates a highly important p r in c ip le — the law o f demand: a demand curve nearly always slopes downward (n e g a tiv e ly ) to the r i g h t , so th a t with price plo tted on the v e r t ic a l axis and q u a n tity on the horizontal axis the q uantity of a good purchased per u n it time varies inversely with p ric e . As the p rice o f a good r is e s , the corresponding q ua n tity taken declines; or a l t e r n a t i v e ly , as the p rice decreases, the amount ris e s . 2 price-consumption curve traces out the e q u ilib riu m q u a n titie s o f two goods purchased when p rice ra tio s change (money income remaining constant). The curve connects the points o f tangency between the budget l in e and individual in d iffe re n c e curves, created by changes in the market price r a t i o . Ferguson, lo c . c i t . , pp. 49-51. 2 An important exception to the law o f demand is the so-called "Giffen good." In th is special case, the q ua n tity o f the good demanded varies d i r e c t l y with p ric e . 28 Up to th is point we have considered demand only in terms o f one consumer or household. Under real world conditions, however, the demand fo r any given commodity is the aggregate amount purchased by large numbers o f households. The tra n s itio n from individual demand curves to market demand curves is accomplished by summing the quanti­ tie s demanded by each consumer at the various possible prices h o ri­ z o n ta lly . The term "demand," then, has a very specialized meaning. It represents a schedule which shows the various amounts o f a product which consumers are w illin g and able to purchase a t each sp e cific price in a set o f possible prices during some specified period of time. In an economic sense, i t is often desirable to consider “e ffe c tiv e demand;" the amount of a good or service which consumers are w illin g and able to purchase (pay f o r ) , versus the mere longing or want fo r ce rtain products or services. What causes a demand schedule to change? By d e f i n i t i o n , a th eo retic al demand curve involves a number o f assumptions. Several "determinants" of demand must remain constant or fixed in order fo r one to define the location o f a demand curve. of demand consist of: The basic determinants (1) the tastes or preferences o f consumers, (2) the money income of consumers, (3) the prices o f re lated goods, (4) consumer expectations with respect to fu tu re prices and incomes, and (5) the number of consumers in the marketJ A change in any one of these determinants, since i t w il l a f f e c t the data in the demand ^C. R. McConnell, Elementary Economics; P rin c ip le s , Problems, and Policies (New York: McGraw-Hill Book Company, I9 6 0 ), p. 64. 29 schedule, w i l l necessarily s h i f t the location o f the demand curve. A s h i f t in the position o f the demand curve ( r i g h t or l e f t ) is regarded as a change in demand. A change in the demand schedule or curve, however, is d if f e r e n t from a change in the "quantity demanded." A change in the quantity demanded is associated with movement from one point to another on a fixed demand curve. Such movement along the demand curve re su lts from a change in the price o f the commodity con­ cerned. The s ta tic assumptions o f th eo retic al demand curves, as we have noted above, postulate fixed tastes and preferences o f consumers. Tastes and preferences consist o f a set o f non-price variables which are d i f f i c u l t to measure and q u a n tify. In the present study, con­ siderable emphasis w i l l be placed upon tastes and preferences as they re la te to the demand fo r recreational b oatin g.1 In Chapter I , several factors were cite d as contributing to higher levels o f p a rtic ip a tio n in outdoor recreation (see page 3 ) . One of the most important aspects o f outdoor recreation demand centers around the re la tio n s h ip between recreation and the consumer's le is u re time. I t has been pointed out by many w riters th at Americans have generally held to a "work ethic" in times past; re je c tin g idleness or play and holding to strong social customs and mores favoring hard work ^Sociological studies have shown, fo r example, th a t various elements o f socio-economic status are correlated with the tastes and behavior of consumers. Measurable elements include occupation, edu­ cation , fam ily composition, age, place of residence, sex, and income. Since demand i s , in p a rt, a function o f tastes and preferences o f consumers, and tastes and preferences in turn are re lated to socio­ economic fa c to rs , demand can be viewed as a p a r tia l function o f such variables. See R. Havinghurst and K. Feigenbaum, American Journal of Sociology, Vol. 64 (January, 1959), pp. 397-411. 30 as a v ir tu e . That the work eth ic has been a strong force motivating peoples' behavior through the years is c le a r. The classical economists had some strong values and b e lie fs regarding work and le is u re : . . . the consumption . . . o f productive labourers is not a l l of i t productive consumption. There is unproductive consumption by productive consumers. What they consume in keeping up or improving t h e i r h ea lth , strength and capacities o f work, or in rearing other productive laborers to succeed them, is productive consumption. But consumption on pleasures or lu x u rie s , whether by the id le or by the industrious, since production is n eith er i t s object nor is any way advanced by i t , must be reckoned un­ productive: with a reservation perhaps o f a c e rta in quantum of enjoyment which may be classed among necessaries, since anything short of i t would not be consistent with the greatest e ffic ie n c y of labour. That alone is productive consumption, which goes to , maintain and increase the productive powers o f the community. . . . Leisure may be considered as the time l e f t over fo r use by the individual beyond th a t required fo r sleep, necessary personal chores and work. In th is sense, one might think o f "discretionary leisu re " in the same way we think o f discretion ary personal income—a residual l e f t over to the individual which may be used in a manner of his own choosing. Recreation and le is u re are highly c o rre la te d , although not synonymous. According to Clawson, le is u re is ". . . a l l time beyond existence and subsistence tim e." 2 A consumer may choose to devote c e rtain amounts o f his le is u re to outdoor re crea tio n , as one major form o f le is u re time a c t i v i t y . I t is c le a r th a t "time" is a scarce resource in an economic sense. One cannot accumulate a stock o f time, ^Cf. John Stuart M i l l , Principles of P o lit ic a l Economy, ed. by S ir W. J. Ashley (New York: Augustus M. K e lly , 1961), pp. 51-52. 2 pp. 1-2. Marion Clawson, Land and Water fo r Recreation, lo c . c i t . , 31 however, as one might accumulate a stock o f c a p ita l. One's le is u re time budget may be completely f i l l e d or i t may be overcommitted, with no residual amount a v a ila b le fo r recreation a c t i v i t i e s . As Linder puts i t , there is a c e rta in demand and a c e rta in supply o f time, and . . the demand by individuals is usually s u f f i c i e n t ly high in re la tio n to the supply to make time a scarce commodity. . . . I t has been estimated th a t the annual national time budget by the year 2,000 w il l to ta l about 2,907 b i l l i o n hours. Of th is to ta l estimated time, 1,794 b i l l i o n hours may be taken up by work, school, housekeeping, personal care, and sleep. The remaining 1,113 b i l l i o n hours could be a v a ila b le fo r le is u re time a c t i v i t i e s (including outdoor re c re a tio n ). This to ta l would exceed the le is u re hours a v a ila b le to Americans in 1950 by approximately two and one-half times. As nearly as can be determined from a v a ila b le data, approximately one h a lf of the increase in projected le is u re hours fo r the year 2,000 would re s u lt due to higher population. The remaining increase, however, would re s u lt from more le is u re hours becoming a v a ila b le per cap ita. 2 As nearly as can be determined, about 3 to 4 per cent o f a l l leisu re time (composed p r in c ip a lly o f le is u re hours a v a ila b le d a ily , on weekends, fo r vacations and to the r e tir e d ) is devoted to outdoor recreation a c t i v i t i e s . Thus, outdoor recreation is not seen to be the ^Linder goes on to suggest th at there is no reasonable analysis o f time in the economic l i t e r a t u r e . Economists, he fe e ls , t y p ic a lly assume consumption is an instantaneous a c t, having no temporal conse­ quences. Time in working l i f e i s , however, treated as a scarce resource. See, Steffan B. Linder, The Harried Leisure Class (New York: Columbia University Press, 1970), pp. 1-8. 2 Clawson, o jj. c i t ., p. 5. 32 major area o f le is u re time a llo c a tio n f o r most o f the population. One o f the reasons which may contribute to th is rather modest time a l l o ­ cation is th at nearly 40 per cent o f the estimated time a v a ila b le comes as d a ily l e i s u r e - - a f t e r work or a f t e r school closes--and i t is not s u ff ic ie n t to allow people to drive any distance to a recreation area or f a c i l i t y . Moreover, much o f th is d a ily le is u re comes during periods o f the year when climates do not permit p a rtic ip a tio n in many kinds o f recreation a c t i v i t i e s . When d a ily le is u re is excluded i t appears th a t outdoor recre­ ation occupies about 7 per cent o f the aggregate le is u re time a v a ila b le . I t should be noted, however, th a t the percentage o f a l l a v a ila b le le is u re time taken up by outdoor recreation has increased ra p id ly over the la s t several decades; and, on the basis o f av ailab le trends, w il l continue to increase in the fu tu re . In the fu tu re , r e t ir e d , vacation, and weekend le is u re probably w i l l account fo r most of the increases in the le is u re hours a v a ila b le on both an aggregate and per capita basis, p a r t ic u la r ly i f fu tu re reductions in the length o f the average workweek take place, re su ltin g in a three-day weekend rather than reduced d a ily work hoursJ The average work week has been reduced considerably in the United States. In 1850, the average work week was about 69.8 hours. I t declined to 60.2 hours in 1900, 44.0 hours in 1940, and 39.5 hours in 1960. By 1976 and 2000, the average work week is expected to drop ^I b i d . , p. 7. 33 to 36.6 hours and 30.5 hours, re s p e c tiv e ly J expected to increase: Paid holidays are in 1960, the average worker received 6.3 paid holidays; by the years 1976 and 2000, i t is expected th at average paid holidays w ill increase to 8 .5 and 10.1 days, resp ectively. paid vacation w il l also undergo change. Average In 1960, the average worker received 2 .0 weeks of paid vacation time; by the years 1976 and 2000, the average paid vacation is projected to increase to 2.8 weeks and 3.9 weeks, resp ectively. 2 The changing amounts and timing o f le is u re can have d i f f e r ­ e n tia l e ffe c ts on various segments o f the population. That i s , a v a ila b le s t a t is t i c a l information does not segment or c la s s ify the population in very fin e d iv is io n s. The most th a t can be said about expected changes in le is u re time is th a t the "average" worker w ill probably experience an increase in le is u re . Specific population segments, such as those who own recreational w a te rc ra ft, are thus "buried," insofar as they are only one group of people whose le is u re time a v a i l a b i l i t y is computed (along with th at fo r a l l other people) in a national aggregate account. The Outdoor Recreation Resources Review Commission studies indicated th at p a rtic ip a tio n in seventeen d if f e r e n t outdoor recreation a c t i v i t i e s amounted to about 4 .4 b i l l i o n separate " a c t iv ity occasions" during the summer o f 1960. ORRRC fu rth e r estimated th a t, by the years ^Outdoor Recreation Resources Review Commission, Projections to the Years 1976 and 2000: Economic Growth Population, Labor Force and Leisure, and tra n s p o rta tio n , ORRRC Study Report 23 ( Washington: U.S. Government P rinting O ffic e , 1962), p. 181. 2 I b id . , pp. 68-71. 34 1976 and 2000, to ta l p a rtic ip a tio n could well expand to 6.9 b i l l i o n and 12.4 b i l l i o n a c t i v i t y occasions. A number o f in te re stin g population ch a ra c te ris tic s appear to be associated with p a rtic ip a tio n : age, income, education, fam ily s iz e , occupation, and place o f residence were a l l found to have s ig n ific a n t e ffe c ts upon both the amount and type of outdoor recreation in which people p a rtic ip a te .^ Age was found to be highly important in influencing the type of outdoor a c t i v i t y engaged in . Studies indicated th at as age in ­ creases, there is a decline in the most ac tiv e recreation a c t i v i t i e s - b icyclin g, hiking, horseback r id in g , water skiin g , and camping. Except fo r walking or driving fo r pleasure and fis h in g , however, p a rtic ip a tio n in most outdoor recreation a c t i v i t i e s was found to decline with ad­ vancing age. Income was very in flu e n tia l in influencing rates of p a r t i c i ­ pation, p a r tic u la r ly those recreation a c t i v i t i e s requiring substantial outlays o f money fo r recreational equipment--boating, water skiin g , camping, horseback rid in g , etc. I t was found th at higher income groups most often p articipated in such a c t i v i t i e s . ORRRC also found th at ". . . in general, p a rtic ip a tio n tends to go up as income does." P a rticip a tio n rates were found to ris e s te a d ily between $3,000 fam ily income and the $7,500-$10,000 class; beyond th is level declining s lig h t ly . The association between income and recreation a c t i v i t y was very pronounced fo r metropolitan area residents. P a rticip a tio n rates were found to increase d ir e c t ly with education le v e ls , p a r tic u la r ly fo r such a c t i v i t i e s as swimming, ^Outdoor Recreation fo r America, lo c . c i t . , pp. 27-32. 35 playing games, sightseeing, walking, and driving fo r pleasure. No consistent c o rre la tio n was found between education and other forms of recreation a c t i v i t y . ORRRC found th at fam ilies tend to p a rtic ip a te in outdoor recreation together. Approximately 60 per cent o f the fam ily heads surveyed (or t h e i r wives) indicated th at the e n t ir e fam ily p a rtic ip ate d in two o f the same kinds o f a c t i v i t i e s together. A number o f ORRRC studies indicated th a t occupation has con­ siderable influence upon p a rtic ip a tio n . However, the published study indicated th a t occupation was probably most i n f lu e n tia l with respect to levels o f income and the amount of paid vacation associated with a p a rtic u la r job or p osition. However, professional people were found to enjoy the most re c re a tio n , and farm workers the le a s t. Managers and proprietors p artic ip ate d a t a ra te which was less than the average fo r a l l occupations. Generally, the s e lf employed (and t h e i r wives) also showed lower levels o f p a rtic ip a tio n than others. Suburban residents, and rural non-farm people were shown to have higher levels o f recreation a c t i v i t y than c i t y residents. Country residents tended to do more camping, fis h in g , and hunting, while c i t y residents emphasized sightseeing, pleasure d riv in g , p ic ­ nicking and swimming most. People residing in rural areas, in general, showed the highest p a rtic ip a tio n rates. Location and access to recreation areas and f a c i l i t i e s appeared to be important factors in the higher levels o f p a rtic ip a tio n exhibited by country residents. In a more recent study, G ille s p ie and Brewer carried out a household survey in the St. Louis Metropolitan Area to . . determine 36 the q uantity o f recreation demanded by th a t population in r e la tio n to socioeconomic c h a ra c te ris tic s ." ^ In th is study, an econometric model was developed, using days o f p a rtic ip a tio n in "water-oriented outdoor recreation" as the dependent v a ria b le , and selected socioeconomic c h a ra c te ris tic s o f the St. Louis (SMSA) population as independent variables. Water-oriented outdoor recreation was defined to include fourteen separate recreation a c t i v i t i e s , i . e . , swimming, water s k iin g , ice skating, camping, picnicking, boating, boat fis h in g , hunting, sight-seeing, nature walks, g o lfin g , h ik in g , and "others." The e f f e c t o f price (transport cost) on p a rtic ip a tio n levels was assumed constant fo r purposes o f the study. The SMSA population was treated as i f i t originated a t a single point in space, where the structure o f transport costs faced by a l l households in order to engage in recreation a c t i v i t i e s in a "vast rural mountainous area" adjacent to the metropolitan area was the same. Continuous variables included in the model were annual fam ily income, age of the head o f household, education of the head of house­ hold, age squared, education squared, and the product of income and age. Dummy ("zero-one") variables were used in order to assess the effe c ts o f q u a lita tiv e variables (occupation, sex, and race) upon p a rtic ip a tio n rates. ^Glenn A. G ille s p ie and Durward Brewer, "Effects o f Nonprice Variables Upon P a rtic ip a tio n in Water-Oriented Outdoor Recreation," American Journal o f A g ricu ltural Economics, Vol. 50, No. 1 (February, 1968), pp. 82-90. 2 The c o e ff ic ie n t o f m u ltip le determination {R ) f o r the model was O. 6 2 J However, some variables were retained in the model which lacked significance a t the .05 level (income, age, age squared, and sex o f household head). The researchers claim g e n e ra lity o f a p p li­ cation o f the model, s ta tin g th at . . i t may be used fo r p re d ic tiv e purposes fo r a population o f a metropolitan area by use o f the mean values o f the socioeconomic c h a ra c te ris tic s o f the population, m u lt i­ plied by the number of fam ilies o f th at population." statement appears to be open to challenge. This e x p l i c i t C o efficients between socio­ economic variables and recreation p a r tic ip a tio n , i t would appear, are im p li c it l y assumed to remain constant over time. Clawson notes, fo r example, th a t "my best, but extremely rough, estimates of past changes in recreation use suggests th a t such c o e ffic ie n ts have changed g re a tly in the past; and th is a t le a s t suggests th at they may change s i g n i f i cantly in the fu tu re ." 2 Mueller and Gurin did a national study o f outdoor recreation p a rtic ip a tio n rates in 1959 and 1960, involving a cross-section of 3 household heads and t h e ir spouses. A to ta l o f 2,750 home interviews ^The c o e ffic ie n t o f m u ltip le determination gives the per­ centage o f the variance in the dependent va ria b le explained by (or associated w ith) changes in the independent v a ria b les . 2 Marion Clawson, "Effects o f Nonprice Variables Upon Par­ tic ip a tio n In Water-Oriented Outdoor Recreation: Comment," American Journal o f A g ricu ltu ral Economics, Vol. 50, No. 4 (November, 1968), p. 1039. 3 Eva Mueller and Gerald Gurin, P a rtic ip a tio n in Outdoor Recreation: Factors A ffecting Demand Among American Adults, ORRRC Study Report 2Q—(Washington: U.S. Government P rin tin g O ffic e , 1962). 38 were completed. Respondents were asked "how do you usually spend most o f your le is u re time, both indoors and outdoors, in the evenings, in your time o f f and on weekends?" Persons interviewed usually gave a spontaneous response, c it in g p a rtic u la r a c t i v i t i e s which were o f in te re s t to them. In order to focus on p a rtic ip a tio n in outdoor recreation a c t i v i t i e s , each respondent was l a t e r given a printed card, l i s t i n g eleven outdoor a c t i v i t i e s : (2) (1) outdoor swimming or going to a beach, boating and canoeing, (3) fis h in g , (4) hunting, (5) skiing and w inter sports, (6) h ikin g , (7) d riving fo r sight-seeing and re la x a tio n , (8) nature or bird walks, (9) picnics, (10) camping, and (11) horseback rid in g . Respondents were then asked whether they had engaged in th is a c t i v i t y "not a t a l l , " "once or tw ice," "three or four times," or "more o fte n ," in the la s t year. Each person interviewed was also instructed to reply with respect to his own a c t i v i t i e s ra th e r than those o f the fam ily as a whole. Most o f the findings o f the study were presented by use of an " a c t iv it y scale," constructed from the sequence o f questions above. Each respondent was given a score o f 1 fo r each o f the above 11 a c t i v i t i e s engaged in four times or less, and a score o f 2 fo r each a c t i v i t y engaged in more than four times in the past year. 11 a c t i v i t i e s studied, scores could thus range from 0 to 22. For the In addition to these ra tin g s , a respondent was awarded an additional score o f two fo r an a c t i v i t y which was mentioned spontaneously (before the a c t i v i t y card was presented); and an additional score o f four was added i f he spontaneously mentioned two or more o f the 11 a c t i v i t i e s . Thus, the a c t i v i t y scale could range from 0 to 26. 39 The survey revealed th a t 38 per cent o f a l l respondents p articip ated In fis h in g during the previous year; 28 per cent had p artic ip a te d in boating and canoeing; 17 per cent in hunting; 19 per cent in hiking; 15 per cent in camping; 14 per cent engaged in nature study or bird walks; 7 per cent went horseback rid in g ; 6 per cent en­ gaged in skiing and other w inter sports; 45 per cent p articip ated in outdoor swimming or going to the beach; 66 per cent went on picnics; and 71 per cent went automobile rid in g fo r sight-seeing and re la x a tio n . Using the outdoor recreating " a c t iv ity scale" as the dependent v a ria b le , Mueller and Gurin u t il i z e d a m u ltip le c la s s if ic a tio n analysis (a m u ltip le regression technique) to determine the net influence of nine socioeconomic-demographic ch a ra c te ris tic s o f the national sample of households. The independent variables included income, education, occupation, length o f paid vacation, race, age, l i f e cycle stage, region, and place o f residence. men and women. The analysis was made separately fo r The nine socioeconomic-demographic ch a ra c te ris tic s explained about 28 per cent o f the v a ria tio n in the a c t i v i t y scale fo r men, and 29 per cent fo r women. portion For the to ta l sample, the pro­ o f to ta l variance in the a c t i v i t y scale explained by the independent variables was about 30 per cent. The researchers conclude th at " . . . i t is c le a r th at factors other than socioeconomic ch a ra c te ris tic s are major determinants of outdoor recreational a c t i v i t y . Such things as time a v a ila b le , the goals and in te re sts which the individual seeks to promote in his le is u re time, the le is u re time preferences o f other fam ily members and frie n d s , physiological factors, recreational experience in childhood, 40 in te re s t in such competing a c t i v i t i e s as g o lf and tennis or a v a ila ­ b i l i t y o f f a c i l i t i e s come to mind re ad ily ."^ The Outdoor Recreation Commodity j As was pointed out in the preliminary chapter, outdoor recre­ ation has been produced h is t o r ic a lly by both the public and p rivate sectors of the economy. According to some scholars, public production and public control o f recreation resources has been more prevalent in the United States than p rivate production. Existing data on the r e la t iv e importance o f public and p riv a te resources i s , however, decidedly fragmentary. The merits o f public vs. p rivate provision o f recreation f a c i l i t i e s and services w ill not be debated in th is section. Rather, emphasis w ill be placed upon id e n tify in g some of the ch a ra c te ris tic s and p e c u lia ritie s o f the outdoor recreation commodity. One of the p eculiar a ttrib u te s of outdoor recreation is that recreation areas and f a c i l i t i e s are dispersed geographically over space. This means th at the consumer must travel to the resource in order to p a rtic ip a te in a p a rtic u la r recreation a c t i v i t y . Transfer costs, then, become an important item in the consumers fam ily budget, to the extent th at members of the household p a rtic ip a te in outdoor recreatio n . As Kalter and Gosse point out: Usually the to ta l d i s u t i l i t y associated with the purchase o f a good or service is approximated by the market price of th at good or service. A ll other costs in terms of money, time, and bother are neglected as being of small magnitude r e la t iv e to the purchase 1 1bid. , pp. 26-27. 41 p rice. These l a t t e r costs can be called " tra n s fe r costs" and include any cost associated with the process o f exchange. The market prices or entrance fees fo r many o f the most popular recreational a c t i v i t i e s are very low or even non­ e x is te n t. Some public recreational site s are e n t i r e ly sup­ ported by general tax funds while others charge only a small fe e , often ju s t fo r parking. Many p riva te landowners permit free use o f t h e ir land fo r recreational purposes. In the case o f many forms o f recreatio n , th ere fo re, the tra n s fe r costs can­ not be ignored because they outweigh the market price of the a c tiv ity .! One o f the principal ch a ra c te ris tic s o f outdoor recreation product, then, revolves around the nature of the pricing policy pursued on public areas. Many outdoor recreation f a c i l i t i e s , i t should be noted, are provided by the p riva te sector ( e . g . , camping, g o lf courses, shooting preserves), and recreation services on such areas have been sold on the market in accordance with pricing rules which are not un­ l i k e the rules adopted in the sale o f products from any other (p riv a te ) investment p ro ject. However, in the case o f the recreation f a c i l i t i e s and services provided by the public sector, pricing policies have presumably not been in accordance with such ru les , re su ltin g in much outdoor recreation being provided to consumers a t zero (or nominal) prices. 2 According to the National Ad Hoc Water Resources Council, fo r example: ^Robert J. Kalter and Lois E. Gosse, "Recreation Demand Functions and the Id e n tif ic a tio n Problem," Journal of Leisure Research, Vol. 2, No. 1 (Winter 1970), p. 47. 2 For example, a recent survey o f state le g is la tio n in 12 Northeastern States indicated th a t v i r t u a l l y no defined c r i t e r i a was contained in laws authorizing state agencies to charge user fees fo r public campground use. Agency heads were simply authorized to charge such fees as they deemed "appropriate" and "reasonable" under a general grant o f discretionary au th o rity : R. S. Bond, M. I . Bevins, and P. R. Fiske, "Public Campground Policy in the Northeast," Unpublished 42 The recreational services o f public water and re la te d land resource developments are c u rre n tly provided to the users fre e o f charge or f o r a nominal fe e , usually covering only a part o f the cost. Thus, although i t is known th a t there is a large and growing demand fo r these services, there i s , in the formal sense, no w e llestablished market f o r them and few data are a v a ila b le on market prices th a t r e f l e c t the value o f the service provided by public p rojects. Under the circumstances, i t becomes necessary to derive simulated market p ric e s J The essential provision o f Supplement No. 1 is t h a t , in the absence of formal market pricing fo r outdoor recreation services, desirable uniform ity in the treatment of recreation in the planning of projects and programs and in cost allo c atio n s w i l l be accomplished through the application o f u n it values th a t r e f l e c t the concensus judgment o f q u a lifie d technicians." have a panel of experts which would Supplement No. 1, then, would (1) estimate the number o f users fo r a p a r tic u la r recreation s i t e , and (2) choose an acceptable price which, when m u ltip lie d by the estimated number o f users, would give a fig u re which could be regarded as to ta l tan g ib le benefits (in d o lla r terms). Supplement No. 1 implies th a t a single non-varying price is acceptable fo r evaluating the benefits generated by e x is tin g public Manuscript f o r a Regional B u lle tin to be printed by the Massachusetts A g ricu ltural Experiment Station Under Regional Project NEM-42, Economic Analysis o f the Campground Market in the Northeast, March, 1973. ^Ad Hoc Water Resources Council, Evaluation Standards fo r Primary Outdoor Recreation B e n e fits . Supplement No. 1, June 4, 1964. Supplement to U .S ., Congress, P o lic ie s , Standards and Procedures in the Formulation, Evaluation and Review o f Plans fo r Use and Development of Water and Related Land Resources, Senate Document 97, 87th Congress, 2nd Session, October 29, 1962, p. 5 (in supplement). 2 I b i d . , p. 5. . 43 recreation f a c i l i t i e s , expansions contemplated fo r e x is tin g f a c i l i t i e s and f i n i t e - s iz e d new recreation areas. A fu rth e r im plication o f th is policy is th a t the price e l a s t i c i t y fo r each public recreation f a c i l i t y is i n f i n i t e , i . e . , th a t the demand curve is h o riz o n ta l. According to th is r a tio n a le , consumers are presumed to demand more o f what already is provided a t the ex istin g price le v e l. C ic c h e tti, Seneca, and Davidson point out th at the d ire c tiv e s of Supplement No. 1 are inappropriate fo r such a complex problem as estimating the benefits o f public recreation p ro je c ts J They point out th at under normal expectations the demand curve fo r s p e c ific out­ door recreation a c t i v i t i e s w ithin a given region would be downward sloping. Further, given a downward sloping demand curve, one i n t r o ­ duces the problem o f how to handle the estimation o f recreation benefits in cases where the demand fo r a p a r tic u la r recreation a c t i v i t y is in e la s t ic . They point out th at policy makers faced with the problem o f providing a lte r n a t iv e recreation areas a t d if f e r e n t scale (supply) le v e ls , would find "market" price inappropriate as the fig u re to be used in estimating tangible benefits which would accrue to the a l t e r ­ native projects. I f the equilibrium price defined where a downward sloping demand curve and an upward sloping supply curve were used, how would one handle the problem o f a case where supply was increased? For example, i f a la rg e r supply was contemplated ( i . e . , a downward s h if t 1Charles J. C ic c h e tti, Joseph J. Seneca, and Paul Davidson, The Demand and Supply o f Outdoor Recreation (New Brunswick, New Jersey: Bureau o f Economic Research, Rutgers U n iv e rs ity , June 1969), pp. 6-13. 44 in the supply curve, other things held constant), the in te rs ec tio n of the new supply curve and the old demand curve would re s u lt in a lower market p rice . The q uantity o f recreation presumed to be taken a t th is lower price would, accordingly, increase with the accompanying movement along the demand curve. However, as C ic c h e tti, e t a l . , , point out " I f the demand curve is downward sloping . . . a crucial fa c to r in comparing the benefits (a t the a lte r n a tiv e supply le v e ls ) is the price e l a s t i c i t y o f this schedule." and P^) f a l l I f , fo r example, both the "market" prices (say P-j in the in e la s tic portion o f the demand curve, the benefits as measured by Supplement No. 1 procedures would give a re s u lt such th at the tangible benefits generated by using P-j (the higher price with smaller q u antity) would be higher than the benefits calculated by use of (the lower price and higher quantity consumed), even though we would have a la rg e r number o f users a t the la rg e r scale o f development. Another issue which is closely related to the question of project evaluation is the aspect o f reimbursement p olicy. In the l i t e r ­ atu re, the p ractice o f divorcing economic evaluation o f resource develop­ ment projects from considerations concerning reimbursement o f project costs has come to be known as "the evaluation— reimbursement dichotomy." Outdoor recreation has been p r a c t ic a lly a fre e good in the past, stemming la rg e ly from public p olicy decisions. Such p o lic ie s , according to several scholars, have led to "premature excess demand" fo r outdoor recreation resources. As Stoevener and Brown note: . . . to in s is t upon compensation has important e ffic ie n c y implications in i t s e l f . The good or se rvice, when made a v a ila ­ ble below cost, w i l l be demanded not only by those able to pay the compensation but also by a l l those who value i t more highly than the price a t which i t is a c tu a lly obtainable to them. This 45 means an increase in use o f the good or se rv ice, an increase in the use o f other imputs with which the former is combined in production, an increase in the product produced by i t , and cor­ responding decreases in the production o f goods from which the factors o f production have been withdrawn.! Generally, decision making in the f i e l d o f outdoor recreation has proceeded on the basis o f in s is tin g th at recreation services be provided fre e (or nearly so), and th a t such practice could be j u s t i f i e d on the basis o f the meritorious nature o f recreation in general. That i s , in ce rta in circumstances i t may be argued th a t i t would be inappro­ p ria te to in s is t upon recovery of project costs by means o f compensation provided by pro ject b e n e fic ia rie s . The burden o f th is argument rests on the thesis th at public investment projects fo r outdoor recreation resources have income d is t r ib u t iv e e ffe c ts . 2 Even on purely i n t u i t i v e grounds, i t appears th a t recreation resource development projects do have some income d is t r ib u t iv e e ffe c ts . However, in the case of outdoor recreation projects o f a resource-based character ( i . e . , those located some distance from population centers, and which require th at pro ject Herbert H. Stoevener and W illiam G. Brown, "Analytical Issues in Demand Analysis fo r Outdoor Recreation," in Journal o f Farm Economics, Vol. 49, No. 5 (December, 1967), p. 1298. 2 Income re d is trib u tio n is thought o f te c h n ic a lly as a conscious public policy directed toward relaxing the budget constraint faced by sp e cific disadvantaged ind ividuals or groups. Or, in other cases, . . a s making provision fo r some items, catering to what are referred to as 'm e rit wants,' to enter in to the consumption patterns o f i n d i ­ viduals whose incomes are inadequate fo r th is purpose. Subsidization o f producer goods and services via reimbursement p o lic ie s , . . . has the e ffe c t o f re d is trib u tin g several stages removed from the point of intended impact with the consequent d iffu s io n o f r e d is tr ib u tiv e e ffe c ts among many individuals and groups not q u a lifie d on Welfare grounds." See, John V. K r u t i l l a , "Is Public Intervention in Water Resources Development Conducive to Economic Efficiency?" Natural Resources Journal, Vol. 6, No. 1 (January, 1966), pp. 68-69. 46 b en eficiarie s necessarily incur s ig n ific a n t tra n s fe r c o s ts ), predominantly higher-income groups would be the market segment catered to. A conscious public p olicy b u i l t upon a ra tio n a le o f ju s t if y in g the construction o f outdoor recreation projects so lely on the basis o f income d is t r ib u t iv e e ffe c ts does not appear warranted. projects do have such e ffe c ts , " . . . While recreation t h e ir effectiveness must be questioned when they are employed as tools p rim a rily fo r th is purpose. This is true es p ecially o f outdoor recreation developments which cater predominantly to upper income groups. By the same token, recreation developments located in low-income areas such as the urban ghetto may contribute toward a more equal income d is tr ib u tio n . Outdoor recreation areas represent a diverse set o f charac­ te ris tic s . Public areas are administered by a large number o f s ta te , federal and municipal agencies. In a d d itio n , there are large numbers of p riva te areas and f a c i l i t i e s . A ll o f these areas d i f f e r in terms of physical c h a ra c te ris tic s , c h ie f uses, f a c i l i t i e s provided, location with respect to users, etc. However, as Marion Clawson points out, many o f these areas e x h ib it s i m il a r it i e s which permit c la s s ific a tio n into fewer groups, thereby f a c i l i t a t i n g understanding and analysis. Clawson has suggested a th re e -fo ld c la s s ific a tio n o f outdoor recre­ ation areas, distinguished p rim a rily upon the basis of economic 1 That i s , r e l a t i v e l y higher levels o f fam ily income would be required o r d in a r ily before consumers would have adequate resources to (a) purchase recreational equipment, and (b) cover the tra n s fe r costs involved in t r a v e llin g from home to the recreation area i f they are to enjoy ce rta in kinds o f outdoor recreation a c t i v i t i e s ( e . g . , boating, camping, snow s k iin g ). 2 Stoevener and Brown, of>. c i t . , p. 1297. 47 s im ila ritie s : (1) resource-based areas, (2 ) user-oriented areas, and (3) interm ediate areas: 1. Resource-based areas are characterized by t h e i r outstanding physical a t t r ib u t e s . Major areas in th is class would include national parks, national fo re s ts , some s ta te parks, and some p riv a te lands such as large timber!and ownerships, seashores, and major lakeshores. Such areas are usually located a t considerable distances from major con­ centrations o f population. Therefore, f o r most people, a v i s i t to a resource-based area involves considerable t r a v e l , and thus both time and money in moderately large amounts. V is it s to resource-based areas are those normally undertaken during extended vacation periods. Most resource-based areas are q u ite large in s iz e , usually encompassing several thousand acres of land and/or water area. 2. User-Oriented areas l i e a t the other end o f the scale f o r the most p a rt. They consist c h ie f ly o f parks and playgrounds adminis­ tered by c i t y , county, or other local governmental u n its . recreation service firms also f a l l Some p riv a te in th is category, such as g o lf courses, amusement parks and the l i k e . Their most important charac­ t e r i s t i c is t h e i r closeness and ready a c c e s s ib ilit y to users. Travel distance (and th ere fo re tra v e l time and costs) are at a minimum fo r such areas. User-oriented areas are v is it e d a f t e r school by c h ild re n , a f t e r work by a d u lts , and during the day by many mothers and small c h ild re n . The use o f these areas, then, is c lo s e ly co rrela te d with the fre e (or d is c re tio n a ry le is u r e ) time a v a ila b le each day. 3. Intermediate areas l i e between the other two types of areas geographically and in terms o f use. They g en erally l i e w ith in 48 a range o f 1-2 hours d riv in g time from major concentrations o f popu­ l a t io n . V is its to such areas t y p i c a ll y involves a l l - d a y outings and weekend use. Less tra v e l time and expense is involved in in d ivid u al v i s i t s to interm ediate areas than fo r t r i p s to resource-based f a c i l i ­ tie s . Federal re s e rv o irs , s ta te parks and p riv a te f a c i l i t i e s f a l l th is area. into Camping, p icnicking , h ik in g , swimming, hunting, and fis h in g are usually the dominant a c t i v i t i e s undertaken a t interm ediate a r e a s J Much o f the p a r tic ip a tio n in outdoor re crea tio n tends to f a l l into a p attern such as th a t described in the c la s s if i c a t io n system described above. In p ra c tic e , however, there tends to be some overlap in use patterns a t the various types o f areas. The amount and timing o f a v a ila b le le is u re does appear to be clo sely re la te d to where one p a rtic ip a te s in outdoor re c re a tio n . A change in the length o f the average work week from f i v e to four days, fo r example, would have the p o tential o f a lt e r in g present patterns of outdoor re c re a tio n . Shorter work weeks, together with higher real incomes and improvements in travel f a c i l i t i e s , might mean an increased demand fo r re creatio n services and f a c i l i t i e s a t interm ediate recreatio n areas, fo r example. Likewise, longer paid vacations might mean more time devoted to outdoor recreatio n during f a l l , w in te r, and spring periods ra th e r than during the summer months, w ith consequent s h if ts in demand fo r various kinds o f outdoor recreation resources. There is also the d i s t i n c t p o s s ib ilit y th a t increases in the amount of le is u re time a v a ila b le w i l l r e s u lt in the pursuit o f other types o f c u ltu ra l and educational a c t i v i t i e s , with ^Clawson, Held, and Stoddard, Land fo r the Future, loc. c i t . , p. 126. 49 correspondingly less time and resources being devoted to outdoor re cre­ ation a c t i v i t i e s . Public, P rivate and Mixed Goods Exchange in the market place depends upon the existence of exclusive t i t l e among property owners to those goods which are to be exchanged. A consumer who wishes to obtain a p a rtic u la r commodity from a p riva te supplier must o r d in a r ily meet the terms o f exchange set by th at owner. An exclusion p rin c ip le thus usually comes into play fo r those commodities which are exchanged on the p riv a te market. Consumers may be prevented from acquiring ownership rights or the r ig h t to use and enjoy many types o f goods and services unless they are w illin g to pay the stip ulated market price demanded by the owner or supplier. Market exchange performs an important function in the economy. Among other things, the process of exchange provides a mechanism of communication between producer and consumer. A market bid by a consumer reveals his preference fo r p a rtic u la r goods and services and indicates to resource owners what types of commodities should be produced under p revailin g cost conditions. In recent years, considerable a tte n tio n has been given in the th eo retic al l i t e r a t u r e to special resource a llo c a tio n problems created by public provision o f certain goods and services. A pure public {or so c ia l) good may be thought of as being a t nearly a polar opposite from a p r i v a t e good. Much o f the l i t e r a t u r e places heavy emphasis upon the non-market demand aspects o f c e rta in goods, and upon t h e i r "equal consumption" a t t r ib u t e s . According to Musgrave, social wants are: 50 . . . those wants s a tis fie d by services th a t must be consumed in equal amounts by a l l . People who do not pay fo r the services cannot be excluded from the benefits th at r e s u lt ; and since they cannot be excluded from the b en efits* they w i l l not engage in voluntary payments. Hence, the market cannot s a t is f y such wants. Budgetary provision is needed i f they are to be s a tis fie d a t a l l . Determination o f the required budget plan is complicated by two fac to rs. . . . A primary d i f f i c u l t y arises because true p re fe r­ ences are unknown. A second d i f f i c u l t y arises because there is no single most e f f i c i e n t solution to the s a tis fa c tio n o f social wants or to the problem o f supplying services th a t are consumed in equal amounts by a l l . ' The usual examples c ite d as public goods include such things as national defense, the ju d ic ia r y system, police and f i r e p ro tectio n , and public roads. Unlike most goods, national defense cannot be "consumed" in d if f e r e n t q u a n titie s by d if f e r e n t in d iv id u a ls . A person residing in C a lifo rn ia is as well protected as one who liv e s in Michigan. Put another way, the good provided is not f i n e l y d iv is i b l e . National defense could not be sold in d if f e r e n t q u a n titie s to d if f e r e n t people. This leads to another major d is tin c tio n to be made about public goods; another o f t h e ir peculiar a ttr ib u te s is th a t they are " jo i n t l y supplied." The ra tio n a le fo r considering outdoor recreation a c t i v i t i e s which u t i l i z e natural resources a t a public park as public goods is due p rim a rily to th is jointness in supply c h a ra c te r is tic . Maintaining adequate water q u a lity a t a public beach fo r one person a t the same time provides clean water fo r other people. Once the cost o f p u rify in g the water has been covered, the additional cost o f supplying clean water to other users is zero. As C icch etti puts i t : ^Richard A. Musgrave, The Theory o f Public Finance (New York: McGraw-Hill Book Company, I n c . , 1959), p. 9. 51 Outdoor recreation is a public good not because o f the demand side o f the market but because o f the f a c t th a t a f a c i l i t y or natural resource is e ith e r provided or not in large in d iv is ib le lumps e ith e r as a pure public good or as a mixed good. Once provided up to the point of crowding or d e te rio ra tio n fo r fu tu re gener­ atio ns, the . . . cost o f supplying user space or an additional v i s i t o r day is z e r o J The th eo retic al l i t e r a t u r e stresses fo r the most p art th at a pure public good is la rg e ly a polar case which is not often found in the real world; and th at many goods and services, even though p u b lic ly provided, are a c tu a lly mixed goods. We have already noted, fo r example, that outdoor recreation f a c i l i t i e s , even though constructed with public funds, involve p riva te costs. Even though public f a c i l i t i e s are constructed and made a v a ila b le to public use a t zero or nominal p rice s, i t is s ig n ific a n t th at high user (or tra n s fe r) costs must be incurred by re c re a tio n is ts in order to transport themselves from t h e i r place o f residence to the recreation f a c i l i t y . Transfer costs are usually highest fo r resource-based areas which are located some distance away from population centers. Outdoor re crea tio n , then, usually involves both public and p rivate components, and may be thought o f as a mixed good. Individuals may thus e x h ib it a p riv a te demand fo r camping in the Porcupine Mountains, re fle c te d by a w illingness to pay the tra n s fe r costs associated with travel to the campground. as a p riva te component o f the recreation good. We may think o f th is The fa c t th a t public funds were used to reserve the natural resources of the Porcupine Mountains area fo r public use serves as a public component o f the i Charles J. C ic c h e tti, e t a l . , op. c i t . , p. 32. 52 recreational camping good. The area is e ith e r provided or not, in a large lump, and the f a c i l i t y is thus " j o i n t l y supplied" to a l l who care to use i t . While i t is true th a t the natural resources of the Porcupine Mountains area, in a w h o lis tic sense, are not re a d ily d iv i s i b l e , th is may be tre a tin g the problem too s i m p ! i s t i c a ll y . Special f a c i l i t i e s constructed fo r the use o f the public are d iv i s i b l e , and compensation may be required o f those people who u t i l i z e the services made a v a ila b le ( e . g . , campsites, boat marinas, bathhouses, lockers, e t c . ) . Even public ownership and control o f nonproduced resources ("nature products") does not, in i t s e l f , preclude the p o s s ib ilit y o f defining ce rtain d iv is ib le s c a rc itie s which may be rationed among users. According to Bator, the problem does not e x is t because of public ownership but rather because of in s t itu t io n a l arrangements, d i f f i c u l t y in product id e n t if ic a t io n , and the f e a s i b i l i t y o f keeping track o f "what is consumed," and who consumes i t . Tangible values and ownership t i t l e to ce rta in factors are simply not assigned. In Bator's words: This is an . . . ownership e x te r n a lit y . I t is e s s e n tia lly an unpaid fa c to r case. Nonappropriation, divorce o f sc arcity from e f f e c t iv e ownership, is the binding consideration. Certain "goods" (or "bads") with determinate . . . values are simply not a t t r i ­ buted. I t is irre le v a n t here whether th is is because the lake where people fis h happens to be in the public domain, or because "keeping book" on who produces, and who gets what, may be impossible, clumsy, or costly in terms o f resources. For whatever legal or f e a s i b i l i t y reasons, certain variables which have p ositive or negative . . . value are not assigned axes.l Francis M. Bator, "The Anatomy of Market F a ilu re ," The Quarterly Journal of Economics, Vol. LXXII, No. 3 (August, 1958), pp. 364-65, 53 Problems o f Measuring Demand Much o f the th eo retic al work underlying techniques f o r meas­ uring the demand fo r outdoor recreation has been contributed by Dr. Marion Clawson. In a paper presented a t the U niversity o f Wisconsin on January 13, 1959, Clawson set fo rth some important princip les underlying construction o f economic demand curves fo r attendance a t a single recreation s i t e J Using attendance data fo r Yosemite National Park in C a lifo rn ia , demand curves were approximated fo r C a lifo rn ia v is it o r s , and o u t-o f-s ta te v is it o r s . In estimating the demand curve fo r a p a rtic u la r recreation area, a two-stage procedure was employed: (1) construction o f one curve fo r the to ta l recreation experience, and (2) d erivation o f a demand curve fo r the recreation opportunity per se. The curve fo r the to ta l recreation experience is based upon actual attendance figures fo r large numbers o f people; and the curve fo r the recreation opportunity is derived from the f i r s t . Throughout th is chapter, emphasis has been placed upon the importance o f tra n s fe r (or user) costs in discussing the demand fo r outdoor recreatio n . Any discussion o f the outdoor recreation experi­ ence, then, cannot lo g ic a lly be lim ite d to the actual o n -s ite a c t i v i t y engaged in. I f the d e fin itio n o f user costs is re s tric te d to those incurred while the re c re a tio n is t is a t the s i t e , the cost o f the recreation experience would be s l i g h t , i . e . , entrance or user fees at the s it e may be zero or very low in re la tio n to the cost o f the whole recreation experience. A c tu a lly , there is a "threshhold cost" ^Marion Clawson, Methods o f Measuring the Demand fo r and Value of Outdoor Recreation, lo c . c i t . , 36 pages. 54 which must be paid before one can enjoy an a c t i v i t y day o f re c re a tio n . I f one wishes to spend a day boating, f o r example, he must f i r s t purchase a boat, perhaps a t r a i l e r to transport i t to a lake or pond, and also pay a r e g is tr a tio n fee i f i t is a powered w a te rc r a ft. In a d d itio n , trans p o rta tio n costs (g aso lin e , highway t o l l s , food and lodging en ro u te, e t c . ) must be paid, usually on a roundtrip basis. There may also be a launch or boat storage fee a t the d e s tin a tio n . Thus, the cost o f the whole re crea tio n experience is composed of an aggregate "package" o f costs. Clawson divides the whole recreatio n experience in to f i v e d is t in c t phases: (1) a n tic ip a tio n , (2) tra ve l to the actual s i t e , (3) o n -s ite experiences and a c t i v i t i e s , (5) re c o lle c tio n .^ (4) tra ve l back home, and Much discussion about outdoor recreation is con­ fined to the o n -s ite experience. This phase is presumably why a fa m ily goes to the bother o f making a t r i p to a public or p riv a te campground. However, the o n -^ ite experience " . . . may be less than h a l f o f the t o t a l , whether measured by time involved, expense incurred, or to ta l s a tis fa c tio n gained." 2 Viewed in th is way, then, the whole recreatio n experience consists o f a set or package o f s a tis fa c tio n s (or d is ­ s a tis fa c tio n s ) obtained through the various phases o f a recreatio n trip . The sum o f the s a tis fa c tio n s re a liz e d from the various phases of the experience would have to be balanced against the sum o f the ^Marion Clawson and Jack L. Knetsch, Economics o f Outdoor Recreation (Baltimore: The Johns Hopkins Press, 1966), pp. 33-35. 2 I b i d . , p. 34. 55 costs incurred in order to determine whether or not one would be w il lin g to repeat any or a l l of the whole experience. In constructing a demand curve fo r Yosemite National Park, Clawson assumes th a t the fam ily is the u n it which decides which re cre­ ation area i t w ill v i s i t . Even though fam ily members may engage in d if f e r e n t a c t i v i t i e s while a t the park, i t is assumed th a t an in d i­ vidual t r i p is j o i n t l y planned. Further, he assumes th a t members o f the fam ily r e a liz e sa tisfac tio n s {or d is s a tis fa c tio n s ) in the form o f an tic ip a tio n before the t r i p begins, from the actual o n -s ite experience, and through reco llection s about the whole t r i p a f t e r returning home. A demand curve based upon the concept o f the whole recreation experience is assumed to be l ik e the demand curve fo r other services and commodities. I t is applied to large numbers o f people, rather than to in d ivid u als . That is , any one person may have an individual demand curve which is extreme in some form, but a large group o f people w ill together provide a more measurable and predictable reaction to an outdoor recreation opportunity. ■ Moreover, i t is assumed th at i f a demand curve fo r a large group o f people can be constructed, " . . . then i t is probable th a t another large group chosen more or less at random but with s im ila r c h a rac teris tic s to the f i r s t group, w il l respond in s im ila r fashion to costs and other c h a ra c te ris tic s o f the recreation experience."^ Using attendance data from Yosemite National Park, Clawson separated the v is it s by point o f o rig in o f the v i s it o r s , and divided them into distance zones based upon one-way milage from the park. ^Clawson, 0 £. c i t . , p. 15. In 56 fig u rin g distance zones, C a lifo r n ia residents were kept separate from v is it o r s o r ig in a tin g in o ther s ta te s . The t o ta l number o f v i s it o r s from each distance zone was then divided by the population in th a t zone in order to obtain the estimated number o f v i s i t s per 100,000 population. An estimated cost per v i s i t was then c a lc u la te d , using an average cost o f $9.00 per day plus 10 cents per m ile f o r car f o r double one-way distance (d ivid ed by four on assumption o f 4 passengers per c a r ) . The number o f v i s i t s per 100,000 population and mated cost per v i s i t were then p lo tte d , and the e s t i ­ demand curves were ap­ proximated fo r C a lif o r n ia residents and o u t - o f -s t a t e v i s i t o r s . C alcu latio n o f the average cost per v i s i t was based upon a major assumption— th a t tra v e l to Yosemite Park was the c h ie f purpose of the t r i p , and th a t i t should, th e re fo r e , bear the costs o f tra v e l from home to the park as well as w ith in the park. the as­ Despite sumptions made about costs per t r i p , the approximated demand curves appeared to be much more p r i c e - e l a s t ic fo r distance zones closest to the park (where estimated costs per v i s i t were lowest) than fo r the most d is ta n t zones on the eastern seaboard. Building upon the Clawson technique, Brown, Singh, and Castle undertook a study involving economic evaluation o f the Oregon salmon and steelhead sport fis h e r y in 1964.^ The researchers p o in t out th a t there are some real lim it a t io n s associated with the Clawson method o f estimating demand. They point out th a t more than the monetary cost o f ^William G. Brown, Ajmer Economic Evaluation o f the Oregon Technical BulletTn 7 8 T C o rv a T lis , S ta tio n , Oregon State U n iv e rs ity , Singh, and Emery N. C a s tle , An Salmon and Steelhead Sport F is h e ry , Oregon: A g ric u ltu ra l Experiment 1964), 47 pages. 57 the v i s i t is involved in determining the number o f v i s i t s per 100,000 population o f various distance zones. The cost o f the t r i p in time "would be one e ff e c t th a t could s h i f t the demand curve to the r ig h t or to the l e f t depending upon whether the v i s i t o r regards the tra ve l time as pleasant or onerous."^ Also, distance could be expected to s h i f t the demand curve to the l e f t fo r another reason: "The g reater the distance a zone is from a p a r t ic u la r recreation s i t e , the greater are the number and appeal o f a v a ila b le substitutes fo r th at p a rtic u la r s it e , because other site s become r e l a t i v e l y cheaper in time and money." The Oregon salmon-steel head study employed the use o f mail questionnaires. Based upon estimated cost per respondent and an estimated 50 per cent re tu rn , i t was planned th a t 6,000 questionnaires be mailed. However, because response was g reater than the expected 50 per cent r a t e , only 5,751 questionnaires were a c tu a lly mailed. The researchers attempted to reduce e rro r from memory bias by mailing ques­ tionnaires to anglers a t the end o f each month during the year 1962. Questions re la tin g to expenditures made on fis h in g trip s were thus answered on a monthly basis by respondents. Angler expenditures were obtained on a "per a n g le r--fa m ily basis," rather than on a "per angler" basis. About 80 per cent o f the questionnaires a c tu a lly mailed were completed and returned by respondents. Sport fishermen selected in the sample were divided into distance zones fo r the analysis. Using information from the returned mail questionnaires, average va ria b le costs per angling day was ^I b i d . , p. 9. 2Ib id . 2 58 computed fo r each distance zone. Anglers were also asked to supply information on average miles per t r i p . An average miles per steelhead- salmon fish in g t r i p fig u re was then computed fo r each distance zone. A s ig n ific a n t re la tio n s h ip was found between number o f fish in g days taken per u n it of population f o r each distance zone and average v a ria b le cost per day o f fis h in g . Days o f fish in g taken was also found to have a s ig n ific a n t re la tio n s h ip with average fam ily income, and average miles per t r i p taken. In 1967, Cole undertook a study of outdoor recreation p re fe r­ ences of households w ith in the Philadelphia--Baltimore--W ashington Metropolitan region.^ The study was based upon 1963-64 household p a rtic ip a tio n rates in pleasure rid in g , p icnicking, walking, swimming, boati.ng, camping, fis h in g , hunting, g o lfin g , horseback r id in g , ice skating, snow sk iin g , tobogganning, and vacation and weekend t r i p s . A mail questionnaire was used in the study. The questionnaire was mailed to a sample o f 2,000 households in the study area by National Family Opinion, an independent pollin g firm . The completed question­ naires were returned to National Family Opinion as w e ll. A to ta l of 1,718 usable .questionnaires were completed and returned by respondents. M u ltip le regression analysis was used in the study, r e la tin g household p a rtic ip a tio n in various outdoor recreation a c t i v i t i e s to: (1) socio-economic c h a ra c te ris tic s o f respondents, (2) distance tra v e lle d to p a r tic ip a te , (3) time required to p a r t ic ip a t e , and {4} admission fees ^Gerald L. Cole, "Toward the Measurement of Demand fo r Outdoor Recreation in the Philadelphia— Baltimore— Washington Metropolitan Region with Implications fo r A g ricu ltu ral Resource Use" (unpublished Ph.D. d is s e rta tio n , Michigan State U n iv e rs ity , 1967). 59 charged. In general, the c o e ffic ie n t o f m u ltip le determination was less than 0.50 fo r individual a c t i v i t i e s . Rates o f p a rtic ip a tio n in recreational boating were found to be p o s itiv e ly correlated with both distance tra v e lle d and time required to reach a body o f water where the boating a c t i v i t y took place. were no natural lakes. Within the sample area, there Suitable boating water was thus thought to be lim ite d to the A tla n tic Ocean, the Delaware and Cheasapeake Bays, and tr ib u t a r y riv e rs emptying into the bays or oceans. P articipants indicated th at they drove an average o f 100 miles to reach water su itab le fo r botaing. Publicly-owned m ill ponds w ithin the region re s tric te d outboard motor size to 5 horsepower or less. P a rtic ip a tio n in recreational boating was also found to be p o s itiv e ly correlated with automobile ownership and household income o f respondents. Automobile ownership and income l e v e l, as well as travel time and distance t r a v e lle d , were also p o s itiv e ly co rrelated . Much of the empirical work undertaken in the past has con­ centrated heavily in two major areas: (1) prediction o f p a rtic ip a tio n rates of households based upon socioeconomic-demographic character­ i s t i c s , and (2) construction o f economic demand curves based upon estimated tra n s fe r costs between the zone o f o rig in of p articip an ts and destination recreation areas. More re c e n tly , considerable a tte n tio n has been placed upon the importance o f supply variables in explaining va ria tio n in recreation p a rtic ip a tio n ra te s . A number o f researchers have pointed out the need fo r taking account of supply factors facing re c re a tio n is ts . According to Knetsch: Recreation demand studies, to be useful fo r planning purposes must consider the e f f e c t o f both supply and demand factors on 60 recreation use or p a rtic ip a tio n . Use data in the form o f popu­ la tio n segment p a rtic ip a tio n rates or v i s i t s to recreation areas must be obtained, but the in te rp re ta tio n should consider that both demand and supply variables explain or determine these rates. That i s , the emphasis should be placed on determining and explaining patterns o f use which emerge, given an a v a ila ­ b i l i t y o f opportunities and the ch a ra c te ris tic s o f the using p o p u la tio n .' One o f the d i f f i c u l t i e s in u t i l i z i n g socioeconomic factors such as fam ily income, education l e v e l , average work week, family s iz e , e t c . , to explain observed patterns o f p a rtic ip a tio n in outdoor recreation a c t i v i t i e s is th at projections o f fu tu re levels o f use depend heavily upon the a v a i l a b i l i t y o f recreation f a c i l i t i e s (supply). Indeed, concentration upon projected increases in socioeconomic factors overlooks the fa c t th a t the required supply o f recreation f a c i l i t i e s . . may not be growing a t the same r a t e —and in fa c t may not be 2 growing.11 I t has already been emphasized th at outdoor recreation areas are dispersed geographically over space: and th at the re c re a tio n is t must travel to the point o f supply in order to p a rtic ip a te . The location o f a household, then, with respect to a supply point may have an important influence upon the kind o f recreation a c t i v i t i e s engaged in. This would appear p a r tic u la r ly true i f one accepts the "learning by doing" hypothesis. According to th is proposition, outdoor recre3 ation may be a good which is . . not demanded u n til supplied." ^Jack L. Knetsch, "Assessing the Demand fo r Outdoor Recreation," Journal o f Leisure Research, Vol. 1, No. 1 (Winter 1969), p. 87. 2 C ic c h e tti, Seneca, and Davidson, ^Ib i d . , p. 33. 0 £. c i t . , pp. 38-39. 61 This suggests th a t people may acquire a ta s te f o r a p a r t ic u la r outdoor recreation a c t i v i t y through "want c re a tio n ," induced as a r e s u lt o f constructing re crea tio n f a c i l i t i e s . A number o f empirical studies mentioned in t h is chapter empha­ size the d i f f i c u l t i e s involved in attempting to measure recreatio n demand. Such d i f f i c u l t i e s appear to a ris e f o r several reasons: public provision o f areas and f a c i l i t i e s , zero p ric e s , and geographical d is ­ persion o f f a c i l i t i e s and natural resources over space, giving r is e to high tra n s fe r costs. The theory o f consumer demand is not e a s ily applied d ir e c t ly to such a market. Besides these problems, there is an even more fundamental consideration facing the researcher interested in empirical study o f outdoor re crea tio n demand: the id e n t i f i c a t i o n problem. The i d e n t i f i c a t i o n problem consists o f d i f f i c u l t y in i n t e r ­ preting observations in the marketplace fo r any p a r t ic u la r good, as q u a n titie s and prices in a supply-demand diagram trace out points o f eq u ilib riu m between both the supply and demand curve. T r a d i t io n a l ly , the i d e n t i f i c a t i o n problem has been most c lo s e ly associated with in te rp re ta tio n o f time series d ata, as supply and demand curves show the e x is tin g market conditions a t only a given point in time; and e x is tin g market conditions may be expected to change. Indeed, " . . . the supply and demand curves which ac cu rately represent the market s itu a tio n o f to-day w i l l not represent th a t o f a week hence. The curves which represent the average or aggregate o f conditions th is month w i l l not hold tru e fo r the corresponding month next year."^ ^E. J. Working, "What do 'S t a t i s t i c a l Demand' Curves Show?" Quarterly Journal o f Economics, Vol. 41 (February, 1927), p. 217. \ 62 In analyzing time series data on attendance a t a public park, a public boating marina, or other outdoor recreation f a c i l i t y , fo r example, an adm inistrator or planner is faced with the problem o f resolving the question as to whether changes in levels o f use o f the area r e f le c t demand responses or supply responses, or both. As Klein points out, what is observed in the market fo r any p a rtic u la r good a t a moment in time is simultaneous solution o f a system o f three equations: (1) a demand function, where price equals a function of quantity demanded plus e r r o r , (2) a supply function, where price equals a function o f quantity supplied plus e r r o r , and (3) a market clearing function, where supply equals demand plus e r r o r J In cases where there is considerable v a ria tio n in both the supply and demand function over time, estimation becomes d i f f i c u l t . There is no assurance th at a demand pattern exists in such a s itu a tio n --th e r e may be a "mongrel11 function. Some researchers hold the view that there is considerable v a r i a b i l i t y in both the supply and demand func­ tions in the outdoor recreation market: . . . i t is widely assumed th a t price is not an explanatory v a r i ­ able in the supply function fo r most recreation services and that such a function is v e rtic a l in nature fo r any given time period because of it s public provision. The r e la t iv e s h ifts in the supply and demand curves over time are unknown. Thus, the essential elements required to trace the structural demand function are missing. Assuming th at s h ifts over time in the supply function due to changes in public policy help in tracing the demand r e la ­ tionship is not s u f f ic ie n t i f s h ifts in the demand re latio n sh ip i t s e l f are unknown.2 ^Lawrence R. K lein , An Introduction to Econometrics (Englewood C l i f f s , New Jersey: Pren tice-H al1, In c ., 1962), p. 10. 2 Kalter and Gosse, 0 £. c i t . , pp. 47-48. 63 The present study w i l l be cognizant o f these problems in re la tio n to empirical investig atio n of recreational boating. Refer­ ence to the "learning by doing phenomenon" has already been made. A person who is taken fo r a boat rid e and "learns" something about operating a w ate rcraft may, fo r example, then e x h ib it a demand fo r boating, assuming the experience was pleasurable. He may not have acquired any desire to go boating a t a l l had he not learned by doing. In order fo r one to learn about boating, an accessible supply of boatable water would have to e x is t . Recreational boating p a rtic ip a tio n may, then, be correlated with supply fa c to rs . Recreational Boating— A Case Study In 1960, i t was estimated th at 22 per cent o f the United State's population 12 years o f age and over engaged in boating one or more times. On a national basis, th is represented a per capita rate o f 1.22 occasions fo r the 3-month period June-AugustJ and a l l indicators point to the fa c t th at recreational boating has grown very rap id ly in popularity over the past several decades. The popularity o f recreational boating has also been re a d ily apparent in the State of Michigan during the past several years. At the end o f calendar year 1965, Michigan had a to ta l o f 398,902 re g is ­ tered w a te rc ra ft, and ” . . . a t le a s t another 100,000 rowboats and ^Outdoor Recreation Resources Review Commission, National Recreation Survey, ORRRC Study Report 19 (Washington: U.S. Government P rinting O ffic e , 1962), p. 24. other c r a f t th a t do not require r e g is t r a t io n ." 1 Beginning in 1958, a l l people owning and operating powered w a te rc ra ft in the state were required to re g is te r them with the Michigan Secretary o f S tate. A to ta l o f 217,533 w a te rc ra ft were registered in the f i r s t year. By 1968, the number had risen to 438*017. 2 Table 1 shows the change in boat re g is tra tio n s , by length class, between 1965 and 1968. Accompanying th is steady growth in the size o f the Michigan recreational boating f l e e t , there has been a substantial expenditure o f public funds by the State o f Michigan, the federal government, and local communities on the construction o f public boat marinas. V irtu a lly TABLE 1 . — Numbers o f Registered W atercraft in Michigan, by Size Class, fo r Selected Years. Registered W atercraft Less than 20 Feet Total Length Registered W atercraft 20 Feet or Greater Total Length Year No. Per Cent 1965 337,763 94.8 21,139 5.2 398,902 100 1968 413,949 94.6 24,068 5.4 438,017 100 Source: No. Per Cent Total All W atercraft No. Per Cent Michigan Department o f S ta te , Vehicle and W atercraft Records D ivision. Michael Chubb, Outdoor Recreation Planning in Michigan by a 5ystems Analysis Approach; Part I I I , The Parctical Application of Program RECSYS and SYMAP, Technical Report No. 12 (Lansing, Michigan; Michigan Department o f Conservation, December 1967), pp. 11-12. 2 Division o f Vehicle and W atercraft Records, "Size and Type o f Registered boats in Michigan Counties," Unpublished Report, Michigan Secretary o f S tate 's O ffic e , December 31, 1968. 65 a l l o f these public expenditures have been made fo r the construction o f "Harbors o f Refuge" on the Great Lakes (including Lake Michigan, Superior, Huron, E rie , Lake St. C l a i r , and connecting waters).^ This Great Lakes marina development program has been undertaken la rg e ly by the Michigan State Waterways Commission. Table 2 gives a tabular summary o f expenditures on the marina development program between 1964 and 1970. TABLE 2 . — Expenditures fo r the Michigan Waterways Commission Marina Construction Program, 1964-1970. Biennium Waterways Commission Expenditures 1964-1966 $1,708,505 1966-1968 2,781,988 1968-1970 TOTALS Source: Federal Sources $ 811,397 Local Expenditures Total A ll Sources 195,664 $2,716,747 3,281,051 490,236 6,552,094 4,884,381 1 ,199,548 1,502,726 7,586,655 $9,374,874 $5,291,966 $2,188,626 $16,855,496 $ Waterways D iv is io n , Michigan Department o f Natural Resources. As w ate rcraft ownership and use has grown in p op ularity in Michigan, so to has in te re s t in research on boating p a r tic ip a tio n . A number of past studies have contributed to e x is tin g knowledge in th is area. A 1965 survey, sponsored by the Michigan Waterways commission, Substantial expenditures o f public funds have also been made fo r acquisition and development of public access site s and boat launching f a c i l i t i e s on inland lakes and streams in the s ta te . These expenditures have been made by a number o f d if f e r e n t s ta te and federal agencies fo r the purpose o f providing boating opportunities fo r the public. In addi­ tio n , there are a number o f commercial boat marinas throughout the s ta te . A complete inventory of a l l such f a c i l i t i e s is beyond the scope o f th is study, however. 66 estimated th at approximately 16 m illio n boat-use periods were generated by re crea tio n is ts during the calendar y e a r J Most past research on recreational boating in Michigan has d e a lt with problems o f (1) inven­ tory and analyzing current lev e ls o f w a te rc ra ft use on a statewide basis, and (2) with developing q u a n tita tiv e projection techniques fo r forecasting fu tu re lev els o f recreational boating in various geographic regions of the state. Past research has placed heavy emphasis upon systems science and systems analysis. Systems models have been developed in order to forecast fu tu re boating p a rtic ip a tio n by means o f origin s and destinations of Michigan boaters. By u t i l i z i n g collected survey data on boating use, component parameters o f the model are "tuned" so th at they w il l forecast boating use w ith in a base year with acceptable accuracy. Component parameters are then changed in order to r e f l e c t expected conditions during a ta rg e t year sometime in the fu tu re . Levels o f boating p a rtic ip a tio n are then predicted fo r each county in the s ta te . While these past studies have contributed s ig n if ic a n t ly to ex istin g knowledge about current and expected levels o f boating a c t i v i t y in the s ta te , they have not d e a lt to any degree with factors associated with va ria tio n s in individual and aggregate levels o f boating ^Michigan Department o f Conservation, Waterways D ivisio n , Transportation P redictive Procedures: Recreational Boating and Com­ mercial Shipping (Lansing, Michigan: Michigan Department o f Commerce, 1967). ^See, D. M. M ils te in and L. M. Reid, e t a l . , Michigan Outdoor Recreation Demand Study; Volume I I , A c t iv it ie s Reports, Technical Report No. 6 (Lansing, Michigan: Michigan Department o f Commerce, 1966); J. B. E l l i s , Outdoor Recreation Planning in Michigan by a Systems Analysis Approach, Part I I , Technical Report No. 7 (Lansing, Michigan: Michigan Department o f Conservation, 1966); also, Chubb, og_. c i t . 2 67 p a r tic ip a tio n . The present study w i l l examine the e ffe c ts o f s p e c ific variables upon in d ivid u al and aggregate boating p a r tic ip a t io n rates in several geographic regions o f Michigan. CHAPTER I I I DATA COLLECTION PROCEDURES The p rin c ip a l o b je c tiv e in th is chapter w i l l be to o u tlin e the research methods u t i l i z e d in conducting th is study. * F i r s t , emphasis w i l l be given to i d e n t i f i c a t i o n and d es crip tio n o f the study area. Next, sampling procedures w i l l be o u tlin e d . F in a l l y , emphasis w i l l be given to describing the procedures followed in preparing and d i s t r i ­ buting the mail q uestionnaire, and with data coding and processing. The Study Area In conducting th is in v e s tig a tio n , the sample area consisted o f the e n t ir e state o f Michigan. Data were co lle cte d from re crea tio n al w a te rc ra ft owners in a l l 83 counties, as well as, from a sample o f registered boat owners residing in other s ta te s . The p rin c ip a l o b je c tiv e o f th is study is to analyze regional differen ces in boating p a r tic ip a tio n in the s ta te . However, a second o b je c tiv e was to estimate the to ta l volume o f re cre a tio n a l boating undertaken in the s ta te by Michigan residents. Very l i t t l e empirical research o f th is nature has been conducted in the past. The studies undertaken by Cole, Brewer and G ille s p ie cite d in Chapter I I were intensive inv es tig atio n s of factors associated w ith v a ria tio n in recreation a c t i v i t y undertaken by la r g e ly urban populations in the Baltimore-Washington-Philadelphia region and the St. Louis, 68 69 Missouri m etropolitan area. This study d if f e r s from these two in v e s t i ­ gations in th a t i t w i l l explore the re la tio n s h ip between recreatio n p a r tic ip a tio n rates f o r a s in g le outdoor a c t i v i t y (boating) and s p e c ific variables over several regions. A series o f f i v e regions were selected fo r th is stu d y .1 The f i v e regions selected f o r intensive in v e s tig a tio n were chosen as a re s u lt o f examination o f previous em pirical research. Studies conducted by the Outdoor Recreation Resources Review Commission suggest, f o r example, th a t recreatio n a c t i v i t i e s engaged in by ru ra l non-farm residents d i f f e r from those pursued by urban resid en ts. In those stu d ie s, ru ra l people were found to have higher o v e ra ll le v e ls o f recreatio n a c t i v i t y than c i t y residents. Location and access to recreation areas and f a c i l i t i e s appeared to be important in the higher o v e ra ll le v e ls o f p a r tic ip a tio n exh ib ited by ru ral resid en ts. 2 The f iv e regions selected fo r study were also selected on the basis o f t h e ir lo c atio n with respect to population centers (metropolitan areas) o f the s t a te , and the nature o f the water resources and f a c i l i t i e s The only other study located which examined socio-economic c h a ra c te ris tic s and preferences o f Michigan residents fo r re cre a tio n a l boating was one undertaken as a p a rt o f the Michigan Outdoor Recreation Demand Study. In th a t study, socioeconomic c h a ra c te ris tic s and p r e f e r ­ ences o f respondents to a mail survey were analyzed f o r the 10 top counties of o r ig in . The 10 top o rig in counties were ranked according to the number o f usable questionnaires returned by respondents. The counties chosen also led the s ta te in terms o f the number o f resident boat re g is tra tio n s . The 10 counties in the order ranked were Wayne, Oakland, Kent, Genessee, Macomb, Ingham, Kalamazoo, Calhoun, Jackson, Saginaw. See, John L. Needy, "Boating," in Michigan Outdoor Recreation Demand Study; Vol. I I , A c t iv i t i e s Reports, Technical Report No. 6 (Lansing, Michigan: Michigan Department o f Conservation, 1966), pp. 10 .24-10.32. 2 Outdoor Recreation For America, l o c . c i t . , pp. 27-32. 70 a v a ila b le to the residents o f each region. For example, two of the regions selected contain one or more Standard Metropolitan S t a t i s t i c a l Areas, and both regions may be considered as major population centers. One o f these regions borders d ir e c t ly on a Great Lake, while the other is situated in the center o f the state with r e l a t i v e l y l i t t l e indigenous surface water area a v a ila b le fo r boating by the resident population. The other three regions selected fo r analysis are located in more rural portions o f the s ta te , and are t y p ifie d by a more scattered pattern of settlement, d if f e r e n t employment s itu a tio n s , and a r e l a t i v e l y close access to surface water and boating f a c i l i t i e s fo r recreational water­ c r a f t use. The f iv e regions selected as study areas fo r th is investig atio n include: (1) Region 1 -D e t r o it, (2) Region 6-Lansing, (3) Region 7c- Roscommon, (4) Region 10-Traverse C ity , and (5) Region 12A-Marquette. The counties included in the f iv e selected regions are shown below: (1) Region 1 Counties Wayne Monroe Washtenaw Livingston Oakland Macomb St. C la ir A Standard Metropolitan S t a t i s t i c a l Area (SMSA) is defined as a county or a group o f contiguous counties which contains a t le a s t one c it y o f 50,000 inhabitants or more; or "twin c it ie s " with a combined population of a t le a s t 50,000. In ad d itio n , contiguous counties are included in an SMSA i f they are e s s e n tia lly metropolitan in character, and are s o c ia lly and economically integrated with the central c i t y . See, U.S. Department o f Commerce, Bureau o f the Census, U.S. Census of Population: 1960; Vol. I , C haracteristics o f the Population, Part 2At Michigan- (Washington: U.S. Government P rinting O ffic e , 1960), pp. XVII and X V III. 71 (2) Region 6 Ingham Eaton Cl Inton (3) Region 7c Roscommon Ogemaw Iosco Clare G1adwi n Arenac (4) Region 10 Manistee Wexford Missaukee Benzie Grand Traverse Kalkaska Leelanau Antrim Charlevoix Emniet (5) Region12A Iron Dickinson Marquette Alger These f i v e regions were selected from the o f f i c i a l Michigan Planning and Development Regions, designated by the Executive O ffic e o f the Governor in February o f 1968. Three o f the regions selected are a c tu a lly so called "recreation sub-plan regions," designated by the Michigan O ffic e o f Planning Coordination. Figure 1 shows the location o f the selected study regions in the s ta te . The regions selected show considerable v a ria tio n in socio­ economic c h a ra c te ris tic s . Between 1960 and 1970, f o r example, two of the counties in Region 1 showed an o verall population increase o f more than 50 per cent (Livingston and Macomb). These counties are located in the immediate area surrounding the c i t y of D e tr o it. High levels of population growth in the outlying counties o f the region CH’-R L V O t lL LEI - * V t C W w F jfc D 1 a*FN*i t ( 4LC0N* !**<,/ ffOlCCK < 0 0 ? * * * legion 1. 6. 7C. 10. ^2A. ** 3 0 * Detroit Lansing Saginaw Bay Traverse Bay Marquette-Iron Mountain ocean* -l.4*E L 4 Kf itw irf I auatWlN 1 AflCftAC ' y t t o s r * (l k * , r - 1* M)0 i **0 " J _L-0 -L. I ' IN9HAM - *ALA*l«i. CA. KUjl. , - - T •A jH rE M A a | Figure 1 . --Michigan Planning and Development and Recreation Sub-Plan Regions U tiliz e d as Study Areas. Source: Adapted from O ff ic ia l Map Delineating Michigan State Planning and Development Regions, February 1968. 73 suggest a continuation o f suburban growth in the metropolitan region. By way o f co n trast, Wayne County {containing the C ity o f D e t r o it ) , showed r e l a t i v e l y l i t t l e change in population between 1960 and 1970— a net increase o f 0.1 per cent. Region 6, consisting o f the Lansing Standard Metropolitan S t a t is tic a l Area (SMSA), showed a ra te o f population increase which was well above the sta te average. The two suburban counties o f the region— Eaton and C linton— showed the highest rates o f population increase with 38.7 and 27.7 per cent, resp ectively. Ingham county {containing the c i t i e s o f Lansing and East Lansing) showed a population increase o f 23.5 per cent. Three counties in Region 7C showed r e l a t i v e ly high levels of population increase during the past 10-year period. In f a c t , Iosco county, with an overall population increase o f 50.9 per cent ranked as the th ird fa s te s t growing county in the s ta te . Clare county showed a population increase o f 43.3 per cent, and Roscommon county, with a net increase o f 37.4 per cent, were among the top 10 "growth" counties between 1960 and 1970. O v e ra ll, th is region showed the most rapid ra te o f population growth of a l l study areas examined. Houghton Lake and the C ity o f Tawas on Lake Huron are both recreation resort centers. There is a considerable acreage o f public land in th is region, adminis­ tered by state and federal agencies. Region 10 showed a much more modest rate o f population change than the other three regions. Manistee, Wexford, Missaukee, and Benzie counties showed a ra te o f population lower than the increase whichwas considerably state average o f 13.5 per cent during the past 10 years. 74 O v e ra ll, the region's ra te o f population change was about 14 per cent between 1960 and 1970. Like region 7C, region 10 may be characterized as a re so rt-ty p e area. A considerable amount o f public land is open fo r outdoor recreation use on Manistee National Forest. State Parks and State Forest Campgrounds are also abundant in th is region. Like Region 7C, Region 10 is close enough to many population centers in the state to be considered a week-end use area. Public and p riva te camp­ grounds, boating f a c i l i t i e s on Lake Michigan and inland lakes and streams, make th is one o f the states most a t t r a c t iv e regions fo r out­ door recreation a c t i v i t i e s o f a l l kinds. Region 12A is located in Michigan's Upper Peninsula. I t is a region which, with the exception o f Marquette county, declined in population between 1960 and 1970. The four counties of th is region are a t about the mid-point geographically in the Upper Peninsula as one travels from east to west. The region has excellent access to two great lakes (Superior and Michigan), as well as excellent inland water resources fo r boating. Also, public recreation f a c i l i t i e s are a v a ila b le in the region on both state and national fo res t areas. By and larg e , th is region was selected because o f i t s r e la t iv e is o la tio n from the population centers of the s ta te . The driving distance Involved is believed to preclude much recreational use in th is area other than by the resident population over much o f the year. Extended vacation trip s are also made to th is area by both Michigan residents and non­ residents. Pertinent population ch a ra c te ris tic s fo r the f i v e study regions are included in Tables 3, 4, 5, and 6. Table 3 summarizes the population 75 TABLE 3 . — Population o f Regional Study Areas and the State o f Michigan, and Percentage Change: 1960-1970. Region and County A p ril 1, 1960 A p ril 1, 1970 Percentage Change 1960-1970 REGION 1 Wayne Monroe Washtenaw Livingston Oakland Macomb St. C la ir Totals 2,666,297 101,120 172,440 38,233 690,259 405,804 107,201 4,181 ,354 2,669,604 118,479 234,103 58,967 907,871 625,309 120,175 4,734,508 0.1 17.2 35.8 54.2 31.5 54.1 12.1 13.2 REGION 6 Ingham Eaton Cl inton Totals 211,296 49,684 37,969 298,949 261,039 68,892 48,492 378,423 23.5 38.7 27.7 26.6 REGION 7C Roscommon Ogemaw Iosco Clare Gladwin Arenac Totals 7,200 9,680 16,505 11,647 10,769 9,860 65,661 9,892 11,903 24,905 16,695 13,471 11 ,149 88,015 37.4 23.0 50.9 43.3 25.1 13.1 34.0 REGION 10 Manistee Wexford Missaukee Benzie Gd. Traverse Kalkaska Leelanau Antrim Charlevoix Emmet Totals 19,042 18,466 6,784 7,834 33,490 4,382 9,321 10,373 13,421 15,904 139,017 20,094 19,717 7,126 8,593 39,175 5,272 10,872 12,612 16,541 18,331 158,333 5.5 6 .8 5.0 9.7 17.0 20.3 16.6 21 .6 23.2 15.3 13.9 REGION 12A Iron Dickinson Marquette Alger Totals 17,184 23,917 56,154 9,250 106,505 13,813 23,753 64,686 8,568 110,820 -1 9 .6 - 0.7 15.2 - 7.4 4.1 7,823,194 8,879,862 13.5 THE STATE Source: Michigan S t a t i s t i c a l A b stract, Ninth e d ., 1972, Table 1-5, pp. 33-36. TABLE 4 . --Median Family Income, and Per Cent o f Fam ilies in Selected Income Classes, fo r Regional Study Areas and the S tate o f Michigan: 1960 and 1970. 1970 1960 Per Cent of Families With Income - Per Cent of Families With Income - Median Family Income (d o lls .) Less than Poverty Level' $15,000 or More Median Family Income (d o lls .) Under $3,000 $ 10,000 REGION 1 Wayne Monroe Washtenaw Livingston Oakland Macomb St. Clair 11,351 11,398 12,294 11,551 13,826 13,110 10,125 8.1 5.7 5.1 5.1 3.8 3.6 8.5 28.7 25.4 34.8 29.2 43.3 36.1 20.8 6,597 5,892 6,890 5,775 7,576 7,091 5,546 15.3 15.5 12.1 18.3 9.2 9.4 20.5 20.4 12.6 23.9 13.0 28.8 20.2 11.2 REGION 6 Ingham Eaton Clinton 11,193 11,423 11,014 6.5 5.4 5.2 27.5 27.9 23.0 6,393 5,821 5,636 12.8 17.6 18.7 18.2 12.7 11.3 6,895 6,545 7,165 7,547 8,157 8,320 14.7 18.8 13.3 15.4 10.7 12.2 13.1 8.3 8.9 10.0 10.2 12.1 4,477 3,874 4,602 4,400 4,481 4,237 33.3 38.6 26.5 33.7 32.7 33.7 8.8 6.9 7.2 4.7 4.9 8.2 Region and County REGION 7C Roscommon Ogemaw Iosco Clare Gladwin Arenac & Over TABLE 4 . — Continued. 1970 1960 Per Cent of Families With Income - Per Cent of Families With Income - Median Family Income (d o lls .) Less than Poverty Lever $15,000 or More Median Family Income (d o lls .) Under $3,000 $10,000 $ Over REGION 10 Manistee Wexford Missaukee Benzie Gd. Traverse Kalkaska Leelanau Antrim Charlevoix Emmet 8,365 8,024 6,820 7,760 9,542 6,686 8,278 8,043 8,535 8,610 11.8 12.4 17.6 11.2 7.3 18.5 11.3 9.9 10.7 10.3 10.7 9.6 7.6 12.1 18.1 7.2 13.1 11.7 12.8 16.4 5,112 4,865 3,678 4,563 5,259 3,876 4,139 4,002 4,502 4,694 21.1 24.9 37.9 28.3 20.6 35.5 33.5 34.2 27.1 26.7 7.3 7.8 6.1 4.1 11.0 2.6 7.2 6.5 6.3 5.5 REGION 12A Iron Dickinson Marquette Alger 7,443 8,316 8,562 8,014 10.6 10.2 8.7 11.1 6.0 10.2 11.3 7.3 5,043 4,770 5,022 5,028 25.5 26.5 19.2 27.5 6.2 6.3 6.8 5.9 11,032 7.3 26.7 6,256 15.7 17.4 Region and County THE STATE The "poverty" definition is based upon an index of poverty income cutoff levels, adjusted by family size, sex of family head, number of children under 18 years of age, and farm and non-farm re s i­ dence. Poverty income cutoffs are revised annually to allow for changes in cost of living reflected in the consumer price index. In 1969, the average poverty threshhold for a nonfarm family of four headed by a male was $3,745. Source: U.S. Census of Population: 1960 and 1970, PC (1) C24, Table 44, p. 243, and PC (1) - C, Table 36, p. 185. TABLE 5 .—Percentage Distribution of Population by Residence Class for Regional Areas and the State of Michigan, 1960 and 1970. 1960 Per Cent of Population Which Was - 1970 Per Cent of Population Which Was - Urban^ Rural nonfarm Rural Farm Urban^ REGION 1 Wayne Monroe Washtenaw Livingston Oakland Macomb St. Clair 97.5 27.7 70.4 12.7 88.2 87.4 49.5 2.4 61.1 24.3 72.1 11.1 10.9 41.5 0.1 11.2 5.3 15.2 0.7 1.7 9.0 98.2 35.0 78.3 10.9 90.0 92.2 53.9 1.7 52.4 17.4 77.2 9.0 6.8 48.6 0.1 12.6 4.3 11.9 1.0 1.0 5.3 REGION 6 Ingham Eaton Cl inton 82.1 38.8 21.9 13.8 40.2 50.3 4.1 21.0 27.8 85.6 42.5 21.3 11.4 44.4 57.9 3.0 13.1 2^.8 REGION 7C Roscommon Ogemaw Iosco Clare Gladwin Arenac 0.0 0.0 0.0 0.0 0.0 0.0 96.5 74.4 91.3 86.1 68.7 72.0 3.5 25.6 8.7 13.9 31.3 28.0 0.0 0.0 41.9 16.2 0.0 0.0 84.2 83.8 50.7 68.8 83.2 85.1 15.8 16.2 7.4 15.0 16.8 14.9 REGION 10 Manistee Wexford 56.3 54.8 45.9 37.1 10.4 8.1 38.5 50.8 53.4 44.5 8.1 4.7 Region or County Rural nonfarm Rural Farm TABLE 5 . — Continued. 1970 Per Cent of Population Which Was - 1960 Per Cent of Population Which Was Urban^ Rural nonfarm Rural Farm 0.0 0.0 55.1 0.0 0.0 0.0 41.2 38.6 61.6 87.0 35.3 80.5 71.3 80.7 43.5 47.2 38.4 13.0 9.6 19.5 28.7 19.3 15.2 14.2 0.0 0.0 46.1 0.0 0.0 0.0 40.4 34.1 73.1 88.2 46.1 96.7 71.1 85.2 52.9 57.1 26.9 11,8 7.8 3.3 28.9 14.8 6.7 8.8 REGION 12A Iron Dickinson Marquette Alger 21.9 73.4 62.0 45.7 72.6 23.3 36.5 44.1 5.5 3.3 1.5 10.2 19.4 71.2 65.3 44.3 77.1 26.5 32.3 49.0 3.5 2.3 2.3 6.7 THE STATE 73.4 21.0 5.6 73.9 21.7 4.4 Region or County Missaukee Benzie Gd. Traverse Kalkaska Leelanau Antrim Charlevoix Ernnet ' Urban^ Rural nonfarm Rural Farm Computed as a residual. The urban population consists of a ll persons living in: (a) places of 2,500 inhabitants or more incorporated as c itie s , villages, bouroughs, and towns . . . , but excluding persons living in rural portions of extended c itie s ; (b) unincorporated places of 2,500 inhabitants or more; and (c) other te r r it o r y , incorporated or unincorporated, included in urbanized areas. Population not classified as urban is ru ra l. Source: U.S. Census o f P op ulation: Table 35, p. 184. 1960 and 1970, PC (1 ) - C24, Table 43, p. 242; PC (1 ) - C, TABLE 6 . — Selected Employment C h a ra c te ris tic s o f Employed Persons fo r Regional Study Areas and the S tate o f Michigan, 1960 and 1970. ____________________ 1960___________________ Region and County Per Cent in Manufacturing Industries Per Cent in Per Cent Working White Collar Outside County Occupations1 of Residence 1970___________________ Per Cent in Manufacutring Industries Per Cent in Per Cent Working White Collar Outside County Occupations1 of Residence REGION 1 Wayne Monroe Washtenaw Livingston Oakland Macomb St. C lair 39.8 43.1 23.3 31.7 41.2 46.6 33.0 41.8 31.8 50.5 35.3 49.4 41.2 36.8 6.3 35.2 9.1 30.7 39.8 47.6 13.1 37.5 41.7 23.1 34.5 34.1 42.3 35.6 44.4 34.8 56.3 41.8 57.8 47.2 39.9 14.5 46.8 12.1 41.1 33.4 42.4 20.7 REGION 6 Ingham Eaton Clinton 24.5 33.6 31.4 49.4 42.0 30.0 5.0 42.8 47.7 21.4 34.3 31.4 55.0 45.1 39.4 8.7 54.9 60.5 REGION 7C Roscommon Ogemaw Iosco Clare Gladwin Arenac 11.4 21.5 17.1 30.1 26.7 23.5 47.5 31.7 40.7 32.0 32.9 30.7 11.1 10.7 3.5 18.2 31.8 23.5 15.2 20.4 14.3 28.2 40.4 33.9 45.6 35.8 45.2 37.8 33.5 29.5 11.0 15.3 7.2 25.0 39.1 32.9 TABLE 6 . — Continued. 1960 Region and County Per Cent in Manufacturing Industries Per Cent in White Collar Occupations^ 1970 Per Cent Working Outside County of Residence Per Cent in Manufacturing Industries Per Cent in White Collar Occupations' Per Cent Working Outside County of Residence REGION 10 Manistee Wexford Missaukee Benzie Gd. Traverse Kalkaska Leelanau Antrim Charlevoix Emmet 37.0 29.9 18.8 20.3 19.0 29.5 17.2 30.3 27.0 13.2 33.0 39.3 27.7 32.9 43.2 36.4 33.6 29.7 33.5 42.0 5.9 8.4 24.9 13.6 4.6 25.2 38.0 15.7 11.3 5.5 39.5 30.4 22.0 20.9 17.7 27.2 15.9 40.6 31.5 15.5 33.5 42.3 35.4 35.1 49.8 38.7 39.5 32.7 38.6 45.7 7.9 5.4 38.6 16.6 5.1 35.2 37.2 19.7 14.5 7.6 REGION 12A Iron Dickinson Marquette Alger 5.5 27.2 14.3 35.3 33.1 39.1 36.4 33.4 4.5 10.3 2.4 8.0 8.9 21.8 6.3 35.8 40.8 43.3 44.8 33.9 15.2 10.0 4.6 9.0 THE STATE 38.0 40.1 13.9 35.9 44.9 19.0 1 Includes Professional, Managerial {except farm), c le r ic a l, and sales workers. Source: U.S. Census o f P opulation: Table 36, p. 185. 1960 and 1970, PC (1 ) - C24, Table 4 4 , p. 243; PC (1 ) - C, 82 change fo r a l l f i v e study areas between 1960 and 1970. Table 4 shows median fam ily incomes f o r counties w ith in the study regions, as well as a d is t r ib u t io n o f the percentage o f fa m ilie s in low and high income classes. Table 5 gives a percentage d is t r ib u t io n o f regional popu­ la tio n s by class o f residence (urban, ru ral non-farm, and ru ra l farm) f o r 1960 and 1970. F in a l l y , Table 6 c ite s selected employment charac­ t e r i s t i c s of the populations in the various study regions. The Sample Design There were two major o bjectives fo r th is study: (1) to estimate the to ta l volume o f re crea tio n al boating undertaken in the s ta te by Michigan re s id e n ts , and i t s geographical d is t r i b u t i o n ; and (2) to examine regional v a ria tio n s in re crea tio n al boating p a r tic ip a tio n patterns. In approaching these two major o b je c tiv e s , one major assump­ tio n was made; namely, th a t the major re crea tio n al boating population in the s ta te consists o f households which have registered powered w a te rc ra ft w ith the Michigan Secretary o f State as required by sta te s ta tu te . This assumption was made a f t e r considering the major com­ ponents of the system. The Sample Universe There appear to be at le a s t four major segments in the Michigan recreational boating system. That i s , re crea tio n al boating a c t i v i t y is believed to be generated by four sub-populations: (1) recrea tio n al boating undertaken in the state by re g istered boat owners who are Michigan residents; (2) re crea tio n al boating undertaken by Michigan residents who own unregistered w a te rc ra ft (rowboats, canoes, unpowered 83 sailboats and other c r a f t ) ; (3) boating done in Michigan by residents of other states who have powered w a te rc ra ft registered with the Michigan Secretary o f State; and (4) boating done in Michigan by non-residents who transport unregistered w ate rcraft into the s ta te . In 1968, there were 438,017 w ate rcraft registered in the records of the Division o f Vehicle and W atercraft Records, Michigan Department of S tate. Of th is t o t a l , an estimated 426,057 were owned by residents of Michigan. Another 11,960 w ate rcraft were registered by residents o f other s t a t e s J for this study. This population was considered as the sample universe While i t was recognized th a t th is d e lim ita tio n meant th at there would be "leakages" o f unknown magnitude re su ltin g from ignoring the other three components in the system, i t was f e l t th at registered w ate rcraft owners accounted fo r most o f the recreational boating in the sta te. Also, i t appeared extremely d i f f i c u l t to obtain an adequate sample o f w ate rcraft users in the other elements of the system. The Sample Unit The sample u n it selected fo r th is study consisted o f in d i­ vidual w ate rcraft. In order to estimate boating use, i t was f e l t that use data should be gathered fo r sp e cific sampled w a te rc ra ft. Accordingly, respondents to the recreational boating survey were requested to e s t i ­ mate the number o f occasions o f use fo r a single w a te rc ra ft, id e n tifie d by i t s Michigan r e g is tra tio n number. i Unpublished records, Division of Vehicle and Watercraft Records, Michigan Department o f State, 1968. 84 The Sample Frame The sample frame consisted o f a computer tape l i s t i n g o f a l l 438,017 registered boat owners in the sta te o f Michigan. A copy of th is tape was furnished on a loan basis by the Michigan Secretary of S ta te 's O ffic e . The contents of th is tape were transferred onto computer tapes a t the Michigan State Computer Laboratory. Drawing o f Sample A s t r a t i f i e d random sampling procedure was used in th is study. A review of previous research o f recreational boating was f i r s t made. A 1965 survey completed by Arthur D. L i t t l e , Inc., fo r the Waterways D ivis io n , Michigan Department o f Conservation^ also employed as s t r a t i ­ fie d sampling procedure. The 1965 survey s t r a t i f i e d registered water­ c r a f t into two length classes: {1) w a te rc ra ft 20 fe e t and less to ta l length, and (2) w ate rcraft greater than 20 fe e t to ta l length. A to ta l of 398,902 recreational w a te rc ra ft were registered in the sta te a t the time o f the 1965 survey: 377,763 in the 20 fe e t or less class, and 21,139 in the over 20 f e e t class. According to the 1965 survey, w ate rcraft were s t r a t i f i e d into these two length classes because " . . . not give . . . completely random sampling would a good response from the boats over 20 f e e t . " However, the researchers note also th a t sample size ". . . was la r g e ly d e te rmined by the funds a v a ila b le . . . . " 2 Mail questionnaires were f i n a l l y mailed to owners o f 2.5 per cent o f the registered w a te rc ra ft 20 fe e t ^Transportation P red ictive Procedures, lo c . c i t . , 1966. 2I b i d . , p. 24. 85 or under, and to the owners o f 20 per cent of the boats over 20 f e e t. A to ta l of 9,444 questionnaires were mailed to owners of the smaller w a te rc ra ft, and 4,226 to owners o f la rg e r w a te rc ra ft f o r a grand t o ta l o f 13,670. A to ta l o f 3,643 usable responses were received from owners o f w a te rc ra ft in the 20 fe e t or less class, and 1,575 returns were received from boat owners in the over 20 fe e t cla ss . O v e ra ll, returns to the mailed questionnaire average about 38.2 per cent. In the present study, an attempt was made to secure data from the 1965 survey on boating p a rtic ip a tio n rates in order to analyze variance in boat use as a basis fo r determining sample s iz e . However, given time lim ita tio n s and scarce research funds, such analysis could not be completed in time fo r the survey. In the 1965 survey, 13,670 questionnaires were mailed, and 5,218 usable responses were received (a 38.2 per cent re tu r n ). The present study was undertaken with the assumption th a t a s im ila r ra te o f response could be obtained in 1968. Based upon the response received in 1965, i t was decided to t r y to secure about 8,800 usable responses in the 1968 survey. c r a f t were again s t r a t i f i e d in to two length classes: and greater than 20 f e e t . Water­ 20 fe e t or les s, In 1968, there were 413,949 registered water­ c r a f t in the 20 fe e t and under length category, and 24,068 registered c r a f t in the over 20 fe e t class. In order to obtain approximately 8,800 usable responses, a decision was made to sample 5 per cent of the w ate rcraft in the 20 fe e t and less c la ss , and 10 per cent o f the w a te rcraft in the over 20 fe e t class. Thus the sample size was d e te r­ mined by m ultiplying these factors by the number o f registered boats in the two length classes: 86 .05 (413,949) = .10 (24,068) = Total Sample 20,697 2,406 23,103 A systematic sampling procedure was used in a c tu a lly drawing the sample. The sample was drawn through use o f the CDC 3600 computer a t Michigan State U n iv e rs ity . A computer tape containing the e n t ir e l i s t o f registered w a te rc ra ft owners in the s ta te was u t i l i z e d . In order to draw the desired number o f sample w a te rc ra ft from each length class, a sampling in te rv a l was computed. The computer was then pro­ grammed to select every twentieth w a te rc ra ft 20 fe e t or less in length, and every tenth w a te rc ra ft over 20 fe e t in length fo r each county. Computer programming errors reduced the number o f w ate rcraft f i n a l l y selected to 21,764. Names and addresses o f owners of the registered boats selected were printed on self-adhesive address la b e ls . Each label contained the name and address o f the w a te rc ra ft owner, the re g is tra tio n number o f the boat selected, and the length o f the boat. The Mail Questionnaire Early in the study, a decision was made to develop a s e l f ­ administered mail questionnaire fo r use in the c o lle c tio n o f data on recreational boating p a rtic ip a tio n in the s ta te . I n i t i a l d ra fts o f the questionnaire were prepared in e a rly October, 1968.^ A fte r a f i r s t d r a f t of the instrument had been prepared, the questionnaire was subjected to a series o f revisions and p re -te s ts . A series o f meetings were held with s t a f f of the Waterways Division and Recreation H h e questionnaire used in th is study is exhibited in Appendix A. 87 Resource Planning D ivis io n , Michigan Department of Natural Resources. Several d ra fts o f the questionnaire were prepared during these con­ su ltatio n s. Following th is series o f revisio ns, the questionnaire was mimeographed, and was pretested under a cover l e t t e r through d i s t r i ­ bution to 50 known registered boat owners among the s ta ffs of the Michigan Department o f Natural Resources, the Natural Resources D ivis io n , Michigan State U n iv e rs ity , and St. Lawrence H o sp ital, Lansing, Michigan. The p re -te s t disclosed several ambiguous questions, and a f in a l d r a f t o f the questionnaire was prepared, incorporating changes suggested by p re -te s t versions o f the instrument completed and returned by respond­ ents. A f in a l d r a f t o f the questionnaire was prepared a t this stage. The f i r s t page of the questionnaire consisted o f a cover l e t t e r w ritte n by the D irecto r o f the Waterways D ivisio n , Michigan Department of Natural Resources. On the reverse side of the cover l e t t e r , an o u tlin e map of Michigan was provided showing county boundaries, and principal highway routes in the s ta te . The map was provided in order to as sis t respondents with answering questions pertaining to the county location of recreational boating undertaken. The cover l e t t e r , which also gave the mailing address o f respondents, was perforated a t the margin so th at persons completing the questionnaire could te a r o f f the f i r s t page in order to insure an anonymous response. There were six principal categories of questions included in the mail questionnaire: (1) information on sp ecification s and type of w atercraft sampled; (2) place of storage o f w ate rcraft during 88 boating season; (3) tra n s p o rta tio n o f w a te rc ra ft during study year; (4) use o f re crea tio n al w a te rc ra ft during study y e a r--c a le n d a r 1968; (5) number o f (re g is te re d and unregistered) w a te rc ra ft owned by respondents; and (6) fam ily c h a ra c te r is tic s o f respondents. An in s tru c tio n s block was p rinted a t the top o f page 3. These in s tru ctio n s requested respondents to answer questions 1-13 fo r the s p e c ific w a te rc ra ft drawn in the sample. That i s , respondents were asked to provide inform ation asked fo r in these questions fo r the w a te rc ra ft bearing the Michigan r e g is t r a tio n number printed in the address label on the cover l e t t e r . M ailing Procedures The q uestionnaire, in f in a l form, was printed and folded by the U n iv e rs ity P rin tin g Service, Michigan S tate U n iv e rs ity . In order to f a c i l i t a t e the m a ilin g , self-ad hesive address la b e ls , printed by the Michigan S tate U n iv e rs ity Computer Center a t the time o f sampling, were a f fix e d to the cover l e t t e r o f the questionnaire. Approximately 80 per cent o f the address lab els did not have postal zip codes printed on them. Since postal zip codes are required by the United States Postal Service f o r bulk m a ilin g , a l l missing zip codes had to be checked in a zip-code d ire c to ry and posted on labels by hand. Self-adhesive address labels were attached to the l a t t e r o f transm ital in a pre-marked box a t the upper le ft-h a n d corner o f the page. Folded questionnaires were then placed in window envelopes bearing the return address o f the Michigan Waterways Commission. postage-free return envelope was also included with each mailed A 89 questionnaire. The questionnaire was mailed during the l a s t two weeks of A p ri1, 1969. Response to the Questionnaire Completed questionnaires were returned to the Waterways Com­ mission O ffic e in Lansing. The returned questionnaires were picked up a t the Commission o ffic e s by s t a f f o f the Recreation Research and Planning U nit a t Michigan S tate U n iv e rs ity . A to ta l o f 6,800 questionnaires were completed and returned by sampled w a te rc ra ft owners. Of th is t o t a l , 250 responses had to be discarded because o f a decreased owner, incomplete information provided, or sale or disposal o f the sampled w a te rc ra ft during the study y e ar. A to ta l o f 5,647 questionnaires were retained f o r s t a t i s t i c a l an a ly sis. Table 7 shows the d is t r ib u t io n o f returned questionnaires by boatlength class. A d e ta ile d breakdown o f numbers o f questionnaires used fo r s t a t i s t i c a l analysis is given in the Appendix section fo r each Michigan County.^ Non-Respondent Interviews A large sample size (23,103) was established fo r th is study as i t was an tic ip a te d th a t no follow -up procedures would be employed. technique fo r increasing the ra te o f response on mail surveys is to send out a series of reminders to non-respondents on predetermined dates follow ing the i n i t i a l mailing o f the survey questionnaire. ^See Appendix B. One 90 TABLE 7 . — Number o f Questionnaires M ailed, and Number of Responses Retained fo r S t a t i s t i c a l Analysis, by Boat-Length Class. Number of Question­ naires Retained fo r Analysis Number of Michigan Registered Watercraft December 1968 Boat Length Class Number o f Ques­ tionnaires Mailed April-May 1969 Number Per Cent o f Total Registered 20 Feet or Less 413,949 19,468 5,049 1.22 20 Feet or Above 24,068 2,296 598 2.49 438,017 21,764 5,647 1.29 Totals Source: Michigan Secretary o f State, "Size and Type o f Registered Boats in Michigan Counties," Unpublished Report, 1968. In s u ffic ie n t research funds were a v a ila b le fo r th is purpose during the study. However, an attempt was made to assess the r e l i a b i l i t y o f responses obtained in the returned questionnaires. Accordingly, a series o f respondent and non-respondent interviews were conducted following mailing o f the survey instrument. Follow-up procedures were employed in three pre-selected control counties in Michigan: Ingham, Grand Traverse, and Leelanau. In itia l mail questionnaires sent to registered boat owners in these three counties were coded on the la s t page, including the name and address o f the sampled boat owner, and the Michigan re g is tra tio n number o f the sampled w a te rc ra ft. A master check-1ist o f a l l sampled w a te rc ra ft in the three control counties was prepared. As completed questionnaires 91 were returned, they were compared with th is master c h e c k lis t. Thus, survey non-respondents could be id e n tifie d following the c u t - o f f date established fo r return o f the questionnaire. In order to assess the e ffe c ts o f a mail follow-up on the ra te of response obtained, two follow-up post cards were also sent to sampled w a te rc ra ft owners in the three counties. was mailed on June 1, 1969, and the second on June 15, 1969. the response to the mail questionnaire was 26 sample. The f i r s t reminder O v e ra ll, per cent fo r the e n t ir e A somewhat higher ra te o f response was obtained in the three control counties, however. Table 8 summarizes the ra te o f response to the mail survey re alized in the three control counties. TABLE 8 . — Questionnaires Mailed and Returned, and Percentage Response fo r Survey Control Counties Number Registered Watercraft December 1968 Survey County Number of Questionnaires Ma i 1ed April-May 1969 Number of Questionnaires Completed and Returned Per Cent Response 13,351 638 216 33.9 Grand Traverse 4,845 226 64 28.3 Leelanau 1,897 89 35 39.3 20,093 953 315 33.1 Ingham Totals Source: "Size and Type o f Registered Boats in Michigan Counties," 1968. In the three te s t counties, a l l sampled w ate rcraft owners who had not returned completed questionnaires six weeks following the i n i t i a l mailing were c la s s ifie d as non-respondents. A ll non-respondents in these 92 three counties were lis t e d on a ch e ck list and assigned a number. ch ecklist was also developed fo r a l l mail survey respondents. A Using a ta b le o f random numbers, 200 names were chosen from the respondent and non-respondent checklists f o r follow-up interview s. A to ta l of 50 survey respondents were chosen in th is fashion (25 from Ingham County, and 25 from Grand Traverse and Leelanau counties combined). The same procedure was u t i l i z e d in selecting non-respondents: a to ta l o f 150 names were drawn from the non-respondent ch e ck list (75 from Ingham county, and 75 from Grand Traverse and Leelanau counties combined). A la rg e r number o f non-respondents than respondents was selected fo r interview as i t was f e l t th a t the p o s s ib ilit y of having s ig n ific a n t differences in information provided in the survey between respondents and non-respondents was a problem which should be in v e s ti­ gated. Personal interviews we^e conducted among a to ta l o f 85 survey non-respondents and 35 respondents during July and August o f 1969. The interview schedule used consisted of the mail questionnaire in the same form as was d is trib u te d in the i n i t i a l m ailing. A to ta l o f 13 respondent and 34 non-respondent interviews were completed in Ingham county. In Grand Traverse and Leelanau counties (combined), a to ta l o f 22 respondent and 51 non-respondent interviews were conducted. All interviews were completed by s t a f f o f the Recreation Research and Planning U n it, Department o f Park and Recreation Resources, Michigan State U n iversity. Information collected in th is series o f interviews was coded and key punched. These data were subjected to s t a t i s t i c a l tes tin g in 93 order to determine i f s ig n ific a n t differences existed between i n f o r ­ mation provided by survey non-respondents and respondents. On the basis o f a chi square analysis completed in 1970, i t was concluded th at (in the three t e s t counties): 1. There is no s ig n ific a n t d ifferen ce in the educational level o f respondents and non-respondents to the 1968 recreational boating survey. 2. There is no s ig n if ic a n t d ifferen ce in fam ily incomes of respondents and non-respondents. 3. There is no s ig n ific a n t d ifference in the amount o f recre­ atio nal p a rtic ip a tio n by respondents and non-respondents to the 1968 boating survey. 4. There appears to be no real d iffe ren c e in the geographical d is trib u tio n o f recreational p a rtic ip a tio n by respondents and non-respondents ". . . although a small sample size prevents the drawing o f a f in a l conclusion in th is regard."^ Data Processing and Coding A to ta l 5,647 questionnaires returned by respondents were retained fo r s t a t is t i c a l analysis. Information from the questionnaires was transferred d ir e c t ly onto s p e c ia lly printed optical scan forms, prepared in consultation with the Evaluation Services O ffic e , Michigan ^Allison Jean Igo, "An Analysis o f the V a lid it y o f Mail Surveys fo r Use in Recreation Research" {unpublished Masters Thesis, Michigan State U n iv e rs ity , 1971), p. 91. State U n ive rsity .^ A fte r coding was completed, optical scan sheets were processed by U niversity Evaluation Services. were produced d ir e c t ly from the o ptical scan forms. IBM punch cards A complete p r i n t ­ out o f en tries made on punch cards was obtained fo r each county in the s ta te . Printout information was cross referenced to the o rig in a l questionnaires fo r each county in order to correct coding errors. The corrected IBM punch cards were then processed at the Michigan State U niversity Computer Laboratory. The data from a l l cards was transferred to magnetic computer tapes fo r s t a t i s t i c a l analysis. ^Optical scan sheets u t il i z e d in th is study are exhibited in Appendix C. CHAPTER IV RESULTS OF THE INVESTIGATION This chapter is devoted to an analysis and presentation of se­ lected data and information collected in the 1968 survey of registered boat owners in Michigan. Frequency o f boating p a rtic ip a tio n information was provided by each respondent to the survey in questions 10 and 12 in the mail questionnaire.^ Sampled w atercraft owners were asked to provide estimates o f the number of boat days ( a c t i v i t y occasions) spent on: (a) Great Lakes and connecting waters, and (b) inland lakes and streams during the previous boating season, and the Michigan county where such boating a c t i v i t y occurred. Geographical D is trib u tio n o f Boating P a rtic ip a tio n In question 10, w ate rcraft owners were asked to . . name the three Great Lakes or connecting waters counties where this boat was used during the past boating season." Respondents were instructed to count each part day spent boating as a f u l l day. Total boating days as pro­ vided by respondents, then, is a c tu a lly an estimate of the number of boating a c t i v i t y occasions. The preceeding question (number 9) defined Great Lakes and connecting waters. For purposes o f the study, Great Lakes and connecting waters were defined to include Lake Huron, Lake E rie, Lake Superior, Lake Michigan, Lake St. C l a i r , the S t. Mary's ^See Appendix A. 95 96 River, the St. C la ir River, and the D e tro it River. To as sis t respond­ ents in naming the Michigan county where boating a c t i v i t y was undertaken, a map was provided in the questionnaire on page 2. The map showed the boundaries of a l l Michigan counties, and the principal highways in the state. Question 12 requested boating p a rtic ip a tio n information fo r a c t i v i t y undertaken on inland lakes and streams in the s ta te . c a lly , respondents were asked to S p e c ifi­ . . name the three Michigan counties where th is boat was used most on inland lakes and streams during the past boating season. Give the number o f days th at th is boat was a c tu a lly in the water under power or sa il in each of these counties." To as sis t respondents in answering the question, one lin e in the boxes provided in both questions 10 and 12 was reserved as an example. Based upon information obtained in questions 10 and 12, to ta l boating a c t i v i t y estimates were made fo r each county in Michigan. Boating a c t i v i t y estimates were made fo r o rig in and destination counties. An o rig in county is defined as the county where the sampled w atercraft owner makes his permanent residence. Destination counties, on the other hand, are those counties where recreational boating a c t i v i t y ac tu a lly took place. Thus, estimates o f recreational boating fo r an o rig in county consists o f a l l boating a c t i v i t y generated by the sampled w atercraft owners who resided in th at county a t the time o f the survey. Recreational boating a t destination counties consists of estimated a c t i v i ­ ty occasions undertaken by sampled w atercraft owners from a p a rtic u la r county in a l l other counties o f the s ta te . Table 9 gives a tabular summary of estimated to ta l boating a c t i v i t y occasions fo r each Michigan 97 TABLE 9 . --Estimated Population, Boat Days, Sample S ize, and Calculated Boat-Use Periods Per 1,000 Population, by Michigan Origin County, 1968. (2) Estimated Total Boat Days 1968 Season (2*1) No. Boat Days Per 1,000 Pop. Sample Size 1-Alcona 5.6 16,120 2,878.57 N= 18 2-Alger 8 .0 30,517 3,814.62 N= 3-Allegan 60.0 114,676 1,911.26 N= 57 4-Alpena 30.4 108,641 3,573.71 N= 39 5-Antrim 9.8 87,800 8,959.18 N= 36 6-Arenac 9.5 12,037 1,267.05 it z: 7-Baraga 7.7 28,376 3,685.19 N= 11 31.4 135,501 4,315.31 N= 57 114.7 137,510 1 ,198.86 N= 71 7.5 40,793 5,439.06 N= 18 11-Berrien 169.4 222,569 1,313.86 N=114 12-Branch 35.7 113,403 3,176.55 it CT> to County (1) Total Population 12/31/68 {000} 13-Calhoun 146.0 270,077 1,849.84 N=106 14-Cass 37.8 172,364 4,559.89 N= 66 15-Charlevoix 16.0 59,186 3,699.12 N= 34 16-Cheboygan 14.4 78,298 5,437.36 N= 28 17-Chippewa 35.3 98,731 2,796.91 N= 26 18-Clare 12.9 17,263 1,338.21 N= 21 19-C1inton 45.1 63,264 1,402.74 N= 33 5.7 17,358 3,045.26 N= 21-Delta 33.2 57,657 1,736.65 N= 34 22-Dickinson 23.9 44,603 1,866.23 N= 25 23-Eaton 58.5 89,204 1,524.85 N= 62 2 4 -Emmet 16.8 76,978 4,582.02 N= 38 442.4 590,340 1,334.40 N=317 26-Gladwin 10.6 21,511 2,029.33 N= 16 27-Gogebic 15.8 25,892 1,307.67 N= 21 9 - Bay 10-Benzie 20-Crawford 25-6ennessee o 8-Barry 9 6 98 TABLE 9 . — C ontinued. County (1) Total Population 12/31/68 (000) (2) Estimated Total Boat Days 1968 Season (2 v l) No. Boat Days Per 1,000 Pop. Sample Size 28-Gd. Traverse 38.3 186,758 4,876.18 N= 64 2 9 -G ratio t 38.9 56,709 1,457.81 N= 16 3 0 -H ills d a le 35.0 98,342 2,809.77 N= 29 31-Houghton 33.0 64,972 1,968.84 N= 35 32-Huron 34.0 22,844 671.88 N= 18 254.1 360,760 1,419.75 N=222 3 4 - Ionia 44.6 55,056 1 ,234.43 N= 38 3 5 - Iosco 22.7 74,966 3,302.46 N= 25 3 6 -Iron 14.1 41,389 2,935.39 N= 22 37 -Is a b e lla 37.7 31,754 842.28 N= 30 38-Jackson 141.0 256,302 1,817.74 N=121 3 9 -Kalamazoo 190.6 211,641 1,110.39 N=170 4.9 -0 -b 3 3 - Ingham 40-Kalkaska -0 -b N- 5 406.7 686,210 1,687.26 42-Keewenaw 2.2 2,194 997.27 43-Lake 4.5 4,559 1,013.11 N= 11 49.4 31,318 633.96 N= 28 9.8 48,400 4,938.77 N= 35 46-Lenawee 81.5 135,996 1,668.66 N= 63 47-Livingston 46.6 98,301 2,109.46 N= 57 4 8 -Luce 6.9 12,432 1,801.73 N= 11 49-Mackinac 9.6 61,726 6,429.79 N= 29 596.3 724,501 1,214.99 N=231 51-Manistee 19.5 71,766 3,680.30 N= 17 52-Marquette 62.9 102,553 1 ,630.41 N= 51 53-Mason 21.8 52,267 2,397.56 N= 23 54-Mecosta 23.6 40,443 1,713.68 N= 25 55-Menominee 22.9 25,622 1,118.86 N= 14 56-Midland 59.6 90,369 1,516.25 N= 60 . 41-Kent 44-Lapeer 45-Leelanau 50-Macomb N=270 N= 4 99 TABLE 9 . — C ontinued. County 57-Missaukee 58-Monroe 59-Montcalm 60-Montmorency 61-Muskegon 62-Newyago 63-0akland 64-0ceana 65-0gemaw 66-0ntonagon 67-0sceola 68-0scoda 69-0tsego 70-0ttawa 71-Presque Is le 72-Roscommon 73-Saginaw 74-Sanilac 75-Schoolcraft 76-Shiawassee 77-St. C la ir 78-St. Joseph 79-Tuscola 80-Van Buren 81-Washtenaw 82-Wayne 83-Wexford TOTALS MEAN (1) Total Population 12/31/68 (000) 6.0 114.7 41.0 4.4 157.3 25.8 851.2 16.4 9.4 10.7 14.5 4 .0 9.3 117.1 12.1 8 .0 218.3 33.9 7.6 61.1 115.7 45.3 47.3 55.3 210.8 2,727.3 18.6 8,663.9 104.38 (2) Estimated Total Boat Days 1968 Season 7,386 172,138 73,933 24,609 291,770 75,895 1,069,379 29,445 38,112 14,279 4,154 7,155 17,319 242,003 39,953 81,295 220,352 25,337 18,688 68,310 228,174 159,337 30,587 121,711 178,273 2,023,200 43,219 11,686,832 140,805.20 (2*1) No. Boat Days Per 1,000 Pop. 1,231.00 1,500.76 1,803.24 5,592.95 1,854.86 2,941.66 1,256.31 1,795.42 4,054.46 1,334.48 286.48 1,788.75 1,862.25 2,066.63 3,301.90 10,161.87 1,009.39 747.40 2,458.94 1,118.00 1 ,972.11 3,517.37 646.65 2,200.92 845.69 741.83 2,323.60 ----- 2,403.10 Sample Size N= 8 N= 60 N= 41 ' N= 13 N=118 N= 36 N=489 N- 17 N= 23 N= 22 N= 21 N= 6 N= 10 N=123 N= 14 N= 41 N=155 N= 18 N= 13 N= 50 N= 83 N= 84 N= 30 N= 59 N=125 N=638 N= 23 5,379 64.81 a"Sales Management," Survey of Buying Power, Vol. 102, No. 12 (June 10, 1969), Section D, pp. 88-95. ^The 5 respondents to the survey from Kalkaska County a l l indicated that no boating was done during 1968 with sampled w a te rc ra ft. 100 county, as well as an estimated ra te o f boating p a rtic ip a tio n per 1,000 county population fo r the study year (1968). In preparing these estimates, the data provided by respondents in questions 10 and 12 was u t i l i z e d . The to ta l boat days figures in the l e f t hand column were f i r s t to ta lle d fo r each d estination county cited by respondents from a p a r tic u la r county o f o rig in (residence). This operation was completed by means o f a computer program developed a t the Michigan State U niversity Computer Laboratory. An o r ig in - destination matrix was produced from th is operation, consisting of aggregated estimates o f boating a c t i v i t y undertaken by a l l sampled w a te rc ra ft owners in destin ation counties. The 83 x 83 matrix thus produced was used as a basis fo r obtaining to ta l boating a c t i v i t y estimates fo r each county in the s ta te . Sample data in the o rig in -d e s tin a tio n matrix were expanded to give an estimate o f to ta l boating a c t i v i t y undertaken. Expansion factors were calculated fo r each county based upon the r a t io between the to ta l number o f registered w ate rcraft per county and the actual number o f sample w a te rc ra ft owners who responded to the mail survey in 1968.^ Boating a c t i v i t y occasions by sampled w a te rc ra ft owners in the o r ig in destination matrix were next m u ltip lie d by the calculated expansion ? fa c to r fo r the county involved. The data in Table 9 indicate t h a t , on the basis o f information supplied by respondents to th is survey, the greatest amount o f to ta l ^Expansion factors calculated fo r each county are shown in Appendix C. 2 A matrix showing expanded boating a c t i v i t y days by Michigan o rig in and destination counties is shown in Appendix D. 101 boating a c t i v i t y was generated in counties where to ta l population was highest, and where the number o f to ta l registered w ate rcraft owners resided. Considerable v a ria tio n appears to e x is t among counties of the s ta te , however. The top 10 o rig in counties in the state (on the basis o f to ta l boating a c t i v i t y generated) were: Wayne, Oakland, Macomb, Kent, Gennesee, Ingham, Muskegon, Calhoun, Jackson and Ottawa. While these counties rank high in terms o f estimated to ta l boating a c t i v i t y , population p a rtic ip a tio n rates appear to be somewhat lower. In Wayne County, fo r example, expanded to ta l boating a c t i v i t y occasions to ta lle d more than 2 m illio n boat days fo r 1968. However, the estimated boating p a rtic ip a tio n ra te fo r the county population was computed a t only 741.8 boat days per 1,000 county population. By way of co n tras t, a number o f counties in the northern portion o f the Lower Peninsula, while generating a r e l a t i v e l y small volume o f to ta l boating a c t i v i t y , a t the same time e x h ib it high boating p a rtic ip a tio n rates. In Montmorency county, fo r example, there was an estimated population of 4.4 thousand persons in 1968 (see Table 9 ) , and the recreational boating survey results indicate th at during the survey year Montmorency county residents had a boating p a rtic ip a tio n rate o f 5.5 thousand a c t i v i t y occasions per 1,000 county population. Mackinac, Antrim, Roscommon, Leelanau, Grand Traverse, Benzie, Cass, Cheboygan, Emmet, Ogemaw, and Barry counties also show r e l a t i v e ly high levels of boating p a rtic ip a tio n . Each o f these counties had an estimated boating p a rtic ip a tio n ra te greater than 4,000 occasions per 1,000 county population fo r the study year. 102 A n aly tic al Procedures In analyzing the regional v a ria tio n in re creatio n al boating p a rtic ip a tio n in Michigan, le a s t squares techniques were used to estimate two types o f equations. Equation type 1 is designed to analyze ind ividu al v a ria tio n in boating p a r tic ip a tio n w ith in f i v e planning and development regions, and the s ta te of Michigan as a whole. type 2 Equation examines v a ria tio n in the ra te o f boating p a r t ic ip a tio n by county populations. The second type of equation w il l be estimated f o r the State o f Michigan as a whole, and fo r the t h i r t y Michigan counties showing: (a) the highest aggregate le v e ls o f to ta l boating a c t i v i t y , and (b) the lowest aggregate le v e ls o f t o ta l boating a c t i v i t y . In a d d itio n , boating p a r tic ip a tio n w i l l be analyzed by using frequency data on socio-economic c h a ra c te ris tic s o f boat owners, c h a ra c te ris tic s o f owned w a te r c r a ft, place o f storage o f w a te rc ra ft during the boating season, and tra n s p o rta tio n o f w a te rc ra ft. Modified U s er-C h ara cte ristics Model As was pointed out in Chapter I I , a number o f studies have shown th a t the demand f o r most goods and services is re la te d to the tastes and preference o f consumers. Demand fo r outdoor re c re a tio n , fo r example, has been shown to be a p a r t ia l function o f socioeconomic status, including occupation, education, fam ily composition, age, sex, place o f residence, and income. Certain socioeconomic c h a ra c te ris tic s of w a te rc ra ft owners were obtained in the 1968 survey. Questions 15-20 (pages 6 and 7) in the mail questionnaire s o l i c ­ ite d information from respondents on socioeconomic status. In addition 103 to these fa c to r s , information was obtained from respondents on number of w a te rc r a ft owned, power system o f w a t e r c r a f t, horsepower o f motor(s) used, place o f storage o f w a te rc ra ft during the boating season, and trans p o rta tio n o f w a te rc ra ft: questionnaire. questions 1, 2, 4 , 6, and 14 in the mail Also, information on w a te rc ra ft length was a v a ila b le fo r each sampled boat from the records supplied by the Michigan Secretary o f S ta te 's O ffic e . The s p e c ific form of the model to be estimated is as fo llo w s : 1 = a + b-, where: i = 1, 2, j = 1, 2, and: yj is the + b2 x2 j + * * * + b38 x38j + uj . . .3 8 . . . N j t h observation o f the dependent v a ria b le . x.jj is the j t h observation of the it h independent v a ria b le . a is the constant term b- is the c o e f f ic ie n t o f the i t h independent v a ria b le uj is the j t h observation o f a random e rro r term, where ( j = 1 , 2, . . . NJ. - The uj are assumed to be independent, and come from a normal d is t r ib u tio n with zero mean and uniform variance Model S p e c ific a tio n The dependent v a ria b le ( y . ) is the number of re creatio n boating a c t i v i t y occasions (boat days) undertaken by sampled w a te rc ra ft users during calendar year 1968. The number o f boating a c t i v i t y occasions Whe general form o f the regression model sp e cifie d here c lo se ly follows th a t o u tlin ed in L. V. Manderscheid, An Introduction to S t a t i s ­ t i c a l Hypothesis T es tin g , Ag. Econ, Mimeo. 867— Revised (East Lansing, Michigan: Department o f A g ric u ltu ra l Economics, Michigan State Uni­ v e r s ity , February, 1964), pp. 17-23. 104 fo r each sampled w ate rcraft was obtained from questions 10 and 12 in the mail questionnaire. The independent variables (x..) are specified in d e ta il as follows: Power system o f w ate rcraft (x ^ -x ^ ) .- -R e la te to the type of power system employed in each sampled w a te rc ra ft. were entered as "zero-one" (dummy) variables. These variables The v a ria b le x-j refers to a w ate rcraft having an outboard motor; Xg was a sampled w a te rcraft which was a sailb o at with motor; denotes a w a te rc ra ft having an inboard motor; and x^ was a c la s s ific a t io n assigned to a w ate rcraft having an inboard motor with outboard d riv e . Each sampled w a te rc ra ft was thus placed in one of these c la s s ific a tio n s . Each o f the four variables was assigned a value o f one whenever a sampled w atercraft fe ll into th a t p a r tic u la r c la s s if ic a t io n ; otherwise, a value o f zero was assigned. Horsepower ra tin g o f w a te rc ra ft (X g ) .— Each respondent to the mail survey was asked to give the horsepower ra tin g o f the primary motor used on the sampled w a te rc ra ft. Horsepower ra tin g was then entered as a continuous v a ria b le . Place o f storage o f w ate rcraft (Xg - x ^ ) . — Each sampled water­ c r a ft owner was asked to give the usual place o f storage o f his water­ c r a f t during the boating season. Respondents were asked to check one o f several response categories (see question 4 in the questionnaire). The response categories were: Xg At my permanent home, which is not on a lake or r i v e r . x^ At waterfrontage located a t my permanent home l o t . 105 Xg At a commercial marina-berth. Xg At a summer cottage. x ^0 At a p u b lic ly owned marina. At a boat or yacht club. The place o f storage c la s s ific a tio n s were entered as "zeroone" v a ria b les . A value of one was assigned f o r a p a r tic u la r v a ria b le when respondents checked th a t c la s s if ic a t io n category and zero otherwise. Boat Transportation ( x ^ ) * — Each respondent was asked to ind icate whether or not he transported his w a te rc ra ft " . . . from your house or other location to p a rtic u la r launching s ite s during the past boating season {calendar year 1968)." In a l a t e r question (number 7) w a te rc ra ft owners were also requested to indicate the to ta l number o f times that the sampled w a te rc ra ft was transported " . . . or mooring to the place o f use." from the place o f storage Response to th is l a t t e r question proved to be less than adequate, as many respondents l e f t i t blank. Thus, v a ria b le was entered as e ith e r zero or one. I f a respondent indicated (yes) th a t the w a te rc ra ft was transported during the past boating season, a value o f one was entered, and zero otherwise. Number o f boats owned ( x ^ ) . - - T h i s v a ria b le was designed to measure the e f f e c t o f m u ltip le boat ownership upon the amount of recreational boating p a rtic ip a tio n undertaken. In question 14 in the mail survey, respondents were requested to give the number of other registered and unregistered boats owned ". . . by you, and by the members o f your immediate fam ily residing with you." The value assigned th is va ria b le fo r each individual boat owner was obtained through a summation o f the number of boats lis te d in question 14 (including the w ate rcraft drawn in the sample). 106 Boat Length ( x ^ ) . - - B o a t length was the specified hull length of each sampled w a te rc ra ft given in the l i s t of Michigan registered w a te rc ra ft owners, obtained from the Michigan Secretary o f S ta te 's O ffic e . For each individual observation, the value o f th is v a ria b le was entered as the specified raw b oat-hull length. Age o f Family Head ( xi g ) - ^— Respondents to the boating survey were asked “what is the age . . . o f the head o f your family?" in question number 16 o f the mail questionnaire. Individual observations fo r the va ria b le were taken from th is question, and were the age in years specified fo r the fam ily head, irre s p e c tiv e of sex. I t should be noted th a t because o f the l a t e mailing date ( A p r il, 1969) the i n f o r ­ mation on age supplied in th is question was subject to some change. That is , "age of fam ily head" could have been interp reted to mean age a t the time the questionnaire was received by registered boat owners. On the other hand, since the e n tir e calendar year (1968) was included in the survey, age o f household head would reasonably be expected to vary w ith in th at span o f time. Thus, i t is not c le a r "which age" respondents a c tu a lly gave in th is question: age at the time the questionnaire was received, age a t the end of the calendar year, or age a t some other point between January 1, 1968, and December 31, 1968. Age Squared ( x ^ ) . — The measure used fo r th is variable was obtained from question 16 in the mail questionnaire, and consisted of the age o f the household head squared (x^g ). I t should be noted, however, th at th is va ria b le is subject to measurement e rro r o f unknown ^Variable X15 does not appear in th is sequence of independent variables since i t was the dependent v a ria b le (boat days), described at the beginning of th is section. 107 magnitude re su ltin g from possible m is in te rp re ta tio n o f the question re la tin g to age in the questionnaire. Family Size (x-jg) .--T h is v a ria b le was entered in order to measure the e f f e c t of family size o f w a te rc ra ft owners upon the level o f recre­ ational boating p a rtic ip a tio n . The measure used fo r the va ria b le was obtained from questions 16 and 17, in the survey instrument. Each sampled w ate rcraft owner was asked to give the age and sex o f ". . . each member o f your fam ily residing with you (excluding the head o f household)," in question 17. The measure used consisted o f a summation o f a l l fam ily members lis t e d in question 17, including the head of house­ hold lis t e d in question 16. This v a ria b le may also be biased due to the length o f time involved. Respondent's fam ily size could e a s ily have changed, and may have been la rg e r (or sm aller) a t the time the questionnaire was received and completed than i t would have been had the survey been re s tric te d to a more compact time horizon. Occupation of Family Head ( x ^ g - x ^ ) .--T h e measure fo r th is variable was obtained from question 18 in the mail questionnaire. Each respondent was asked "What is the occupation of the head of your family? (please indicate the type of job th a t you hold, not the organization fo r which you work)." A series o f eighteen occupational classes were established, and each response given was assigned to one of these categories.^ All occupational classes were treated as "zero-one" ^Occupation classes used follow clo sely the c la s s if ic a t io n system developed by the U.S. Bureau o f the Census. One o f the occu­ pational classes ("other employment") was l a t e r suppressed in order to obtain a determinate solution in the computer analysis. Thus, seventeen occupational classes were a c tu a lly u t il i z e d in the regression equation. 108 variables. Whenever an individual response to question 18 resulted in a person being assigned to a p a rtic u la r occupational class, th at class was assigned a value of one fo r th a t observation, and a l l other classes zero . The seventeen occupational classes used were as follows: x-jg - Professional x2fl - Farm Managers x28 ~ Farm laborers x2g - Laborers Xg-j - Managers and O ffi c ia ls XgQ - Student x22 " C lerica l Workers Xg3 - Sales Workers x3-| - Housewife *24 “ Cra^tsmen x25 " CPGra*ives Xgg - Household Workers x 32 - Retired - M i li t a r y x34 - Unemployed X35 - Other factory x2 7 - Service Workers Family Income ( * 3 5 ) • — The value used fo r th is v a ria b le was obtained fo r each individual observation from question 19 in the mail questionnaire. Each respondent was asked in th is question to . . estimate your to ta l fam ily income fo r 1968 by checking the box (opposite the appropriate income class) below." were provided: A series o f seven income classes to ta l fam ily income ( 1 ) under $3,000 annually, (2) $3,000 to $5,999 annually, (3) $6,000 to $7,999 annually, (4) $8,000 to $9,999 .annually, (5) $10,000 to $14,999 annually, ( 6 ) $15,000 to $24,999 annually, and (7) $25,000 and above. This a p rio r i ordering o f income classes poses real d i f f i c u l t y in choosing an appropriate value fo r the fam ily income v a ria b le. The procedure followed was to develop a weighting system fo r the seven income classes* A value o f 1 was assigned to income class one where the d o lla r in te rv al ranged between 0 and $2,999, a value o f 2 S im ila r ly , was assigned to income class two since the w ith in -c la ss 109 in te rv al remained $2,999. However, income class three had a w ith in - class in te rv a l of only $1,999. assigned to th is class. Therefore, a value o f only 2.66 was A s im ila r procedure was followed with the remaining income classes {class fo ur—3.3 2, class f i v e —4 .9 7 , class s ix —8 .2 7 , and class seven— 11 .57 ). The weighting assigned to class seven required an additional assumption: since th is income class was "open-ended" ($25,000 and above), i t was a r b i t r a r i l y decided to weight th is class in proportion to the w ith in -c la ss in te rv a l o f the preceeding class— $9,999. I t should be noted th at the procedure o f rank-ordering fam ily income into seven classes in the mail questionnaire introduced a source o f s t a t is t i c a l bias. Such a procedure has the e ff e c t of con­ straining the incomes o f respondents into a lin e a r ordering when in fa c t th is may not be the case, i . e . , p a rtic ip a tio n in recreational boating may not be related lin e a r ly with fam ily income. The seven rank-ordered income classes force th is im p lic it assumption, however. The fam ily income va ria b le is introduced as a te s t of the hypothesis th at there is no s ig n ific a n t influence o f income upon recreational boating p a rtic ip a tio n . A rigorous te s t o f th is hypothesis would demand th at raw fam ily income values be used as the measure fo r th is v a ria b le. This would allow the data to determine the re la tio n s h ip J ^Some empirical work has shown, fo r example, th at there may be a c u rv ilin e a r re latio n sh ip between recreation p a rtic ip a tio n and family income, i . e . , family income appears p o s itiv e ly correlated with increasing levels o f p a rtic ip a tio n up to some "threshhold" level o f income, beyond which fu rth e r p a rtic ip a tio n declines. That is , the commodity in question (recreation p a rtic ip a tio n ) is treated as an " in f e r io r good," where less of the commodity is taken a t higher levels of fam ily income (assuming no change in p rice s). See, fo r example, Outdoor Recreation fo r America, lo c . c i t . , pp. 27-32. 110 Furthermore, as Stevens notes: . . . the customary procedure o f assigning a value . . . by in te rp o la tin g l i n e a r l y w ith in a class in te rv a l i s , in a l l s t r i c t ­ ness, wholly out o f bounds. Likewise, i t is not s t r i c t l y proper to determine the m id-point o f a class in te rv a l by lin e a r in te rp o ­ l a t i o n , because the l i n e a r i t y o f an ordinal scale is p re c is e ly the property which is open to question. (A ls o ). . . i t is proper to point out th a t means and standard deviations computed on an ordinal scale are in e r ro r to the extent th a t the successive in te rv a ls on the scale are unequal in s i z e . ' The i m p li c it assumptions inherent in the procedure o f ranking fam ily income a p r i o r i into income classes (w ith unequal i n t e r v a l s ) , together with the assigning o f d is c re te weights to each o f the seven income classes based upon lin e a r in te rp o la tio n w ith in each c la s s , serves to in v a lid a te the s t a t i s t i c a l te s t o f th is hypothesis. The procedure followed implies a p r i o r i knowledge about the d is t r ib u t io n o f actual incomes o f respondents which was not in fa c t knowable. Family Income Squared ( x ^ . - T h e measure used fo r th is v a ria b le was obtained by squaring fam ily income ( x 3 g) ^or observation. e a c *1 in d ivid u al This v a ria b le was introduced in the s t a t i s t i c a l model in order to te s t the hypothesis th a t the change in the dependent v a ria b le (boating a c t i v i t y occasions) is associated with n o n -lin e a r changes in fam ily income. Because o f the procedures o u tlin e d above in entering the fam ily income v a r ia b le , however, entering squared values (d is c re te weights) which were calculated fo r the seven income classes does not represent a v a lid te s t o f the hypothesized re la tio n s h ip . The Product of Family Income and Age ( x ^ g ) .“ -The measure used fo r th is v a ria b le was the cross product between Family Income ( x 3 g) ^S. S. Stevens, "On the Theory o f Scales o f Measurement," Science, Vol. 103, No. 2684 (June, 1946), p. 679. Ill and Age o f Family Head Cx -jg) • Past empirical work has indicated th at family income and age o f p artic ip an ts are primary variables influencing p a rtic ip a tio n in ce rtain outdoor recreation a c t i v i t i e s . Further, some studies have shown th a t such variables are s ig n if ic a n t ly i n t e r r e l a t e d . 1 Changes in family income may have d if f e r e n t e ffe c ts upon recreation p a rtic ip a tio n a t d if f e r e n t income and age levels o f p a rtic ip a n ts . Limitations in both the income and age variables (x^g and x-jg) have already been discussed above. In te rp re ta tio n o f regression results w ill have to be made cautiously, recognizing these e x p l i c i t lim ita tio n s . Education o f Family Head ( x3 q ) *— The measure used fo r th is variable was taken d ir e c t ly from respondent re p lie s to question the mail questionnaire. 20 in Question 20 asked respondents to ". . . ind icate the to ta l years o f education completed by the head o f your fa m ily ." While actual years o f education completed was the measure used fo r th is v a ria b le , there appear to be a t lea st three possible sources o f bias inherent in the wording and structure of th is question. F i r s t , there was no opportunity fo r a respondent to answer th is question i f he had received zero years of formal education. cant number of respondents f e l l To the extent th at a s i g n i f i ­ in th is category, the re su ltin g d i s t r i ­ bution of education attainment fo r respondents is skewed, i . e . , a computed population mean would be of greater magnitude conceivably as a re s u lt o f counting only those respondents who had a non-zero response to the question. ^ e e , Brewer and G ille s p ie , lo c . c i t . , pp. 85-86, and Outdoor Recreation fo r America, loc. c i t . , pp. 27-32. 112 Secondly, question 20 was structured ambiguously over the high bound o f the range considered. Seventeen boxes were provided in th is question—years o f education completed could thus range between 17 years. 1 and However, an eighteenth box was provided which respondents could check i f years o f education completed was g reater than 17. Almost a l l respondents checking th is box wrote in the actual number o f years completed (above 17). These figures were thus accepted as the measure for the education va ria b le fo r a sp ecific observation. Where no response was given, other than a check, the observation was dropped from the analysis. F in a lly , the wording o f the question may not have been c le a r to respondents. There is a p o s s ib ilit y th a t some respondents counted non-formal education (such as non-credit short courses, in -s e rv ic e tra in in g , e t c . ) in a r riv in g a t t h e i r response. There may also have been confusion on the part o f some respondents as to which time (during the calendar year) should be used as a point o f reference in responding to the education question. Computational Procedures In testin g study hypothesis one, the regression equation speci­ fie d above was estimated by u t i l i z i n g a stepwise d eletion procedure.^ The s t a t i s t i c a l analysis was performed a t the Michigan State U niversity Computer Laboratory on a CDC-3600 computer. ^See, Mary E. Rafter and W illiam L. Ruble, Stepwise Deletion of Variables from a le a s t Squares Equation, STAT Series Description No. 8 — LSDEL '{Eastf"Lansing, Michigan: A g ric u ltu ra l Experiment S tatio n , Michigan State U n ive rsity , November 1969), pp. 12-13. 113 The stepwise d eletion routine u t i l i z e d proceeds by p rin tin g le a s t squares c o e ffic ie n ts and re la te d s t a t is t i c s with a l l beginning independ­ ent variables (38) in the equation. A new le a s t squares equation is then estimated, following d eletion o f one (independent) v a ria b le . A second v a ria b le is then deleted, and the equation is again re -c a lc u la te d . Independent variables continue to be deleted in th is fashion u n til a variable selected as a candidate fo r deletion meets one or more specified stopping c r i t e r i a . A lte rn a tiv e stopping c r i t e r i a may be used in the stepwise deletion program a v a ila b le . th is problem, however: Only a single c r it e r io n was u t i l i z e d fo r MINSIG = .05—deletion o f variables from the specified equation one a t a time, re ca lcu la tin g the le a s t squares equation each time a (independent) v a ria b le was deleted u n til the sig nificance level a o f the computed regression c o e ffic ie n t o f the candidate fo r d eletion was < .05. In order to obtain a determinate solution to the problem, one fu rth e r procedure was followed with respect to handling the dummy variables in the i n i t i a l equation. Zero-one values were used to represent the e ffe c ts o f c e rta in independent variables upon recreational boating p a r t ic ip a tio n , e . g . , power system o f sampled w a te rc ra ft (x-j-x^ ), place o f storage of w a te rc ra ft during the boating season ( x g - x ^ ) , and occupation o f fam ily head (x^g-x^g). In each case, a value o f e ith e r zero or one was assigned to the variables w ith in each set o f classes. A sampled w a te rc ra ft e ith e r had an outboard motor, or i t did not. A sampled w a te rc ra ft was e ith e r stored a t a commercial boat marina during the boating season, or i t was not. Likewise, the head o f the fam ily 114 e ith e r had an occupation which could be c la s s ifie d as professional, or he (or she) did not. I n i t i a l runs o f the model did not give a determinate solution, i . e . , regression c o e ffic ie n ts and other lea st squares s t a t is t i c s "would not compute." The LSDEL routine is autom atically programmed to compute an in te rc e p t term. As Johnston points out, however, i f one attempts to estimate the in tercep t term where only dummy independent variables are used, the estimation procedure may break down " . . . since the appropriate matrix cannot be inverted."^ For example, consider a case where two q u a lita tiv e classes of observations are involved in which individual observations o f the two classes are "pooled." I t would be possible to in s e rt two dummy variables into the equation in order to obtain estimates o f the class e ffe c ts , such th a t: y = a where D-j = 1 Dg = 1 o + a n D, + I I 2 d + bx + u i f an observation f a l l s in class 1; 0 i f in class 2. i f an observation f a l l s in class 2 ; 0 i f in class 1 . 2 As L e i s t r i t z points o ut, however, the above equation cannot be estimated, since the dummy variables D-j and Dg and the constant term have a perfect lin e a r re la tio n s h ip (D^ + Dg = constant). In order to obtain determinate estimates o f the parameters in the above equation, ^J. Johnston, Econometric Methods (New York: Company, In c ., 1963), p. 222. 2 McGraw-Hill Book F. Larry L e i s t r i t z , The Use o f Dummy Variables in Regression Analysis, Ag. Econ. Misc. Report No. 13TFargo7 North Dakota: A g ric u ltu ral Experiment S ta tio n , August 1973), p. 2. 115 additional constraints have to be imposed upon the a . . One recommended J procedure is to set one of the a. = 0 , thus dropping one o f the dummy J variables from the equation so th a t: y - a„ + a 0 D„ + bx + u o 2 2 i f a-j is set equal to zero. In the new equation, aQ becomes the intercept term fo r observations of class 1, and (aQ + a2 ) becomes the in te rc ep t term fo r the observations o f class 2 .1 The above procedure was followed in order to obtain a determinate solution to the problem, except th at observations w ithin the three classes involved were not "pooled." For example, in question 4 in the mail questionnaire, respondents were asked where they stored the sampled w ate rcraft during the boating season. There were seven response categories in th is question— respondents were requested to check a single box opposite one of these seven categories. was lis te d as "other." The seventh category This category was dropped from the equation, and zero ( 0 ) or one ( 1 ) values were entered fo r the remaining six categories. The same procedure was followed with the remaining two classes of q u a lit a t iv e variables: of sampled w a te rc ra ft. occupation of fam ily head, and power system In the case o f the power system of w ate rcraft class, an "other" category was dropped from the equation and zero ( 0 ) or one ( 1 ) values were entered fo r the remaining four categories. Likewise, an eighteenth category under the occupation class ("other") ^I b i d . , p. 3. 116 was dropped from the equation, leaving seventeen categories fo r which zero ( 0 ) or one ( 1 ) en tries were entered in the equation estimated. As a re s u lt o f incorporating zero-one values into the regression equation, a simple covariance model is thus obtained (AN0C0VA). Such a model involves regression on both categorical and numerical variables. Aggregate P a rtic ip a tio n Model Hypothesis 2 re lates to the rate o f recreational boating p a rtic ip a tio n by regional (county) populations. hypothesis, le a s t squares techniques wereagain a lin e a r equation which measuresthe In testin g the stated u t il i z e d to e ffe c ts o f estimate specified (independent) variables upon the ra te o f recreational boating p a rtic ip a tio n by county populations. The model parameters were estimated fo r the State of Michigan as a whole; and fo r (a) t h i r t y Michigan counties which were estimated to generate the highest levels o f to ta l (aggregate) boating a c t i v i t y during 1968; and (b) t h i r t y Michigan Counties which were estimated to generate the lowest levels o f to ta l a c t i v i t y during 1968. The sp e cific form o f the equation is as follows; Y. - a + b, X, . + b0 X0 . + . . . + J 1 lj 2 2j 1, 2 , 1, 2, (aggregate) boating 26 xoc. + u. 26j j where: i = j = . . . 26 . . .n and: Yj is the j t h observation o f the dependent v a ria b le . X ij is the j t h observation o f the it h independent v a ria b le. a is the constant term. b-j is the c o e ffic ie n t o f the it h independent v a ria b le . 117 uj is the j t h observation o f a random e rro r term, where ( j ° 1» 2, . . . n ). The Uj are assumed to be independent, and come from a normal d is t r ib u t io n w ith zero mean and uniform variance o 2 . Model S p e c ific a tio n The dependent v a ria b le ( Y .) is the estimated number o f boat w days ( a c t i v i t y occasions) per calendar year 1968. 1,000 county population during the The measure used was ca lcu la ted separately fo r each Michigan county, based upon information obtained from the 1968 survey o f re g istered Michigan w a te rc ra ft owners. Estimates o f t o ta l recreational boating a c t i v i t y occasions were f i r s t calculated fo r the 83 Michigan counties. This estimate was then divided by the estimated to ta l county population on December 31, 1968, in order to obtain a boating p a r tic ip a tio n ra te per 1,000 population (see Table 9 ). Travel Distance ( X ^ ) . — The measure used fo r th is v a ria b le was the weighted average one-way tra v e l distance (in m iles) calcu lated fo r a l l 83 Michigan counties on the basis o f re s u lts obtained from the 1968 survey o f Michigan registered w a te rc ra ft owners. The s p e c ific value calcu lated fo r each county was obtained from the data presented in the county o rig in -d e s tin a tio n m atrix exh ib ited in Appendix D. These tables show the estimated boating a c t i v i t y occasions generated by o r ig in county (county o f residence o f sampled w a te rc ra ft owners), the d i s t r i ­ bution o f these a c t i v i t y occasions by d es tin atio n counties (county where boating a c t i v i t y took p la c e ), and the percentage o f estimated to ta l boating a c t i v i t y generated by an o rig in county which was undertaken in each Michigan d es tin atio n county.^ ^An o r ig in county also was tre a te d as a d es tin atio n county since much o f the boating a c t i v i t y generated takes place w ith in the county o f 118 One major assumption was made in order to ca lcu la te an estimated average tra v e l distance fo r the boating tr ip s made by the residents o f a p a rtic u la r o rig in county; namely, th a t the number o f boating trip s taken by registered w ate rcraft owners between an o rig in county and a destination county was d ir e c t ly proportional to the percentage o f to ta l boating a c t i v i t y occasions estimated fo r the d estination county during the survey year. Information on the actual number of recreational boating t r ip s taken by sampled boat owners was not obtained in the survey instrument. In calcu latin g the estimated average tra ve l distance fo r each o rig in county, the percentage o f to ta l boating a c t i v i t y occasions for a destination county was treated as a weight. One-way travel d is ­ tance (in miles) between o rig in and destination counties was obtained from the Michigan State Highway Department, and consisted o f the shortest calculated highway d riving distance between the centers of population fo r o rig in and destination co u ntiesJ residence o f boat owners. For each Michigan o rig in county, there were, th ere fo re, 83 possible counties o f destination w ithin the S tate. ^The highway d riving distances used are referred to as "skim distances." In obtaining th is measure, a computer program was used to examine a l l possible combinations o f highway routes between centers of population in o rig in and destination counties. A stopping c r i t e r i a was used such th at absolute highway travel distance (in miles) was minimized by the program. I t should be noted th at th is measure does not necessarily minimize highway d rivin g time between o rig in -d e s tin a tio n counties. I t is conceivable th at a lte rn a te travel routes could be selected which, although ex h ib itin g greater absolute highway mileage, may involve less driving time, p a r tic u la r ly i f the combination of travel routes selected included 1imited-access expressways. Richard Esch, "Highway Skim Distance," Unpublished data, Highway Planning D ivision, Michigan Department o f State Highways, Lansing, Michigan, June 1973. 119 Computation o f the weighted average (one-way) tra ve l distance fo r each o rig in county involved ( 1 ) determining weights fo r each d is tin a tio n county— calculated from the o rig in -d e s tin a tio n m a trix, and consisting o f the percentage o f boating a c t i v i t y occasions which took place in a p a r tic u la r destination county. This percentage was treated as a proxy fo r the number o f actual boating tr ip s taken between o rig in -d e s tin a tio n counties by registered boatowners. (2) M u ltiplyin g the calculated weight by the one-way highway d rivin g distance, obtained from State Highway Department Skim distance tables fo r each o r ig in destination county combination. (3) Summing these to ta ls and d iv id in g the re su ltin g fig u re by the sum o f the weights used fo r a l l combinations of o rig in -d e s tin a tio n counties. The mathematical procedure followed is also shown in Appendix D. Aggregate Disposible Income (x .j).--T h e measure used fo r th is variable was obtained from Sales Management, In c ., and consists of the Net E ffe c tiv e Buying Income (EBI) in thousands of d o lla rs fo r each Michigan county in 1968. This measure corresponds closely to "disposable personal income'1 per county. I t consists of estimates o f what in d i­ viduals receive in wages, s a la r ie s , and commissions; p ro p rie to r's income, rental income from real property, dividends and in te re s t from se cu rities and savings, social security b en efits, pension, and w elfare payments. In addition to these sums, allowance is made (where re lev an t) ^"Sales Management," Survey o f Buying Power, Vol. 102, No. 12 (June 10, 1969), Section D, pp. 88-95. Copyright by Sales Management, In c ., June 10, 1969. Reproduced by w ritte n permission o f Sales Manage­ ment, In c ., August, 1973. Further reproduction of these data in any form may be made only upon w ritte n request to Sales Management, In c ., 630 Third Ave., New York, N.Y. 10017. 120 fo r including imputed re n ta ls fo r owner-occupied homes, and an imputed value f o r fuel and food raised and consumed on farms. A fte r a r riv in g a t t o ta l personal income, an allowance is made fo r d ir e c t taxes— fe d e r a l, s ta te , and lo c a l. The estimate fo r d ir e c t taxes, when subtracted from to ta l personal income leaves a residual called E ffe c tiv e Buying Income (E B I). Households with less than $3,000 Annual Cash Income ( x ^ ) . — Consists o f the percentage o f households with net cash incomes in the range o f $0 - $2,999 fo r the calendar year 1968, by Michigan County. The values fo r th is v a ria b le were also obtained from Sales Management, Inc J Households with g reater than $10,000 Annual Cash Income ( x g ) . — The value used fo r th is v a ria b le consisted o f the percentage o f house­ holds with net cash incomes which were equal to or greater than $ 1 0 , 0 0 0 fo r the calendar year 1968, by Michigan county. 2 County Population Density (X g ). --Consisted o f the estimated number of persons per square mile fo r each Michigan County. Values were calculated by d iv id in g the to ta l land area o f each county (in 3 square m iles) by the estimated 1968 county population. 1 IM d . 2 Ib id . o County Land Areas were obtained from Michigan S t a t is t ic a l Abstract (Sixth ed .; East Lansing, Michigan: Bureau o f Business and Economic Research, Graduate School o f Business Adm inistration, Michigan State U n ive rsity , 1966), Table 11- 1 , p. 73. The 1968 county popu­ la tio n estimates were obtained from Sales Management, Survey o f Buying Power, op. c i t . , Section D, pp. 88-95. 121 Distance from a Great Lake ( X y ) . —The measure used fo r th is variable was the shortest one-way highway distance (in m iles) between the county seat in each Michigan county, and the closest point of boating access on a Michigan Great Lake. Michigan Highway map. Distances were scaled on a Great Lakes were defined to include Lakes Huron, E rie, Superior and Michigan; Lake St. C l a i r , the St. Mary's R iver, and the D e tro it River. This va ria b le is not a measure o f "time-distance" in the sense th a t a v a rie ty of tra ve l routes were used in estimating the road mileage between counties and Great Lakes. is a physical proximity parameter. The measure used In some cases, the estimated high­ way mileage consisted la rg e ly of highway routes which were lim ite d access expressways; while in other cases, the most d ir e c t (shortest) combination of highway tra ve l routes were p r in c ip a lly secondary roads.^ Proportion of M inority Races in Population (X g ). - - S p e c ific county values fo r th is va ria b le were obtained from the U.S. Census of Population. 2 U t i l iz i n g census data, the percentage of m inority races in the to ta l county population was computed. The procedure f o l ­ lowed consisted of summing the to ta l number o f persons in each c la s s ifie d m inority race (In d ia n , Japanese, Chinese, F i l i p i n o , Negro, and a l l o th e r), and dividing th is to ta l by the estimated 1970 population. It should be noted th at the percentage o f m inority races was calculated ^Map measurements were taken from Rand McNally Road A t la s ; Supplement to the 104th Edition o f the Rand McNally Commercial Atlas and Marketing Guide (Chicago: Rand-McNally & Company, 1968), p. 54. U.S. Department o f Commerce, Bureau of the Census, 1970 Census of Population; General Population C h a ra c te ris tic s , PC ( 1 ) -B24 Michigan (Washington: uTs.—Government Printing" Office', 1970), Table 34, pp. 178180. 122 fo r 1970. Survey data on boating p a r tic ip a tio n , however, was collected fo r calendar 1968. This means th a t the values calculated fo r th is variable are biased in unknown d irec tio n s to the extent th at the proportion of m inority races in county populations s h ifte d over various points in time between April 1, 1970, and the study year (calendar 1968). For purposes o f th is study, i t is assumed th a t the percentage o f m inority races in each county which existed as o f April 1, 1970, held constant during the study year (1968). Since comparable county data could not be obtained fo r the boater survey year (1968), i t was decided to tes t the re la tio n s h ip between county boating p a rtic ip a tio n rates and ra c ia l composition of the population using the 1970 data. Distance from an SMSA— Size-Distance (X g ).--T h is va ria b le constitutes a hypothesis about the e f fe c t o f urban areas upon the ra te o f recreational boating p a rtic ip a tio n by regional (county) popu­ la tio n s . The size-distance v a ria b le is introduced in the equation as a te s t o f the "opportunity theory." P a rtic ip a tio n in various forms of non-urban recreation (such as recreational boating) is theorized to depend upon resource a v a i l a b i l i t y . Urban residents,^ th e o r e t ic a lly , Urban residents are here defined to mean a l l persons liv in g in (a) places o f 2,500 inhabitants or more incorporated as c i t i e s , v illa g e s , boroughs, and towns, but excluding those persons liv in g in the rural portions o f extended c i t i e s ; (b) unincorporated places of 2,500 inhabitants or more; and (c) other t e r r i t o r y , incorporated or unincorporated, included in urbanized areas. Urbanized area can be characterized as the "physical c i t y , " as distinguished from the "legal c ity " and the metropolitan community. The boundaries o f metropolitan areas (SMSA's) are determined by p o l i t i c a l lin e s , while those of urbanized areas arc determined by the pattern o f urban land use. Standard Metropolitan S t a t is tic a l Areas (SMSA's) were defined more e x p l i c i t l y in Chapter I I I . Also, see U.S. Department o f Commerce, Bureau of the Census, 1970 Census o f Population; Volume 1, Charac­ t e r is t i c s o f the Population, Part A, Number of Inhabitants (Washington: U.S. Government P rinting O ffic e , 1970), pp. X-XIV. 123 have less physical opportunity to p a r tic ip a te in resource-oriented a c t i v i t i e s (such as boating) because o f the urbanized nature o f t h e i r liv in g environment. I f the theory holds, both the population o f the urban area and the physical size o f the area taken up by the urban land uses (such as in d u s tria l areas, business and commercial s tru c tu re s , highways, schools, cemetaries, r e s id e n tia l subdivisions, e t c . ) may in te ra c t to influence re creatio n p a r tic ip a tio n rates o f regional populations.^ Where one l iv e s — in r e la tio n to urban areas— may l i m i t the amount o f re cre a tio n a l boating undertaken. The values fo r th is v a ria b le were calculated fo r a l l 83 Michigan counties. The procedure followed involved s e ttin g up a series o f scale values, based upon each county's location with respect to an SMSA. SMSA counties population. 2 were assigned a value o f one fo r each 100,000 SMSA counties containing populations between 50,000 and 100,000 were assigned a value o f 0 . 5 . Based upon the population c r i t e r i a used, no county could be assigned a value g reater than 27— 3 that assigned to Wayne County. In assigning in d ivid u al county values, a distance decay p r i n c i ­ ple was followed. Distances were measured from the center of the central c i t y in an SMSA to the county l in e which is fa r th e s t from the SMSA. ^See, fo r example, John C. Hendee, "Rural-Urban Differences Reflected in Outdoor Recreation P a r tic ip a t io n ," Journal o f Leisure Research, Vol. 1, No. 4 ( F a l l , 1969), pp. 335-36. 2 Those counties in which there was located a Standard Metro­ p o litan S t a t i s t i c a l Area (SMSA) during 1968. 3 1968 population lev els fo r SMSA counties were obtained from Sales Management, Survey o f Buying Power, op. c i t . , Section D, pp. 8 8 95. 124 Counties located less than 50 miles from the central c i t y o f an SMSA were assigned a value o f four less than the value calculated fo r the SMSA county. Counties located in a distance zone between 50 and 100 miles o f an SMSA were assigned values which were four less than the value assigned to counties located w ithin the 50-mile zone, etc. Using th is ra tin g scheme, counties located a t a distance o f 300 miles or more from an SMSA were assigned a value o f z e ro J In some cases, p a rtic u la r counties had a potential o f being assigned two values since they were located w ithin the influence zone o f two SMSA's. In such cases, the county in question was always assigned the higher o f the two a lte r n a tiv e values. In cases where two SMSA counties were located w ithin a zone o f mutual influence, the value derived fo r the SMSA county in question was assigned on the basis of i t s own calculated value plus the value fo r the influencing SMSA. The value assigned in a l l cases, however, was never larg e r than the value of the influencing SMSA. I t should be noted th at a lte r n a tiv e population and distance values might be used fo r th is v a ria b le . Public and Private Campsites ( x^q )*—The value used fo r th is variable consisted o f the to ta l number o f individual campsites (a t both public and commercial areas) which had the services of constructed boatlaunching f a c i l i t i e s w ithin the campground. Separate values were obtained fo r each county in the state. There were f i v e categories of campgrounds included in the inventory: ( 1 ) sta te fo res t campgrounds, (2) sta te park campgrounds, (3) national fo res t campgrounds, (4) county ^This rating method follows closely th at developed in W. K. Bryant, "An Analysis of Inter-community Income D if f e r e n t ia ls in A griculture in the United States" (unpublished Ph.D. d is s e rta tio n , Michigan State U n iv e rs ity , 1963), pp. 72-73. 125 and municipal campgrounds, and (5) commercial campgrounds. Only camp­ grounds which a c tu a lly provided boat-launching f a c i l i t i e s during 1968 were selected.^ Surface Water Acreage The surface water acreage was inventoried fo r each county in the s ta te . Values entered fo r each county consisted o f the to ta l area (in acres) contained in selected surface water bodies: ( 1 ) natural lakes and ponds, ( 2 ) natural lakes with a dam, (3) a r t i f i c i a l lakes, (4) a r t i f i c i a l ponds, (5) hydro electric reservoirs, ( 6 ) small lakes, and (7) flood control reservoirs. Only water bodies covering a t le a s t 4 acres were included in the tabulations fo r each county. Many surface water areas were excluded from the in ­ ventory on the assumption th a t much o f the water acreage involved would not be su itab le fo r power w a te rc ra ft use. Categories excluded were municipal water supply re se rv o irs , fis h and w i l d l i f e floodings, m ill ponds, gravel p i t or quarry ponds, fis h hatchery ponds, underwater borrow p it s , recharge basins, s e ttlin g ponds, beaver ponds, sewage disposal basins, fishbreeding ponds, t a ilin g s ponds, brine storage basins, swamps, marshes, canals, bogs, riv e rs and streams, and Great Lakes.^ As noted above, no inland riv e rs and streams were included in the water acreage summary. Furthermore, c e rta in o f the excluded water Whe inventory o f public and p riv a te campsites was made fo r the State o f Michigan from S t a t i s t i c a l information contained in Woodhall1s T ra ile rin g Parks and Campgrounds (Highland Park, I l l i n o i s : Woodall Publishing Company, 1968), pp. 325-346. 2 Acreage figures were obtained from C. R. Humphrys and R. F. Green, Michigan Lake Inventory B u lle tin s 1-83 (East Lansing, Michigan: Michigan State U n iv e rs ity , Department o f Resource Development, 1962). 126 areas lis t e d above may, in f a c t , be highly desirable as recreational boating areas. To the extent th a t desirable boating areas were excluded from the inventory, th is v a ria b le may not be adequately specified to portray actual water resource a v a i l a b i l i t y . Also, a d if f e r e n t re s u lt might be obtained by changing the minimum acreage r e s t r a in t (4 acres) used in obtaining individual county values fo r th is v a ria b le . Public Boat-Launching Sites ( x - ^ ) * — Values used fo r th is v a ria b le were obtained from tabulations on the number o f p u b lic ly constructed boat-launching s ite s a v a ila b le on inland lakes and ponds and Great Lakes during 1968 fo r each Michigan county. Individual county values were obtained from tabulations o f public access sites prepared by the Michigan Department o f Natural Resources, Waterways Commission. Public access s it e tabulations are broken into f iv e general categories: ( 1) Waterways D ivis io n , (2) State Parks, (3) Recreation Areas, (4) State Forests, and (5) Game Areas. Public access s ite s are summarized by region and county. The value used fo r each county involved a summation o f access site s included under each o f the f i v e ad m in istrative categories. An adjustment was made in the re su ltin g value, however, in order to allow fo r public access s ite s (boat-launching f a c i l i t i e s ) already entered in the public and p riv a te campsites va ria b le ( x -j q ). Cross-tabulations were made fo r each county, and public access (boat-launching) site s counted as being present in public or commercial campgrounds were deducted from the value ^Michigan State Waterways Commission: Biennial Report— 19681970 (Lansing, Michigan: Michigan Department o f Natural Resources, Waterways Commission, 1970), pp. 16-17. 127 for each county entered under the public boat-launching s i t e v a ria b le . Thus, the value used r e f le c t s , insofar as possible, only constructed public access s ite s f o r each Michigan county in 1968 which are not located a t a public or p riv a te campground f a c i l i t y . Hotels, Motels, and Tourist Courts ( xi 3 ) - —This v a ria b le constitutes a te s t o f the s t a t i s t i c a l re la tio n s h ip between recreational boating p a rtic ip a tio n and the number o f commercial lodging f a c i l i t i e s present in a county (other than campground f a c i l i t i e s ) . F a c il i t ie s included in the county parameter values were commercial motels, h otels, to u r is t homes, t r a i l e r parks, and sporting and recreational camps present and in operation as o f July 1, 1967.^ To the extent th at the number of commercial establishments counted under these categories increased (or decreased) between Ju ly, 1967, and various time periods during the survey year (1968), the values entered do not r e f l e c t an accurate s p e c ific a tio n o f the va ria b le being tested. However, more precise data fo r 1968 was not a v a ila b le fo r use in th is study, and the values entered are assumed to hold constant during calendar 1968. Amusement, Recreation Services ( x ^ ) . --T h is v a ria b le is entered in order to te s t the s t a t i s t i c a l re la tio n s h ip between recreational boating p a rtic ip a tio n and the a v a i l a b i l i t y o f su b stitute le is u re time amusement and recreation services a v a ila b le w ith in a county. Values entered fo r each county represent an aggregate estimate o f a l l commercial 1 U.S. Department o f Commerce, Bureau o f the Census, Census of Business, 1967; Vol. V, Selected Services— Area S t a t i s t i c s , Part 11, Michigan {Washington: U.S. Government P rin tin g O ffic e , 1970), Table 3, pp. 8 - 1 2 . 4 128 amusement and recreation service firms (except motion p ictures) which were in operation w ith in each Michigan county as o f July 1, 1967.^ The aggregate number of firms was composed o f: a. Producers, orchestras, e n te rta in e rs . b. Bands, actors, other e n te rta in e rs . c. Dance bands, orchestras (except symphony). d. Symphony orchestras, other cla ss ic al groups. e. Entertainers (ra d io , TV), except c la s s ic a l. f. Theatrical producers and services. g. Bowling a lle y s , b i l l a r d , pool establishments. h. Dance h a lls , studios, and schools. i. Commercial sports— baseball, fo o tb a ll clubs, e t c . , promoters, racetrack operations, including racing stables. j. Public g o lf courses. k. Skating rin ks . 1. Amusement parks (including kiddie-theme parks). m. Coin-operated amusement devices. n. Concession operators o f amusement devices, rid e s , c a rn iv a ls , circuses, and f a i r s . o. Other commercial recreation and amusement. Individual county values were not a v a ila b le fo r s p e c ific types o f recreation-amusement service firms lis te d above--only aggregate county t o ta ls . There may have been increases (or decreases) in the to ta l number o f recreation-amusement service firms between July o f 1967 and p a r tic u la r points in time during the study year (1968). Values are assumed to hold constant during the study y e ar, however. 2 Occupations o f County Population ( x j 5 "x2 o ; x23~x27* x29^* — The values entered fo r these variables consisted o f the percentage of ^ Ibid. ^Variables *21”x?3 do not appear in th is sequence as the i n t e r ­ vening columns were u t il i z e d as data control cards in the computer card deck. Variable X28 appeared as a separate v a ria b le and is described following the occupation variables. 129 a county's employed labor force The accounted f o r by 12 percentages were ca lcu la ted fo r each occupation occupation classes. c la s s , basedupon s t a t i s t i c a l data presented in the U.S. Census o f Population,^ Per­ centages were entered fo r each Michigan county (83) fo r the follow ing occupation classes: x 15 P rofessional, Technical and Kindred Workers, x-jg Managers and Administrators (except farm ). Sales workers, x^g C le ric a l and Kindred Workers, x-jg Craftsmen, Foremen and kindred workers. X£q Operatives (except tra n s p o rt). x^3 Laborer (except farm ), x24 Farmers and farm managers. Xgg Farm laborers and farm foremen. x26 Service workers (except p riv a te household). x27 P riv a te household workers. x29 tra n s p o rt equipment operatives. Registered W atercraft in County f X2 S ^ va^ue used fo r th is va ria b le consisted o f the number o f registered w a te rc r a ft per county population during 1968. 1,000 The value was calculated f o r each Michigan county by d iv id in g t o ta l number o f registered w a te rc ra ft by the estimated 1968 county population. 1 U.S. Department o f Commerce, Bureau o f Census, 1970 Census o f Population; General Social and Economic C h a r a c te r is tic s , PC (1}-C24 (Washington: U.S. Government P rin tin g O ff ic e , 1970), Table 122, pp. 558-564. 2 The to ta l number o f re g istered w a te rc ra ft per county was obtained from D ivision o f Vehicle and W atercraft Records, "Size and Type o f Registered Boats in Michigan Counties," Unpublished Report, Michigan Secretary o f S ta te 's O ffic e , December 31, 1968. County population data was obtained from Sales Management, Survey o f Buying Power, l o c . c i t . , Section D, pp. 88-95. 130 For purposes of th is study, i t was assumed th at the number o f registered w atercraft in each Michigan County was uniform during each month o f the calendar year (1968), and coincided with y e arly summary s t a t is t ic s compiled as of December, 1968. A s im ila r assumption had to be made concerning the population o f Michigan counties a t various points in time during the calendar year. To the extent that these two assump­ tions are not met, values calculated fo r each county may be biased in unknown d ire c tio n s , depending upon (a) the rate o f aggregate population change— increases or declines— from one time period to another during the calendar year, and (b) increases or declines in the to ta l number of registered w atercraft owned by boat owners in each county. Computational Procedures In testing study hypothesis two, the equation specified above was estimated by u t i l i z i n g the stepwise d eletion program outlined for equation number one. The s t a t is t i c a l analysis was completed at the Michigan State University Computer Laboratory on a CDC-3600 computer. As before, only a single stopping c r ite r io n was u t il i z e d in the program used to calcu late least squares s t a t is t i c s : MINSIG = .05— deletion of variables from the specified equation one a t a time, recalculating the le a s t squares equation each time a (independent) variable was deleted u n til the sig nificance p ro b a b ility of the computed regression c o e ffic ie n t o f the candidate fo r deletion was ~ .0 5 . Only continuous variables were included in the model. Data Analysis--Results The remainder o f th is chapter w i l l be devoted to a presentation of the principal findings o f the study. The f i r s t section w il l involve 131 a summary o f regional va ria tio n in recreational boating a c t i v i t i e s by registered Michigan w ate rcraft owners, u t i l i z i n g the f i v e study regions id e n tifie d in Chapter I I . The second section w il l be devoted to a summary o f the observed e ffe c ts o f sp e cific variables (sp ecified in model number 2) upon recreational boating p a rtic ip a tio n rates exhibited by county populations. Results of the s t a t i s t i c a l analysis o f e s t i ­ mated county population p a rtic ip a tio n rates w i l l be presented fo r the State o f Michigan as a whole, and separately fo r (a) the t h i r t y Michigan counties which had the highest estimated aggregate boating p a rtic ip a tio n levels during 1968, and (b) t h i r t y Michigan counties which exhibited the lowest estimated aggregate boating p a rtic ip a tio n levels during 1968-^ Modified User Characteristics Model Linear regression was used to determine the e ffe c ts o f s p e c ific socioeconomic ch a rac teris tic s o f a sample of registered w atercraft owners (and t h e ir immediate fa m ilie s ) upon the number o f boat days ( a c t iv it y occasions) undertaken during the calendar year 1968. In addition to these v a ria b les , the model specified contained variables re la tin g to place o f storage o f w a te rc ra ft, type o f power system o f sampled w a te rc ra ft, length o f sampled w a te rc ra ft, horsepower o f primary ^In th is case, a l l 83 Michigan counties were ranked according to the to ta l estimated number o f boating a c t i v i t y occasions calculated fo r the study year. All counties were ranked based upon to ta l boat days computations, made in Table 9 (see page 9 7 ). From th is rankordered l i s t , the top t h i r t y counties were selected, as were the bottom t h i r t y . Model two could not be estimated separately fo r the fiv e study regions id e n tifie d due to a lack o f s u ffic ie n t degrees o f freedom (the number of observations minus the number o f constants f i t t e d in the equation minus o n e --N -K -l). In the case o f Region 6 --Lansing, fo r example, there were only three observations, and twenty-six independent variables. 132 motor used on sampled w a te rc ra ft, transpo rtatio n of w a te r c r a ft, and number of (registered and unregistered} w a te rc ra ft owned by sampled w atercraft owners. Regression re su lts w il l be presented in th is section fo r the f i v e selected study regions, as well as fo r the State of Michigan as a whole. Region 1— D e tro it Region 1 contains a l l (or portions o f) three Standard Metro­ politan S t a t is t ic a l Areas: D e tr o it, Ann Arbor, and the Monroe County portion o f the Toledo, Ohio, SMSA. There are seven counties contained in th is region, including Wayne, Monroe, Washtenaw, Livingston, Oakland, Macomb, and St. C la ir . The computer program u t il i z e d fo r th is study, as noted p re v i­ ously, consisted of a stepwise d eletion procedure. Independent variables were deleted from the i n i t i a l equation one a t a time in successive ite ra tio n s u n til a l l candidate variables remaining met a specified stopping c r i t e r i o n . In order to be retained in the f i n a l equation, the significance p ro b a b ility o f the computed regression c o e ffic ie n t of an (independent) v a ria b le had to be ~ .0 5 . The income variables ( * 3 5 * * 3 7 > flnd the cross-product o f income and age--Xgg) were not found to be s t a t i s t i c a l l y s ig n ific a n t in th is region. However, th is re s u lt should be weighed cautiously as these variables may have been entered in c o rre c tly in the s t a t i s t i c a l analysis. Frequency data suggest, for example, th a t the weighting procedure assigned to the fam ily income classes u t il i z e d in the survey instrument (question 19, page 6) represents a source o f s t a t i s t i c a l bias, and does not properly r e f le c t the actual income d is tr ib u tio n o f respondents from 133 th is region. The actual d is t r ib u tio n o f fam ily income, by cla ss , among sampled w a te rc ra ft owners from region 1 is given in Table 10. TABLE 10. — Income Class D is trib u tio n o f Sampled W atercraft Owners from Region 1, 1968. No. o f Sampled Boat Owners Per Cent Under $3,000 33 3.12 $ 3,000 - $ 5,999 54 5.11 $ - $ 7,999 93 8,80 $ 8,000 - $ 9,999 142 13.43 $10,000 - $14,999 375 35.48 $15,000 - $24,999 255 24.13 $25,000 and Over 105 9.93 1,057 1 0 0 .0 0 Income Class 6 ,0 0 0 TOTALS ★ Income classes shown here are the same ‘as those u t i l i z e d in the mail questionnaire (question 19, page 6 ). In order to obtain additional in sig h t into the re latio n sh ip between fam ily income and frequency of boating p a r t ic ip a t io n , two addi­ tional tables have been prepared. An inspection o f the d is tr ib u tio n of fam ily incomes among respondents in Table 10 above shows th at the income v a ria b le was in c o rre c tly sp ecified in the regression equation.^ Tables 12 and 13 show the re la tio n s h ip between fam ily income, by cla ss , and frequency of boating p a rtic ip a tio n by sampled w a te rc ra ft owners in The weighting procedure u t il i z e d i m p li c it l y assumes a p r io r i that a constant income d is tr ib u tio n exists among sampled w ate rcraft owners in a l l study regions. TABLE 11.--Frequency o f Boating on Great Lakes by Number and Percentage o f Respondents in Selected Income Classes, Region 1, 1968. 11-21 0-10 Occasions Income Class Occasions 22-32 Occasions •k No. 33-43 Occasions 44-54 Occasions 55-65 Occasions % No. % No. 0A /? No. % No. % No. % Under $3,000 29 87.88 3 9.09 0 0 .0 0 0 0 .0 0 1 3.03 0 0.0 0 $ 3,000 - S 5,999 41 75.93 5 9.26 5 9.26 2 3.70 1 1.85 0 0 .0 0 $ 6,000 - $ 7,999 70 75.27 8 8.60 6 6.45 4 4.30 2 2.15 2 2.15 $ 8,000 - $ 9,999 113 79.58 10 7.04 6 4.23 4 2.82 2 1.41 3 2.12 $10,000 - $14,999 266 70.93 37 9.87 29 7.73 17 4.53 10 2.67 5 1.33 $15,000 - $24,999 178 69.80 22 8.63 22 8.63 8 3.14 10 3.92 6 2.35 $25,000 and Over 63 60.00 10 9.52 10 9.52 8 7.62 4 3.81 5 4.76 760 71.90 95 8.99 78 7.38 43 4.07 30 2.84 21 1.99 TOTALS 77-87 66-76 88-98 Totals 99'-109 Under $3,000 0 0 .0 0 0 0 .0 0 0 0 .0 0 0 0 .0 0 33 100.00 $ 3,000 - $ 5,999 0 0 .0 0 0 0 .0 0 0 0 .0 0 0 0 .0 0 54 100.00 $ 6,000 - $ 7,999 0 0 .0 0 0 0 .0 0 1 1.08 0 0 .0 0 93 100.00 $ 8,000 - $ 9,999 1 0.70 1 0.70 1 0.70 1 0.70 142 100.00 $10,000 - $14,999 5 1.33 4 1.07 1 0.27 1 0.27 375 100.0 0 $15,000 - $24,999 3 1.18 4 1.57 1 0.39 1 0.39 255 100.00 $25,000 and Over 3 2.8 6 2 1.91 0 0 .0 0 0 0 .0 0 105 100.00 12 1.13 11 1.04 4 0.38 3 0.28 1057 100.00 TOTALS Income classes fo llo w those used in the mail questionnaire (page 6 , question 1 9 ). TABLE 1 2 .— Frequency o f Boating on Inland Lakes and Streams by Number o f Respondents in Selected Income Classes, Region 1, 1968. 0-10 11-21 Occasions Income Class * No. Occasions 22-32 Occasions % No. % No. - % 33-43 Occasions 55-65 Occasions 44-54 Occasions No. % No. % No. % Under $3,000 21 63.64 5 15.15 2 6.06 0 0 .0 0 0 0 .0 0 2 6.06 $ 3,000 - $ 5,999 33 61.11 12 22.22 2 3.71 0 0 .0 0 3 5.55 1 1.85 $ 6,000 - $ 7,999 53 56.99 17 18.28 9 9.68 5 5.37 1 1.07 3 3.23 $ 8,000 - $ 9,999 79 55.63 20 14.09 18 12.68 8 5.63 7 4.92 3 2.11 $10,000 - $14,999 202 53.87 81 21.60 40 10.67 23 6.13 10 2.67 9 2.40 $15,000 - $24,999 137 53.73 42 16.47 23 9.02 15 5.88 10 3.92 9 3.53 $25,000 and Over 69 65.72 12 11.43 6 5.71 3 2 .86 5 4.76 4 3.81 594 56.20 189 17.88 100 9.46 54 5.11 36 3.41 31 2.93 TOTALS 77-87 66-76 88-98 Totals 99--109 Under $3,000 0 0 .0 0 0 0 .0 0 2 6.06 1 3.03 33 100.00 $ 3,000 - $ 5,999 0 0 .0 0 0 0 .0 0 2 3.71 1 1.85 54 100.00 $ 6,000 - $ 7,999 0 0 .0 0 2 2.15 3 3.23 0 0 .0 0 93 100.00 $ 8,000 - $ 9,999 2 1.41 2 1.41 1 0.70 2 1.41 142 100.0 0 $10,000 - $14,999 1 0.27 3 0.80 2 0.53 4 1.06 375 100.00 $15,000 - $24,999 3 1.18 3 1.18 6 2.35 7 2.74 255 100.00 $25,000 and Over 1 0.95 1 0.95 4 3.81 0 0 .0 0 105 100.00 7 0 .6 6 11 1.04 20 1.89 15 1.42 1057 100.00 TOTALS Income classes fo llo w those used in the mail questionnaire (page 6 , question 1 9 ). 136 Region 1 on (a ) Great Lakes and connecting waters, and (b) inland lakes and streams. A summary o f least squares s t a t is t i c s f o r the D e tro it Region is presented in Appendix F. Regression c o e ffic ie n ts presented in th at tab le are fo r the i n i t i a l equation estimated, with a l l independent variables retained in the model. However, as noted previously, the computer program u t il i z e d consisted of a stepwise d eletion procedure, whereby candidate independent variables were deleted from the i n i t i a l equation in successive ite ra tio n s u n til a l l remaining variables met a specified stopping c r it e r io n . Table 13 presents selected le a s t squares s t a t is t ic s fo r a l l independent variables retained in the fin a l regression equation fo r th is region. Table 13 shows th at one o f the "place o f storage" variables (x^) was retained in the f in a l regression equation. Registered boat owners included in the sample who stored t h e i r w a te rc ra ft a t t h e i r place o f residence during the boating season, as a group, boated less than other respondents during the study year. This va ria b le had a negative e ff e c t upon boating p a r tic ip a tio n , and was highly s ig n ific a n t s t a t i s t i c a l l y . Number-of boats owned (by sampled w a te rc ra ft owners) was p o s itiv e ly correlated with boating a c t i v i t y . Boat length was also p o s itiv e ly correlated with boating a c t i v i t y . For the sample o f registered water­ c r a f t from th is region, the number o f boating a c t i v i t y occasions (boat days) is expected to increase with boat length. This suggests that higher o verall boating p a rtic ip a tio n rates may be expected among water­ c r a ft owners who own the largest w a te rc ra ft. TABLE 13.—Statistics from the Final Regression Equation for Region 1, Detroit. Regression Coefficients 3 Variable Standard Errors of Regression Coefficients Level of . Significance Mean (a) 27.116661 (x6) -12.051651 2.100010 <.0005 Number of Boats Owned (x13) 3.069490 1.060438 .004 1.59603 Boat Length (XK ) 0.958455 0.186614 <.0005 15.92999 -0.346322 0.088178 <.0005 48.27247 1.335662 0.553897 .015 3.60833 -5.249418 2.314773 .022 .20341 Intercept Storage of Water­ craft at Permanent Home (not on a lake or river) Age of Family Head Family Size ( xie) (xi 8 ) Occupation of Family Head-Professional ( Xig) R = . 3409c R2 = .1163d 6.76109 .40019 Syx = 29.6016e Values which appear in this column for X13 , X14 , Xi 6 * and Xl 8 are for continuous variables, and show the estimated effect of these variables on the slope of the regression lin e . Values for Xg and X19 assume equal slope coefficients for both zero-one variables. These la t te r values give the estimated net effect of the two variables on the intercept. bFor 1,050 degrees of freedom. cMultiple correlation coefficient. A Coefficient of multiple determination. eStandard error of estimate. 138 Age of fam ily head, as in the i n i t i a l equation, was negatively correlated with recreational boating p a r tic ip a tio n , and th is re s u lt was highly s ig n ific a n t s t a t i s t i c a l l y . Family size was again also p o s itiv e ly related with boating p a rtic ip a tio n . In the fin a l equation, one o f the occupation variables (x-jg) was also retained. For the sample of w atercraft owners from th is region, boat owners c la s s ifie d as holding professional occupations appear to p a rtic ip a te in boating a c t i v i t y s ig n ific a n tly less than boat owners holding other occupations. The in te rp re ta tio n of th is finding would be th at the net e ffe c t o f the professional occupations c la s s ific a tio n (x-jg) would be to change the level o f the intercep t negatively by an estimated 5.2 boat days ( a c t iv i t y occasions). Since a l l dummy variables included in the i n i t i a l equation were deleted in the fin a l ite r a t io n (except fo r x^ and x^g); i t should be noted th a t the combined net e ffe c ts of the deleted categorical variables — including those dropped in order to obtain a determinate so lutio n — are contained in the intercep t term shown in Table 13. Also, in te rc o rre ­ lations between variables retained in the f in a l equation and those deleted in the computer program would make the regression c o e ffic ie n ts of independent variables shown in Table 13 less r e l ia b l e . dependent variable is Where the influenced by the combined e ffe c ts o f i n t e r ­ correlated independent va ria b les , part o f the e f f e c t o f the deleted variable is contained in the c o e ffic ie n t o f the va ria b le retained in the equation. I f the regression model is to be used fo r p red iction , a decision has to be made as to whether or not both in te rc o rrela ted independent variables should be retained in the equation, even though 139 one o f the variables may lack s t a t i s t i c a l s ig n ific a n c e . A c o rre la tio n matrix was obtained fo r a l l independent va riables included in the regression equation estimated fo r the State o f Michigan as a whole, and re su lts o f th is analysis w i l l be presented l a t e r in th is section. Region 6 — Lansing This region is located in the south-central portion o f Michigan, and consists o f the Lansing Standard Metropolitan S t a t i s t i c a l Area (SMSA). There are three counties contained w ith in th is region: Ingham, Eaton, and Clinton. The income variables {Xgg, Xgy» and the cross-product o f income and age— x^g) were not s t a t i s t i c a l l y s ig n ific a n t a t the .05 level in this region. In view o f the procedure used in assigning weights to the various income classes supplied respondents, however, fu rth e r examination w ill be undertaken with regard to the re la tio n s h ip between fam ily income and boating p a rtic ip a tio n . Table 14 shows the actual d is tr ib u tio n of reported family income among respondents in the Lansing Region, by class. Table 14 shows th at the weighting procedure followed in speci­ fying the income variables did not adequately r e f l e c t differences in income d is trib u tio n s between survey respondents from the various study regions id e n tif ie d . Given the nature of the income classes supplied respondents in the mail questionnaire, an a lte r n a t iv e procedure fo r specifying the income v a ria b le in the regression model would be to tr e a t i t as a dummy v a ria b le , assigning zero ( 0 ) or one ( 1 ) values to the various income classes. determine the re la tio n s h ip . This would have permitted the data to 140 TABLE 1 4 .--Income Class D is trib u tio n o f Sampled W atercraft Owners, Region 6 , 1968. No. o f Sampled Boat Owners Per Cent 4 1 .53 $ 3,000 - $ 5,999 19 7.25 $ 6,000 - $ 7,999 22 8.40 $ 8,000 - $ 9,999 46 17.56 $10,000 - $14,999 103 39.31 $15,000 - $24,999 55 20.99 $25,000 and Over 13 4.96 262 1 0 0 .0 0 Income Class ★ Under $3,000 TOTALS Income classes follow those used in the mail questionnaire (question 19, page 6 ). In order to fu rth e r examine the re la tio n s h ip between fam ily income and boating p a r t ic ip a tio n , two additional tables have been pre­ pared. Table 15 shows the re la tio n s h ip between respondent income class, and frequency of boating p a rtic ip a tio n on Michigan Great Lakes. Table 16 has been prepared to show the re la tio n s h ip between respondent income class and frequency o f boating p a rtic ip a tio n on Michigan Inland Lakes and Streams fo r the Lansing Region. I t should be noted th a t i t would be possible to obtain additional insights into the v a ria tio n in boating p a rtic ip a tio n among respondents from the various study regions by estimating the regression equation separately from (a) respondents boating on inland lakes and streams, and (b) Great Lakes and connecting waters. On the basis o f the data presented in Tables 15 and 16, i t appears th at frequency of boating p a rtic ip a tio n tends to be greater TABLE 1 5 .--Frequency o f Boating on Great Lakes by Number and Percentage o f Respondents in Selected Income Classes, Region 6 , 1968. 0-1 0 11-21 Occasions Income Class k No. c/ to Occasions 22-32 Occasions 33-43 Occasions No. % No. % No. % 44-54 Occasions 55-65 Occasions No. % No. % 0 0 .0 0 0 0 .0 0 4 100.00 0 0 .0 0 0 0 .0 0 0 0 .0 0 $ 3,000 - $ 5,999 18 94.74 0 0.00 0 0 .0 0 0 0 .0 0 0 0 .0 0 1 5.26 $ 6,000 - $ 7,999 21 95.45 0 0 .0 0 1 4.55 0 0 .0 0 0 0 .0 0 0 0 .0 0 $ 8,000 - $ 9,999 36 78.26 3 6.52 3 6.52 0 0 .0 0 2 4.35 0 0 .0 0 $10,000 - $14,999 91 88.35 5 4.86 2 1.94 0 0 .0 0 3 2.91 1 0.97 $15,000 - $24,999 44 80.00 1 1.82 4 7.27 4 7.27 0 0 .0 0 1 1.82 $25,000 and Over 13 100.00 0 0 .0 0 0 0 .0 0 0 0 .0 0 0 0 .0 0 0 0 .0 0 227 86.64 9 3.44 10 3.82 4 1.53 5 1.91 3 1.14 Under $3,000 TOTALS 66 - 76 ' 88-98 77--87 Totals Under $3,000 0 0 .00 0 0 .0 0 0 0 .0 0 4 100.00 $ 3,000 - $ 5,999 0 0 .0 0 0 0 .0 0 0 0 .0 0 19 100.00 $ 6,000 - $ 7,999 0 0 .0 0 0 0 .0 0 0 0 .0 0 22 100.00 $ 8,000 - $ 9,999 2 4.35 0 0 .0 0 0 0 .0 0 46 100.00 $10,000 - $14,999 0 0 .0 0 1 0.97 0 0 .0 0 103 100.00 $15,000 - $24,999 0 0 .0 0 0 0 .0 0 1 1.82 55 100.00 $25,000 and Over 0 0 .0 0 0 0 .0 0 0 0 .0 0 13 100.0 0 2 0.76 1 0.38 1 0.38 262 100.00 TOTALS Income classes fo llo w those used in the mail qu estionnaire (page 6 , question 1 9 ). « TABLE 1 6 .--Frequency o f Boating o n 'In lan d Lakes and Streams, by Number and Percentage o f Respondents in Selected Income Classes, Region 6 , 1968. Occasions Income Class * No. . Occasions 11-21 0-10 % No. 22-32 Occasions 33-43 Occasions 44-54 Occasions 55-65 Occasions JO No. % No. % No. % No. % 0 .0 0 0 0 .0 0 0 0 .0 0 1 25.00 0 0 .0 0 Under $3,000 2 50.00 0 $ 3,000 - $ 5,999 7 36.84 6 31.58 3 15.79 2 10.53 0 0 .0 0 1 5.26 $ 6,000 - $ 7,999 14 63.63 0 0 .0 0 2 9.09 1 4.55 1 4.55 2 9.09 $ - $ 9,999 17 36.95 8 17.39 4 8.70 4 8.70 2 4.35 6 13.04 $10,000 - $14,999 33 32.04 16 15.54 12 11.65 16 15.54 9 8.73 11 10.68 $15,000 - $24,999 24 43.64 8 14.54 12 21.81 1 1.82 2 3.64 5 9.09 $25,000 and Over 4 30.77 1 7.69 0 0 .0 0 3 23.08 1 7.69 2 15.39 101 38.55 39 14.89 33 12.60 27 10.30 16 6.11 27 10.30 8 ,0 0 0 TOTALS 66 --76 . 77-87 Totals 99--109 88-98 Under $3,000 0 0 .0 0 1 25.00 0 0 .0 0 0 0 .0 0 4 100.00 $ 3,000 - $ 5,999 0 0 .0 0 0 0 .0 0 0 0 .0 0 0 0 .0 0 19 100.00 $ 6,000 - $ 7,999 0 0 .0 0 2 9.09 0 0 .0 0 0 0 .0 0 22 100.00 $ 8,000 - $ 9,999 1 2.17 2 4.35 2 4.35 0 0 .0 0 46 100 .0 0 $10,000 - $14,999 3 2.91 1 0.97 0 0 .0 0 2 1.94 103 100.00 $15,000 - $24,999 1 1.82 1 1.82 1 1.82 0 0 .0 0 55 100.00 $25,000 and Over 0 0 .0 0 1 7.69 1 7.69 0 0 .0 0 13 100.0 0 5 1.91 8 3.05 4 1.53 2 0.76 262 100.00 TOTALS Income classes fo llo w those used in the mail questionnaire (page 6 , question 1 9 ). 143 on inland lakes and streams than on great lakes among respondents from the Lansing Region. Only 38.55 per cent o f a l l respondents indicated that they went boating on while more than 86 0 -1 0 occasions on inland lakes and streams; per cent o f a l l respondents indicated th a t they boated on 10 or less occasions on Michigan Great Lakes. Also, the re latio n sh ip between fam ily income and frequency of boating p a r t i c i ­ pation on Michigan Great Lakes tends to be p o s itive only w ithin a given range, increasing with fam ily income up through the $15,000 - $24,999 class and declining th e re a fte r. In addition to the regression resu lts presented in Appendix F, selected s t a t is t i c s w il l also be presented here f o r the f in a l equation estimated.-' Table 17 gives selected le a s t squares s t a t is t i c s from the f in a l regression equation. The place o f storage variables (x^ and x^) were retained in the f in a l equation, and were highly s ig n ific a n t. The net e f f e c t o f these two classes o f variables upon boating p a rtic ip a tio n .was highly negative in both cases. Sampled w a te rcraft owners who indicated th a t they stored t h e ir w a te rc ra ft a t t h e i r permanent residence during the boating season, as a class, boated s ig n if ic a n t ly less than •watercraft owners who reported storing t h e i r boats a t other locations. M u ltip le boat ownership was also p o s itiv e ly associated with boating p a rtic ip a tio n in the fin a l equation estimated fo r th is region. Just as in the D e tro it Region, higher boating p a rtic ip a tio n rates appear to be associated with sampled w ate rcraft owners from the Lansing Region who reported owning more than one registered (or unregistered) water­ c ra ft. TABLE 17,—Statistics from the Final Regression Equation for Region Regression Coefficients Variable Standard Error of Regression Coefficients 6, Lansing. Level of . Significance Mean 35.459359 7.56418 -15.278457 4.904263 .002 .38550 (x7) -34.831689 10.317919 .001 .04580 Number of Boats Owned (X13 ) 13.016858 2.487568 <.0005 Income Squared ( x37) 0.425664 0.145531 .004 33.54481 -0.110237 0.036135 .003 253.26649 Intercept (a) Storage of Water­ craft at Permanent Home (not on a lake or river) Storage of watercraft at waterfrontage located at Permanent home lo t Income times age .(V ( X38^ R = .4615C R2 = . 2130d 5 1.71374 = 34.2789e Values which appear in this column for Xi 3 , X3 7 , and X38 give estimated effects on the slope of the regression lin e. Values for X6 and X7 assume equal slope coefficients. These la t te r values give the estimated effects of the two variables on the intercept. ^With 255 degrees of freedom. cMultiple correlation coefficient. j Coefficient of multiple determination. eStandard error of estimate. 145 Income squared (x-^ ) and the cross-product o f Income and age (x^g) were also retained in the f in a l regression equation, and were highly s ig n ific a n t. However, the significance o f th is find in g should be con­ sidered cautiously since the values used fo r these variables in the regression model appear to be biased. In order to te s t the r e la t io n ­ ship between boating p a rtic ip a tio n and fam ily income, zero-one values might be inserted in the regression equation fo r the various income classes used in the survey instrument. Region 7C— Saginaw Bay The Saginaw Bay Region is located in the north central portion of Michigan's Lower Peninsula. I t extends from the center o f the state on the western edge to the Lake Huron Shoreline on the eastern side. This region contains abundant inland lakes and streams in the eastern and central portions, centering on the Houghton Lake area, and borders upon one o f the Great Lakes in Arenac and Iosco counties. to ta l o f six counties are contained w ith in th is region: A Roscommon, Ogemaw, Iosco, Clare, Gladwin, and Arenac (see Figure 1, Chapter I I I ) . For th is region, selected s t a t is t i c s from the i n i t i a l regression equation are summarized in Appendix F. None o f the computed regression co e fficien ts fo r the variables contained in the i n i t i a l equation had significance p ro b a b ilitie s of .05 per cent or less. Another in te re s tin g finding in th is region re lates to the income d is trib u tio n among sampled w ate rcraft owners. A much la rg e r proportion of respondents from region 7C appear to be grouped in the lower range of income classes examined than in the previous two regions. For 146 example, 60 per cent o f a l l respondents from region 7C reported 1968 family incomes o f less than $8,000 in 1968. Moreover, 12.50 per cent reported incomes o f less than $3,000; and 29.17 per cent reported annual incomes between $3,000 - $5,999. regions 1 and 6. In region 6, These findings contrast with those fo r only 17.16 per cent o f a l l respondents reported annual incomes o f less than $8,000 during 1968. In region 1, a s im ila r proportion appeared to e x is t--a n estimated 17.02 per cent o f those responding to the survey reported fam ily incomes of less than $8,000. The actual income d is tr ib u tio n of respondents f o r Region 7C is given in Table 18. TABLE 18. — Income Class D is trib u tio n o f Sampled W atercraft Owners from Region 7C, 1968. No. o f Sampled Boat Owners Per Cent Under $3,000 15 12.50 $ 3,000 - $ 5,999 35 29.17 $ 6,000 - $ 7,999 22 18.33 $ 8,000 - $ 9,999 16 13.33 $10,000 - $14,999 21 17,50 $15,000 - $24,999 8 6.67 $25,000 and Above 3 2.50 120 1 0 0 .0 0 Income Class * TOTALS * Income classes fo llo w those used in the mail questionnaire (question 19, page 6 ). The median fam ily income f o r respondents from Region 7C is estimated to be approximately $6,908.44. This s t a t i s t i c was computed from the data presented in Table 18 above, and represents an approxi­ mation o f the actual median. I t is in te rp o late d based upon the ( i m p l i c i t ) assumption th a t individual values w ith in the median class ($6,000 - $7,999) are evenly d is trib u te d over th a t i n t e r v a l. Given the manner in which income data was reported by respondents in the mail questionnaire, the true median cannot be determined from the d is tr ib u tio n shown in Table 18. Actual (ungrouped) data on fam ily income would have to be used in order to determine the true median.^ Following a s im ila r procedure, median fam ily income was c a l­ culated fo r respondents from the D e tro it and Lansing Regions as w e ll. The grouped data on fam ily income in Tables 10 and 14 were u t i l i z e d . For the study year (1968), the median fam ily income o f respondents from the D e tro it Region was estimated to be approximately $12,753.11, and $11,940.59 fo r respondents from the Lansing Region. Based upon these estimates, median fam ily income appears to be c le a r ly higher among respondents from the D e tro it and Lansing Regions than th at calculated fo r the Saginaw Bay Region. ^An estimate of median fam ily income was calculated fo r a l l respondents from Region 7C by using an in te rp o la tio n formula: i ( n / 2 - F) Md = L + ---------------f where: Md L i f F = = = = = the median, the lower l i m i t of the median class, the width o f the median class, the frequency fo r the median class, the cummulative frequency fo r a l l classes below the median class, n = the to ta l number of values o f X (the sum of a l l frequencies). See, W. A. Spurr, L. S. Kellogg, and J. H. Smith, Business and Economic S ta t is tic s (Rev. e d itio n ; Homewood, I l l i n o i s : Richard D. Irw in , I n c . , 1961), pp. 187-88. 148 Caution should be exercised when considering these s t a t i s t i c s . While i t is possible to compute a median value from an open-ended frequency d is t r ib u t io n , the mean value cannot be determined i f the end values are unknown. Also, the median calculated value, as noted previously, should be regarded as only an approximation of the true median because of the uneven d is tr ib u tio n o f values w ith in the median class i t s e l f , i . e . , more than o ne-half o f the o rig in a l values may l i e on one side o f the interp olated median. Per cent values shown in Tables 10, 14, and 18 were treated as ordinary frequencies, and were so u t il i z e d in the in te rp o la tio n formula used in c a lc u la tin g median values fo r each d is tr ib u tio n o f regional fam ily income. Further examination o f the re la tio n s h ip between fam ily income and boating p a rtic ip a tio n fo r the Saginaw Bay Region may be made by re fe rrin g to Tables 19 and 20. Table 19 shows the d is trib u tio n of boating a c t i v i t y occasions by fam ily income class fo r boating p a r t i c i ­ pation on Michigan Great Lakes (and connecting w aters). Table 20 shows the re la tio n s h ip between fam ily income class and frequency of boating p a rtic ip a tio n on Michigan Inland Lakes and Streams fo r the Saginaw Bay Region. Generally, frequency o f boating p a rtic ip a tio n is shown to have considerable v a ria tio n among respondents from th is region. While annual boating p a rtic ip a tio n tends to be higher on Michigan Lakes and Streams, no c le a r pattern appears to e x is t. For example, an estimated 11.67 per cent o f a l l respondents indicated th a t they boated on Inland Lakes and Streams on 11 - 21 occasions; while only 5.83 per cent o f a l l respondents indicated boating on Great Lakes on 11 - 21 occasions. TABLE 1 9 .— Frequency o f Boating on Great Lakes by Numbers o f Respondents in Selected Income Classes, Region 7C, 1968. 11-21 0-10 Occasions Income Class * No. % Occasions 22-32 Occasions 33-43 Occasions No. % No. % No. % Under $3,000 13 86.6 6 1 6.67 0 0 .0 0 0 0 .0 0 $ 3,000 - $ 5,999 32 91.43 3 8.57 0 0 .0 0 0 0 .0 0 $ 6,000 - $ 7,999 21 95.45 1 4.55 0 0 .0 0 0 0 .0 0 $ 8,000 - $ 9,999 14 81.50 1 6.25 1 6.25 0 0 .0 0 $10,000 - $14,999 18 85.72 1 4.76 0 0 .00 1 4.76 $15,000 - $24,999 7 87.50 0 0 .0 0 1 1 12.50 0 0 .0 0 $25,000 and Over 3 100.00 0 0 .0 0 0 0 .0 0 0 0 .0 0 108 90.00 7 5.83 2 1.67 1 0.83 TOTALS 44-54 55-65 Totals Under $3,000 0 0 .0 0 1 6.67 15 100.00 $ 3,000 - $ 5,999 0 0 .0 0 0 0 .0 0 35 100.00 $ 6,000 - $ 7,999 0 0 .0 0 0 0 .0 0 22 100.00 $ 8,000 - $ 9,999 0 0 .0 0 0 0 .0 0 16 100.0 0 $10,000 - $14,999 0 0 ,0 0 1 4.76 21 100.00 $15,000 - $24,999 0 0 .0 0 0 0 .0 0 8 100.00 $25,000 and Over 0 0 .0 0 0 0 .0 0 3 100.00 0 0 .0 0 2 1.67 120 100.00 TOTALS Income classes fo llo w those used in the mail questionnaire (question 19, page 6 ) . TABLE 2 0 .--Frequency o f Boating on Inland Lakes and Streams by Number o f Respondents in Selected Income Classes, Region 7C, 1968. 11-21 0-10 Occasions ★ Occasions 22-32 Occasions 33-43 Occasions 55-65 Occasions 44-54 Occasions No. % No. % No. % No. % 13.33 1 6.67 0 0 .0 0 0 0 .0 0 1 6.67 2 5.71 4 11.43 1 2.8 6 0 0 .0 0 3 8.51 50.00 3 13.64 2 9.09 0 0 .0 0 1 4.54 3 13.64 10 62.50 2 12.50 2 12.50 0 0 .0 0 0 0 .00 1 6.25 $10,000 - $14,999 7 33.33 3 14.29 3 14.29 3 14.29 2 9.52 2 9.52 $15,000 - $24,999 3 37.50 2 25.00 0 0 .0 0 2 25.00 0 0 .0 0 1 12.50 $25,000 and Over 1 33.34 0 0 .0 0 0 0 .0 0 1 33.33 0 0 .0 0 0 0 .0 0 65 54.17 14 11.67 12 10.00 7 5.83 3 2.50 11 9.17 No. % No. Of Jo Under $3,000 11 73.33 2 $ 3,000 - $ 5,999 22 62.86 $ 6,000 - $ 7,999 11 $ 8,000 - $ 9,999 Income Class TOTALS 66 --76 77-87 Totals 99--109 88-98 Under $3,000 0 0 .0 0 0 0 .0 0 0 0 .0 0 0 0 .0 0 15 100.00 $ 3,000 - $ 5,999 0 0 .0 0 0 0 .0 0 1 2 .8 6 2 5.71 35 100.00 $ 6,000 - $ 7,999 1 4.55 0 0 .0 0 0 0 .0 0 1 4.54 22 100.00 $ 8,000 - $ 9,999 0 0 .0 0 0 0 .0 0 1 6.25 0 0 .0 0 16 100.00 $10,000 - $14,999 0 0 .0 0 0 0 .0 0 0 0 .0 0 1 4.76 21 100.00 $15,000 - $24,999 0 0 .0 0 0 0 .0 0 0 0 .0 0 0 0 .0 0 8 100 .0 0 $25,000 and Over 0 0 .0 0 0 0 .0 0 1 33.33 0 0 .0 0 3 100.00 1 0.83 0 0 .0 0 3 2.50 4 3.33 120 100.0 0 TOTALS •k Income classes fo llo w those used in the mail questionnaire (question 19, page 6 ) . 151 S im ila r ly , 10.00 per cent o f respondents reported boating on Inland Lakes and Streams between 22 - 32 occasions, w hile only 1.67 per cent o f the respondents from th is region reported going boating on 22 - 32 occasions. Selected s t a t i s t i c s from the f i n a l regression equation estimated f o r Region 7C are shown in Table 21. variables were retained in the model a f t e r the sp e cifie d stopping c r i - te rio n was met: size o f re g is tere d boat owner ( x-|q ) * anc* occu­ fam ily pation o f fam ily head— service worker Only two o f the independent .■ j )* The standard e rro r o f estimate (S ) is the standard d ev ia tio n yx o f the observed values o f the dependent v a ria b le around the regression l in e . I f the observed values are scattered w idely around the regression l i n e , estimated values o f the dependent v a ria b le based upon the e s t i ­ mating l in e w il l not be very accurate. Table 21 shows th a t the standard e rro r of estimate in the Saginaw Bay equation is 26.93. For an in d i­ vidual forecast o f y (boat days), one could say th a t the tru e value of y would l i e w ith in + 26.93 boat days w ith two chances out o f three of being c o rre c t. In th is region (as well as a l l others) the standard e rro r o f estimate is q u ite larg e . Thus, predicted values o f y w i l l not be very accurate using th is model. Also, a very small percentage o f the t o ta l variance in the dependent v a ria b le is explained by th is model in Region 7C. The computed c o e f f ic ie n t of m u ltip le determination is only .1208, i n d i ­ cating th a t approximately 12 per cent o f the to ta l variance in the dependent v a ria b le is explained by the independent variables retained in the f in a l equation. TABLE 21 . —Statistics from the Final Regression Equation for Region 7C, Saginaw Bay. Regression Coefficients Variable Standard Error of Regression Coefficients Level of Significance (a) 9.693997 5.267375 Family Size (x18) 4.832810 1.649592 .004 Occupation of Family Head—Service Worker (X2?) 35.349367 13.716022 .001 Intercept R = .3475c R2 = .1208d Mean 2.825 .0333 Suy = 26.9332e The value which appears in this column for Xi 8 gives the estimated effect of the variable upon the slope of the regression lin e . The value for X27 assumes a constant slope coefficient. This la t te r value gives the estimated net effe ct of the variable on the intercept value. dWith 117 degrees of freedom. cMultiple correlation coefficient. ^Coefficient of multiple determination. eStandard error of estimate. 153 Region 10--Traverse Bay The Traverse Bay Region is located in the Northwest portion of Michigan's lower peninsula. The area is bounded along i t s westerly edge by the shoreline o f Lake Michigan. Substantial public recreation f a c i l i t i e s are located in th is area in the form o f sta te forests and parks, and the Manistee National Forest. Sleeping Bear Dunes, which has been investigated as a possible National Recreation Area, is also located w ith in th is region. th is region: There are ten counties contained w ith in Manistee, Wexford, Missaukee, Benzie, Grand Traverse, Kalkaska, Leelanau, Antrim, Charlevoix, and Emmet. the i n i t i a l S t a tis tic s from regression equation are summarized fo r th is region in Appendix F. The income variables (x^g, and x^g) were s ig n if ic a n t ly correlated with boating p a rtic ip a tio n in th is region. However, th is re s u lt should be discounted in view o f the lim ita tio n s noted in the s p e c ific a tio n o f these v a ria b le s . The d is t r ib u t io n of to ta l family income among respondents from th is region is shown in Table 22 below. Table 22 shows th at 41.41 per cent o f a l l respondents from Region 10 had fam ily incomes which were less than $8,000 annually during 1968. Nearly 9 per cent o f a l l respondents reported incomes less than $3,000, and 14.84 per cent reported having incomes between $3,000 - $5,999. These findings should be considered ca u tio u s ly, o f course, since only about 26 per cent o f the to ta l number o f questionnaires mailed were a c tu a lly completed and u t i l i z e d in the s t a t i s t i c a l an alysis. Somewhat higher response rates were obtained from respondents in the three fo llo w up control counties {Ingham, Grand Traverse, and Leelanau), but the high 154 TABLE 2 2 .--Income Class D is trib u tio n o f Sampled W atercraft Owners, Region 10, 1968. * No. o f Sampled Boat Owners Per Cent Under $3,000 23 8.99 $ 3,000 - $ 5,999 38 14.84 $ 6,000 - $ 7,999 45 17.58 $ 8,000 - $ 9,999 42 16.40 $10,000 - $14,999 53 20.70 $15,000 - $24,999 36 14.07 $25,000 and Over 19 7.42 256 1 0 0 .0 0 Income Class TOTALS *Family income classes are the same as those u t il i z e d in the mail questionnaire (question 19, page 6 ) . rate o f non-response raises questions concerning the v a l i d i t y o f the income d is trib u tio n s shown in th is study. The estimated median fam ily income fo r respondents from Region 10 is $9,047.04. This r e s u lt contrasts with approximate median incomes of $6,908.44 fo r Region 7C, $12,753.11 f o r Region 1, and $11,940.59 fo r Region 6. The re la tio n s h ip between respondent incomes and boating p a rtic ip a tio n fo r the Traverse Bay Region is fu rth e r examined in Tables 23 and 24. These tables in d ic a te th a t frequency o f boating p a rtic ip a tio n fo r a l l respondents was g rea ter on Michigan inland lakes and streams than on Great Lakes. For example, an estimated 17.58 per cent o f a l l respondents indicated boating on Michigan inland lakes and streams on 11 - 21 occasions, while only 7.81 per cent o f respondents indicated boating on Michigan Great Lakes on 11 - 21 occasions. The data in these tables TABLE 2 3 .— Frequency o f Boating on Great Lakes by Number and Percentage o f Respondents in Selected Income Classes, Region 10, 1968. 0 -■10 Occasions Income Class * No. 22 -■32 11-■21 % Occasions Occasions 33-■43 Occasions 44-■54 Occasions 55- 65 Occasions No. % No. % No. % No. % No. % Under $3 ,000 22 95.65 0 0 .0 0 0 0 .0 0 1 4.35 0 0 .0 0 0 0 .0 0 $ 3,000 - $ 5,999 35 92.11 2 5.26 0 0 .0 0 0 0 .0 0 1 2.63 0 0 .0 0 $ 6,000 - $ 7,999 35 77.78 3 6.67 2 4.44 3 6.67 0 0 .0 0 1 2 .2 2 $ 8 ,000 - $ 9,999 34 80.95 4 9.53 2 4.76 0 0 .0 0 0 0 .0 0 1 2.38 $10,000 - $14,999 42 79.25 3 5.66 4 7.55 2 3.77 2 3.77 0 0 .0 0 $15,000 - $24,999 26 72.22 6 16.67 2 5.55 1 2.78 1 2.78 0 0 .0 0 $25,000 and Over 13 68.43 2 10.53 0 0 .0 0 1 5.26 1 5.26 0 0 .0 0 207 80.86 20 7.81 10 3.91 8 3.13 5 1.95 2 0.78 TOTALS 88 --98 77--87 66 --76 Totals Under $3t,000 0 0 .0 0 0 0 .0 0 0 0 .0 0 23 100 ,. 00 $ 3,000 - $ 5,999 0 0 .0 0 0 0 .0 0 0 0 .0 0 38 100 ,. 00 $ 6,0 0 0 - $ 7,999 0 0 .0 0 0 0 .0 0 1 2 .22 45 100 ,. 00 $ 8,000 - $ 9,999 0 0 .0 0 0 0 .0 0 1 2.38 42 100 ,. 00 $10,000 - $14,999 0 0 .0 0 0 0 .0 0 0 0 .0 0 53 100 ,. 00 $15,000 - $24,999 0 0 .0 0 0 0 .0 0 0 0 .0 0 36 1 0 0 ,. 00 $25,000 and Over 1 5.26 0 0 .0 0 1 5.26 19 100 .00 1 0.39 0 0 .0 0 3 1.17 256 100 .00 TOTALS Income classes fo llo w those used in the mail questionnaire (page 6 , question 1 9 ). TABLE 2 4 .— Frequency o f Boating on Inland Lakes and Streams by Number and Percentage o f Respondents in Selected Income Classes, Region 10, 1968. 11-21 0-1 0 Occasions •k Income Class % No. Occasions 22-32 Occasions 33-43 Occasions 55-65 Occasions 44-54 Occasions No. % No. % No. % No. % No. % Under $3,000 13 -56.52 3 13.04 3 13.04 1 4.35 0 0 .0 0 1 4.35 $ 3,000 - $ 5,999 15 39.47 8 21.05 3 7.90 0 0 .0 0 1 2.63 3 7.90 $ 6,000 - $ 7,999 22 48.89 13 28.89 3 6.67 2 4.44 3 6.67 1 2 .22 $ 8,000 - $ 9,999 23 54.76 4 9.53 4 9.53 2 4.76 1 2.38 3 7.14 $10,000 - $14,999 23 43.40 8 15.09 10 18.87 5 9.43 2 3.77 1 1.89 $15,000 - $24,999 16 44.44 8 22 .2 2 4 11.11 1 2.78 1 2.78 3 8.33 $25,000 and Over 10 52.64 1 5.26 2 10.53 1 5.26 1 5.26 1 5.26 122 47.66 45 17.58 29 11.33 12 4.69 9 3.51 13 5.08 TOTALS 66 --76 8 8 - 98 77-87 Totals 99-109 Under $3,000 0 0 .0 0 0 0 .0 0 2 8.70 0 0 .0 0 23 100.00 $ 3,000 - $ 5,999 2 5.26 0 0 .0 0 2 5.26 4 10.53 38 100.0 0 $ 6,000 - $ 7,999 0 0 .0 0 0 0 .0 0 0 0 .0 0 1 2 .2 2 45 100.00 $ 8,000 - $ 9,999 1 2.38 0 0 .0 0 3 7.14 1 2.38 42 100.00 $10,000 - $14,999 0 0 .0 0 0 0 .0 0 3 5.66 1 1,89 53 100.00 $15,000 - $24,999 1 2.78 1 2.78 0 0 .0 0 1 2.78 36 100.00 $25,000 and Over 0 0 .0 0 1 5.26 2 10.53 0 0 .0 0 19 100.00 4 1.56 2 0.78 12 4.6^ 8 3.12 256 100.00 TOTALS ir Income classes fo llo w those used in the mail questionnaire (page 6 , question 19). 157 also suggest th at frequency of boating p a rtic ip a tio n may have a non­ lin e a r re lation sh ip with family incom e-increasing up to a threshhold level of income and declining th e re a fte r. S ta tis tic s fo r the fin a l regression equation are summarized fo r the Traverse Bay Region in Table 25. The horsepower ra tin g of the primary w atercraft engine used (x^) was p o s itiv e ly correlated with boating p a rtic ip a tio n in Region 10. This finding suggests th at higher levels of boating p a rtic ip a tio n e x is t in th is region among w atercraft owners having larger engines. I t may also indicate th a t r e l a t i v e ly higher rates of boating p a rtic ip a tio n e x is t on Michigan Great Lakes where large w atercraft engines are more e a s ily accommodated. Storage of w ate rcraft variables (x^ and Xg) also had a p o s itive net e f f e c t upon boating p a rtic ip a tio n . Watercraft owners who stored sampled w atercraft at t h e ir permanent residence* which was located on waterfrontage, as a class, had a p ositive e ff e c t on boating p a rtic ip a tio n . Sampled boat owners from th is region who stored th e ir w ate rcraft a t a commercial marina during the boating season (Xg) also had a p ositive e f f e c t upon boating p a rtic ip a tio n . M u ltip le boat ownership ( * 1 3 ) also was p o s itiv e ly correlated with boating p a rtic ip a tio n , and th is re s u lt was s ig n ific a n t a t the .001 level of p ro b a b ility . Age o f household head squared was negatively correlated with boating p a rtic ip a tio n . This indicates th at there is a non-linear re lation sh ip between age and boating p a rtic ip a tio n . The income variables (xgg, * 3 7 * and x^g) were a l l s ig n if ic a n t ly correlated with boating p a rtic ip a tio n in this region. However, there appears to be a strong likeliho od that this re s u lt is biased. Further examination TABLE 25.—Statistics from the Final Regression Equation for Region 10, Traverse Bay. Regression Coefficients Variable Intercept Standard Error of Regression Coefficients Level of . Significance Mean (a) 59.996111 12.607039 Horsepower of Primary Watercraft Engine ( * 5) 0.103405 0.045264 .023 32.28906 Storage of Watercraft at Residence located on waterfrontage (x 7 ) 11.463108 4.392955 .010 0.27734 Storage of Watercraft at Commercial Marina during Boating Season (x8 ) 20.754596 7.472134 .006 0.08594 Number of Boats Owned (X13 ) 6.105275 1.738332 .001 1.85156 Age Squared (X17 ) -0.009359 0.002508 <.0005 -15.251885 4.479506 .001 4.44961 0.499931 0.229369 .030 28.40261 0.148740 0.052964 <.0005 231.85996 Family Income ^X36^ (x37) Income Squared Income Times Age (X38^ R = .4271° R2 = .1824d 3052.99219 Suy = 29.6514e yx aValues in this column for X5 , X13 , X17 , X3 6 , X3 7 , and X38 give the estimated effects of the individual variables on the slope of the regression lin e . Values fo r variables X7 and Xs assume equal slope coefficients for each categorical class. These la tte r values give the estimated net change in intercept attributable to specific zero-one variables in the two classes considered. kwith 222 degrees of freedom. cMultiple correlation coefficient. ^Coefficient of multiple determination. eStandard error of estimate. 159 o f the re la tio n s h ip between fam ily income and boating p a r tic ip a tio n has been undertaken in Tables 22, 23, and 24 in th is section. Region 12A— M arquette-Iron Mountain The M arquette-Iron Mountain Region is located in Michigan's Upper Peninsula. I t bisects the Upper Peninsula--extending from the Lake Superior shoreline on i t s n o rth e rly edge to Lake Michigan on i t s southerly side. Four counties are wholly contained w ith in th is region: Iron, Dickinson, Marquette, and A lger. Regression re s u lts from the i n i t i a l equation are summarized fo r th is region in Appendix F. No s ig n if ic a n t re la tio n s h ip appears to e x is t between the fam ily income v a ria b le s (x^g, x .^ , and x^g) and boating p a r t ic ip a t io n . The actual d is t r ib u t io n o f fam ily income among respondents from Region 12A is shown in Table 26 below. The computed median fam ily income fo r the 119 respondents from Region 12A is approximately $9,046.53. This fig u re can be compared with s im ila r s t a t i s t i c s computed f o r other Michigan Study Regions: Region 1— $12,753.11 , Region 6— $1 1,940.59, Region 7C— $ 6 ,90 8.44 , and Region 1 0 --$ 9 ,0 4 7 .0 4 . For Region 12A respondents, n early 59 per cent had reported fam ily incomes of less than $10,000 annually. A to ta l o f 27.72 per cent o f a l l respondents reported incomes of less than $6 , 0 0 0 annually; and 12.60 per cent indicated receiving annual incomes of less than $3,000 annually. Data r e la t in g to frequency o f boating in d ic a te th a t respondents from Region 12A p a rtic ip a te d more often in boating a c t i v i t i e s on inland 160 TABLE 26. — Income Class D is trib u tio n o f Sampled W atercraft Owners, Region 12A, 1968. Income Class No. o f Sampled Boat Owners * Per Cent Under $3,000 15 12.60 $ 3,000 - $ 5,999 18 15.12 $ 6,000 - $ 7,999 15 12.60 $ 8,000 - $ 9,999 22 18.49 $10,000 - $14,999 33 27.74 $15,000 - $24,999 11 9.25 5 4.20 119 1 0 0 .0 0 $25,000 and Over TOTALS it Income classes fo llo w those used in the mail questionnaire (question 19, page 6 ). lakes and streams th at upon Michigan Great Lakes or connecting waters. For example, Table 27 shows th at approximately 8 per cent o f a l l respond­ ents p artic ip ate d in boating on Great Lakes on 11 - 21 occasions. How­ ever, Table 28 indicates th at about 19 per cent o f a l l respondents particip ated in boating in inland lakes and streams on Moreover, nearly 6 11 - 21 occasions. per cent o f a l l respondents reported boating on Great Lakes on 22 - 32 occasions; while nearly 12 per cent o f the respondents reporting indicated th at they went boating on inland lakes and streams on 22 - 32 occasions. For d e ta ile d information on frequency of boating p a rtic ip a tio n and fam ily income, see Tables 27 and 28. Table 29 summarizes s t a t is t i c s from the f in a l le a s t squares equation fo r the Marquette-Iron Mountain Region (12A). Only three independent variables met the specified stopping c r ite r io n in the LSDEL Program u t i l i z e d . M u ltip le boat ownership ( * 13) was again highly TABLE 2 7 .— Frequency o f Boating on Great Lakes by Number and Percentage o f Respondents in Selected Income Classes, Region 12A, 1968. 11 -■21 0-10 Occasions •k Occasions 22-32 Occasions 33-43 Occasions No. % No. % No. % No. % Under $3,000 14 93.33 1 6.67 0 0 ,0 0 0 0 .0 0 $ 3,000 - $ 5,999 15 83.33 0 0 .0 0 0 0 .0 0 1 5.56 $ 6,000 - $ 7,999 9 60.00 3 20 .0 0 1 6.67 0 0 ,0 0 $ 8,000 - $ 9,999 15 68.18 2 9.09 3 13.63 1 4.55 $10,000 - $14,999 26 78.79 1 3.03 2 6.06 2 6.06 $15,000 - $24,999 7 63.64 3 27.27 1 9.09 0 0 .0 0 $25,000 and Over 5 100.00 0 0 .0 0 0 0 .0 0 0 0 .0 0 91 76.47 10 8.41 7 5.88 4 3.36 Income Class TOTALS 44--54 55-65 66-76 Totals Under $3,000 0 0 .0 0 0 0 .0 0 0 0 .0 0 15 100.00 $ 3,000 - $ 5,999 1 5.55 1 5.56 0 0 .0 0 18 100.00 $ 6,000 - $ 7,999 1 6 .6 6 1 6.67 0 0 .0 0 15 100.00 $ 8,000 - $ 9,999 0 0 .0 0 0 0 .0 0 1 4.55 22 100.00 $10,000 - $14,999 0 0 .0 0 2 6.06 0 0 .0 0 33 100.0 0 $15,000 - $24,999 0 0 .0 0 0 0 .0 0 0 0 .0 0 11 100.00 $25,000 and Over 0 0 .0 0 0 0 .Q0 0 0 .0 0 5 100.00 2 1 .6 8 4 3.36 1 0.84 119 100.00 TOTALS Income classes fo llo w those used in the mail questionnaire {page 6 , question 1 9 ). TABLE 2 8 .— Frequency o f Boating on Inland Lakes and Streams by Number and Percentage o f Respondents in Selected Income Classes, Region 12A, 1968. 0 -■10 Occasions * Income Class Under $3 ,000 $ 3,000 - $ 5,999 11 --21 Occasions 22 --32 Occasions 33--43 Occasions 55-■65 Occasions 44--54 Occasions No. % No. % No. % No. % No. % No. % 7 46.66 5 33.33 0 0 .0 0 0 0 .0 0 0 0 .0 0 1 6.67 11 61,11 3 16.66 2 11.11 1 5.56 0 0 .0 0 1 5.56 $ 6,0 0 0 - $ 7,999 9 60.00 2 13.33 1 6.67 0 0 .0 0 1 6.67 0 0 .0 0 $ 8 ,0 0 0 - $ 9,999 11 50.00 5 22.73 1 4.54 3 13.64 0 0 .0 0 0 0 .0 0 $10,000 - $14,999 17 51.52 6 18.18 5 15.15 1 3.03 1 3.03 2 6.06 $15,000 - $24,999 4 36.37 2 18.18 2 18.18 2 18.18 0 0 .0 0 0 0 .0 0 $25,000 and Over 1 20 .0 0 0 0 .0 0 3 60.00 1 2 0.0 0 0 0 .0 0 0 0 .00 60 50.42 23 19.33 14 11.77 8 6.72 2 1 .68 4 3.36 TOTALS 66 --76 77'-87 88 --98 Totals 99--109 Under $3:,000 2 13.33 0 0 .0 0 0 0 .0 0 0 0 .0 0 15 100 ..00 $ 3,000 - $ 5,999 0 0 .0 0 0 0 .0 0 0 0 .0 0 0 0 .0 0 18 1 0 0 ..00 $ 6,000 - $ 7,999 1 6 .66 0 0 .00 1 6.67 0 0 .0 0 15 100 .,00 $ 8 ,0 0 0 - $ 9,999 0 0 .0 0 0 0 .0 0 1 4.55 1 4.54 22 100 ,. 00 $10,000 - $14,999 0 0 .0 0 0 0 .0 0 1 3.03 0 0 .0 0 33 100 ..00 $15,000 - $24,999 0 0 .0 0 0 0 .0 0 1 9.09 0 0 .0 0 11 100 ..00 $25,000 and Over 0 0 .0 0 0 0 .0 0 0 0 .0 0 0 0 .0 0 5 100 . 00 3 2.52 0 0 .0 0 4 3.36 1 0.84 119 1 0 0 . 00 TOTALS ★ Income classes fo llo w those used in the mail qu estionnaire (page 6 , question 1 9 ). TABLE 29.--S ta tis tic s from the Final Regression Equation for Region 12A, Marquette-Iron Mountain. Regression Coefficients Variable Intercept Number of Boats Owned Age of Family Head (a) { X13 ) t X16> Occupation of Family Head, (X35} Other Factory Worker Standard Error of Regression Coefficients Level of . Significance Mean 44.829237 12.922069 11.278031 2.887559 <.0005 1.67227 -0.697643 0.240251 .004 50.84034 64.837219 31.831160 .044 .00840 R = .4143c R2 = • 1716d Syx = 31.3994e Values in this column for X13 and X] 6 give the estimated effects of the two variables on the slope of the regression lin e. However, the value for X35 assumes a constant slope co efficient, and gives the estimated net change in intercept attributable to a zero-one variable. ^With 115 degrees of freedom. cMultiple correlation coefficient. ^Coefficient of multiple determination. eStandard error of estimate. 164 important in th is region, and was p o s itiv e ly co rrela te d w ith boating p a r tic ip a t io n . Age o f fam ily head was n eg atively c o rrela te d w ith boating p a r tic ip a tio n in the M arquette-Iron Mountain Region. Occupation o f fam ily head (><3 5 ) had a h ig hly p o s itiv e e f f e c t upon the dependent v a ria b le . Other fa c to ry workers, as a c la s s , did s ig n if ic a n t ly more boating than boat owners in other occupational classes. The S tate o f Michigan In ad d itio n to estimating parameters in the regression equation separately fo r f i v e Michigan Planning and Development Regions, the regression model was also estimated separately f o r the S tate o f Michigan as a whole. Counties. That i s , observations were combined from a l l 83 Michigan Selected s t a t i s t i c s fo r the i n i t i a l regression equation estimated are summarized in Appendix F. The income va riables ( * 3 5 * * 3 7 * and x^g) were not s i g n i f i c a n t l y co rrelated with boating a c t i v i t y occasions. This may have been a r e s u lt o f improperly specifying fam ily income in the regression model, however. The actual d is tr ib u tio n o f fam ily income among respondents to the survey is shown in Table 30. The computed median fam ily income fo r a l l survey respondents is approximately $10,840.06. For the e n t ir e sample, 29.17 per cent o f a l l respondents reported fam ily incomes o f less than $8 , 0 0 0 . 0 0 annually. A to ta l o f 10.32 per cent o f the respondents had fam ily incomes o f $3,000 - $5,999, and 5.25 per cent reported fam ily incomes o f less than $3,000. About 55 per cent of a l l survey respondents had fam ily „ incomes o f $10,000 or above during the survey year (1968). 165 TABLE 30. — Income Class D is trib u tio n o f Sampled W atercraft Owners, State o f Michigan, 1968. Income Class No. o f Sampled Boat Owners Per Cent Under $3,000 230 5.25 $ 3,000 - $ 5,999 452 10.32 $ 6,000 - $ 7,999 595 13.60 $ 8,000 - $ 9,999 681 15.55 $10,000 - $14,999 1,376 31.42 $15,000 - $24,999 725 16.57 $25,000 and Over 319 7.29 4,378 1 0 0 .0 0 TOTALS * Income classes fo llo w those u t i l i z e d in the mail questionnaire {question 19, page 6 ). A comparison o f computed median fam ily incomes may be made on a regional basis by r e fe r r in g to Table 31. This ta b le gives a tab u lar summary o f median incomes by study region, and the S tate. Only two study regions (D e t r o it and Lansing) had computed median fam ily incomes which were g reater than the S tate of Michigan s t a t i s t i c . In view o f the constraints imposed by c o lle c tio n o f data on fam ily income in the survey instrument, the s t a t i s t i c a l analysis has been supplemented by the inclusion o f frequency count tables in the data analysis chapter. This p ra c tic e has been followed co n sistently fo r a l l study regions i d e n t i f i e d . S im ila r tables have also been prepared f o r the State of Michigan as a whole. Tables 32 and 33 provide frequency o f boating data by income classes o f respondents fo r Great Lakes and Inland lakes and streams boating, re s p e c tiv e ly . 166 TABLE 3 1 . — A Comparison o f Median F a m ily Income o f Respondents, by Study R eg io n , 1968. Computed Median Family Income 1968 (D o lla rs ) Sample Size (N) The State o f Michigan 10,840.06 4,378 Region 1— D e tro it 12,753.11 1,057 Region 11,940.59 262 Region 7C— Saginaw Bay 6,908.44 120 Region 10— Traverse Bay 9,047.04 256 Region 12A— M arquette-Iron Mountain 9,046.53 119 Area 6 --Lansing As was the case in in d ivid u al study regions, frequency o f boating (number o f occasions) tends to be higher on inland lakes and streams areas than on Great Lakes. For example, about 17 per cent o f a l l respondents indicated th a t they boated on inland lakes and streams on 11 - 21 occasions in 1968; w hile only about 7 per cent o f survey respondents indicated going boating on Great Lakes on 11 - 21 occasions during the study year. Likewise, about 12 per cent of a l l respondents reported boating on inland lakes and streams on 22 - 32 occasions; while only about 5 per cent o f the respondents reported going boating on Great Lakes between 22 - 32 occasions during the study year. Table 34 summarizes selected s t a t i s t i c s from the f i n a l regression equation fo r the to ta l (S tate o f Michigan) sample. A ll o f the "type o f power system" variables (x^-x^) met the sp e cifie d stopping c r i t e r i o n in the LSDEL program. A ll c o e ffic ie n ts had s ig n ific a n c e p r o b a b ilit ie s < .0 5 , and thus were retained in the f in a l equation. A ll four variables had p o s itive e ffe c ts upon the dependent v a ria b le , and calculated a- values ij TABLE 3 2 .— Frequency o f Boating on Great Lakes by Number o f Respondents in Selected Income Classes, S tate o f M ichigan, 1968. 0 -•10 11-■21 Occasions * 22 -■32 Occasions Occasions 33--43 Occasions 44--54 Occasions 55- 65 Occasions No. % No. % No. % No. % No. % No. % Under $3 ,000 203 88.26 15 6.52 3 1.30 2 0.87 2 0.87 3 1.30 $ 3,000 - $ 5,999 398 88.05 24 5.30 14 3.10 4 0.89 4 0.89 4 0.89 $ 6,000 - $ 7,999 502 84.37 34 5.71 27 4.54 10 1.68 5 0.84 10 1 .6 8 $ 8 ,000 - $ 9,999 568 83.41 54 7.93 23 3.38 8 1.17 10 1.47 8 1.17 $10,000 - $14,999 1127 81.90 85 6.18 61 4.43 35 2.54 24 1.75 19 1.38 $15,000 - $24,999 550 75.86 55 7.59 54 7.45 24 3.31 16 2.21 12 1 .6 6 $25,000 and Over 218 68.34 26 8.15 27 8.46 18 5.64 11 3.45 8 2.51 3566 81.45 293 6.69 209 4.78 101 2.31 72 1.64 64 1.46 Income Class TOTALS 66 --76 77--87 8 8 --98 Totals 99--109 Under $3!,000 1 0.44 0 0 .0 0 0 0 .0 0 1 0.44 230 10 0 ..00 $ 3,000 - $ 5,999 1 0 .2 2 0 0 .0 0 1 0 .2 2 2 0.44 452 100 ..00 $ 6,000 - $ 7,999 1 0.17 1 0.17 3 0.50 2 0.34 595 1 0 0 ..00 $ 8,0 0 0 - $ 9,999 4 0.59 2 0.29 3 0.44 1 0.15 681 10 0 ..00 $10,000 - $14,999 12 0.87 7 0.51 2 0.15 4 0.29 1376 100 . 00 $15,000 - $24,999 3 0.41 5 0.69 3 0.41 3 0.41 725 10 0 ,. 00 $25,000 and Over 5 1.56 2 0.63 2 0.63 2 0.63 319 100 .00 27 0.62 17 0.39 14 0.32 15 0.34 4378 100 .00 TOTALS * Income classes fo llo w those u t iliz e d in the mail questionnaire (page 6 , question 1 9 ). TABLE 3 3 .--Frequency o f Boating on Inland Lakes and Streams by Number o f Respondents in Selected Income Classes, S tate o f Michigan, 1968. 0-10 11-21 Occasions ★ Occasions 22-32 Occasions % % % No. % % Under $3,000 151 65.65 27 11.74 22 9.57 3 1.30 4 1.74 8 3.48 $ 3,000 - $ 5,999 251 55.53 87 19.25 44 9.73 17 3.76 7 1.55 16 3.54 $ 6,000 - $ 7,999 309 51.93 109 18.32 77 12.94 29 4.87 21 3.53 17 2.86 $ 8,000 - $ 9,999 332 48.75 118 17.33 92 13.51 43 6.31 27 3.96 28 4.11 $10,000 - $14,999 634 46.08 260 18.90 195 14.17 102 7.41 52 3.78 50 3.63 $15,000 - $24,999 352 48.55 119 16.41 88 12.14 37 5.10 25 3.45 40 5.52 $25,000 and Over 172 53.92 33 10.34 29 9.09 20 6.27 17 5.33 8 2.51 2201 50.27 753 17.20 547 12.49 251 5.73 153 3.50 167 3.82 TOTALS 66-76 % No. 77-87 88-98 No. 55-65 Occasions 44-54 Occasions No. Income Class No. 33-43 Occasions No. 99--109 Totals Under $3,000 3 1.30 2 0.87 6 2.61 4 1.74 230 100.00 $ 3,000 - $ 5,999 5 1.11 2 0.44 7 1.55 16 3.54 452 100.00 $ 6,000 - $ 7,999 4 0.67 6 1.01 10 1 .68 13 2.19 595 100.00 $ 8,000 - $ 9,999 6 0 .8 8 14 2.06 11 1.62 10 1.47 681 100.0 0 $10,000 - $14,999 19 1.38 8 0.58 26 1.89 30 2.18 1376 100.00 $15,000 - $24,999 11 1.52 9 1.24 20 2.76 24 3.31 725 100.00 2 0.63 10 3.13 16 5.02 12 3.76 319 100.00 50 1.14 51 1.17 96 2.19 109 2.49 4378 100.00 $25,000 and Over TOTALS ★ Income classes fo llo w those u t iliz e d in the m ail questionnaire (page 6 , question 1 9 ). TABLE 34.—Statistics from the Final Regression Equation for the State of Michigan. Regression Coefficients Variable c —C X X (a ). Intercept Type 1-1(outboard motor) Type 2-1(sailboat with c. motor) Type 3-1(inboard motor) (X,) Type 4-1(inboard-outboard 01?) motor) Horsepower of Primary (X,) D Engine Storage at Premanent (X,) 0 Residence (not on lake or riv e r) Transportation of Watercraft (X-,«) Number of Boats Owned (X 3 ) Boat length (X 4> Age Squared (X (X I Family Size 18* R = .3237 c Standard Error of Regression Coefficients Level of . Significance Mean 12.049114 6.711649 11.429399 4.227445 2.994954 4.864498 .024 .018 0.87124 0.01494 8.587497 10.655542 3.803828 3.991207 .023 .008 0.05838 0.03236 0.048449 0.012616 <.0005 34.29418 -11.721026 1.161063 <.0005 0.40371 3.464273 4.140232 0.485870 -0.002774 1.037961 1.108551 0.477337 .. 0.146603 0.000505 0.296420 R2 = ■ lM 8 d .002 <.0005 .001 <.0005 .001 0.54899 1.69314 14.99004 2651.97307 3.36999 S„„ = 29.7148e aValues which appear in this column for (X1 -X4 ), X6 , and Xi 2 assume equal slope coefficients. These values give the estimated net effect of the categorical values listed on the intercept term. Values for Xs, Xi 3 , X14 , X-|7 » and X ^ give estimated effects on the slope of the regression lin e . bFor 4406 degrees of freedom. cMultiple correlation coefficient. C o e ffic ie n t of multiple determination. eStandard error of estimate. 170 showed l i t t l e v a ria tio n . This finding suggests two things: (1) f o l ­ lowing the assumptions underlying th is study, the "type o f power system" variables could be "pooled" without s a c r ific in g much s e n s i t iv it y ; and ( 2 ) the study could have been conceptualized d i f f e r e n t l y , i . e . , perhaps these variables would have shown more s e n s it iv it y i f the model variables were estimated separately fo r Great Lakes Boating and Inland Lakes and Streams Boating. Type o f power system may be a more important fa c to r in explaining boating p a rtic ip a tio n as size o f water surface area varies, and when boat launching f a c i l i t i e s (of varying size and so­ p h is tic a tio n ) are provided at ponds, lakes, and streams which are located a t varying distances from the user population. In the State o f Michigan equation, horsepower o f w a te rcraft had a p ositive e f f e c t upon boating p a rtic ip a tio n . This find in g implies th at larg e r w ate rcraft engines are used r e l a t i v e ly more than smaller w atercraft in the s ta te . One o f the "place o f storage" variables (x^) was retained in the fin a l equation. W atercraft owners who stored t h e ir (sampled) w ate rcraft at t h e ir home residence during the boating season, as a class, boated s ig n ific a n t ly less than boat owners who stored t h e i r (sampled) w ate rcraft a t other locations. on the dependent v a ria b le was negative. The e f f e c t of th is variable Boat transportation ( x ^ ) was important in explaining v a ria tio n in the dependent v a ria b le , and its e ffe c t was p o s itiv e . However, the wording of the relevant ques- tio n (s ) in the mail questionnaire may have been such th a t many respond­ ents gave a p o s itiv e response to the question(s) when, in f a c t , they only transported t h e i r w atercraft once or twice during the boating season. 171 M u ltip le boat ownership Cx i 3 ) was also retained in the model through the f in a l i t e r a t i o n . For the sample as a whole, th is v a ria b le had a p o s itiv e e f f e c t upon boating p a r t ic ip a t io n . Many o f the sampled w a te rc ra ft owners had more than one (re g is te re d or unregistered) boat. The s t a t i s t i c a l analysis ind icates th a t sample w a te rc ra ft owners having more than one boat are those who did the most boating during the study year (1968). Likewise, Age Squared (x-jy) had a negative e f f e c t upon boating p a r tic ip a tio n . This suggests th a t age o f boat owner has a c u r v ilin e a r re la tio n s h ip w ith the dependent v a ria b le (boating a c t i v i t y occasions). Family Size ( g) also was retained in the f i n a l it e r a t i o n of the State o f Michigan equation. Family s iz e was shown to have a p o s itiv e e f f e c t upon boating p a r t ic ip a t io n . Within the relevan t range o f fam ily size considered, th is v a ria b le indicates th a t boating a c t i v i t y occasions increase l i n e a r l y with increasing fam ily s ize . As noted previously in th is chapter, in te rc o r re la tio n s between deleted independent v a ria b le s , and s i g n if ic a n t va ria b les retained in the f in a l equation become important i f the model is to be used fo r forecastin g . In order to determine where in te rc o r re la tio n s e x is t between independent v a ria b le s , a c o rr e la tio n m atrix was obtained f o r use in in te rp re tin g the re s u lts obtained in the State of Michigan Equation. I t should be noted th a t the variables specified in the model did not change in the State Equation. Horsepower of w a te rc ra ft (x^) was n eg atively co rrelated with type 1-1 (x ^ ). This fin d in g indicates th a t sampled w a te rc ra ft having outboard motors were not usually those w ith the greatest horsepower ra tin g s . However, horsepower of w a te rc r a ft (x 5 ) was p o s itiv e ly 172 correlated with power system type 3-1 (w a te rc ra ft having inboard motors). Horsepower ra tin g (Xg) was also p o s itiv e ly correlated with type of power system type 4-1 (inboard motor with outboard d r iv e ). There appears to be a strong p o s itive co rre la tio n between place of storage o f w ate rcraft and type o f power system 1-1 (outboard motor), p a rtic u la r ly x ^ -s to ra g e o f w ate rcraft a t permanent residence during boating season. A strong p ositive co rre la tio n exists also between place of storage— commercial marina (Xg) and boat type. Strong p ositive in te rc o rre la tio n is indicated between commercial marina storage (Xg) and w atercraft type 3-1 (inboard motor). Also, commercial marina storage (xg) is negatively correlated with power system type board motor). (o ut­ 1-1 There is a strong p o s itive co rrela tio n between commercial marina storage (xQ) and horsepower ra tin g (Xg) of w atercraft as w e ll. A p ositive co rre la tio n is exhibited between place of storage— yacht club ( x ^ ) and power system type 2-1 (s a ilb o a t with motor). length ( x ^ ) is negatively correlated with type of power system (outboard motor). Boat 1-1 However, i t is p o s itiv e ly correlated with type of power system 3-1 (inboard motor). Boat length is also p o s itiv e ly correlated with horsepower ra tin g o f w atercraft (Xg). A co rrela tio n matrix is exhibited in Appendix E. Aggregate P a rticip a tio n Model Study hypothesis number 2 concerns the aggregate rate of recreational boating p a rtic ip a tio n by regional (county) populations in the State of Michigan. I t hypothesizes th at the rate of boating p a rtic ip a tio n is a lin e a r function of factors such as: ( 1 ) travel 173 distance, (2) disposable income o f boat owners, (3) the proportion o f minority races in the population, (4) population density o f the region being studied, (5) distance from and population o f nearest Standard Metropolitan S t a t i s t i c a l Area (SMSA), ( 6 ) distance o f county from a Great Lake, (7) number o f commercial and public campgrounds in county, ( 8 ) surface water acreage o f county, (9) number o f public boat-launching sites in county, ( 1 0 ) the number o f hotels, motels, to u r is t courts, and camps in county, ( 1 1 ) the number of substitute amusement-recreation service firms in county, ( 1 2 ) number of registered w ate rcraft in county, and (13) occupations o f county residents.^ The aggregate p a rtic ip a tio n model w il l be estimated fo r the State of Michigan as a whole; and fo r (a) t h i r t y Michigan counties which were estimated to generate the highest levels o f to ta l (aggregate) boating a c t i v i t y during 1968; and (b) t h i r t y Michigan counties which were estimated to generate the lowest levels o f to ta l (aggregate) boating a c t i v i t y during 1968. 2 There are d e fin it e lim ita tio n s involved in making inferences about a population estimator obtained by using grouped data. The aggregate p a rtic ip a tio n model used grouped data fo r both the dependent ^In contrast to the procedure followed in the modified user ch aracteristics model, occupation variables were entered as percentages in the aggregate p a rtic ip a tio n model. Twelve occupational classes were u t i l i z e d , following the categories used in the 1970 Census of Population, The percentage of a county's employed labor force repre­ sented by sp ecific occupational classes was the value entered fo r a l l twelve occupations. 2 As explained previously, i t was not possible to estimate model parameters fo r the same f iv e study regions used in testin g hypothesis 1 due to a lack of s u ff ic ie n t degrees of freedom. 174 and independent v a ria b le s . As Prais and Houthakker have observed, however: . . . the c o rre la tio n c o e ffic ie n t obtained from grouped observations is not a s a tis fa c to ry estimator o f the c o rre la tio n c o e ff ic ie n t in the population; fo r while a s a tis fa c to ry estimate can be obtained o f the residual variance, i t is not possible to obtain an estimate o f the o rig in a l variance on the basis of grouped data. . . . Cor­ r e la tio n c o e ffic ie n ts based on grouped data can thus only be used fo r comparative purposes.! County parameters were used in the aggregate p a rtic ip a tio n model. That i s , the dependent v a ria b le consisted o f an aggregate boating p a rtic ip a tio n rate per 1,000 county population. This value was calcu­ lated fo r each county in the State of Michigan, based upon information obtained from the 1968 boating survey. Likewise, values fo r most of the independent variables were obtained by using census figures (or ta b u la tin g ) in order to obtain aggregate county estimates. The State o f Michigan Least squares estimators obtained from the i n i t i a l State o f Michigan equation are shown in Appendix F. S t a t is t ic s from the fin a l (State o f Michigan) regression equation are shown in Table 35 below. In the fin a l equation, high income was p o s itiv e ly correlated with boating p a rtic ip a tio n . The measure used fo r th is v a ria b le was the county percentage o f fa m ilie s having an annual cash income o f $10,000 or more. Percentage o f m inority races w ith in a county popu­ la tio n (xg) was negatively correlated with boating p a r tic ip a tio n . ^S. J. Prais and H. S. Houtakker, The Analysis of Family Budgets (London: Cambridge U niversity Press, 1955), p. 61. TABLE 35.--S ta tis tic s from the Final Regression Equation, State of Michigan. Variable Intercept (a) High Cash Income (X,) Percentage of Minority Races Surface Water Acreage ( X ,,) Occupation— Professional (X 5> Occupation—Sales Workers Occupation—Craftsmen (xl g ) Occupation—Operatives ( x I q) Occupation—Laborers Occupation—Farm (x ff) Laborers Occupation—Househol d (x 2 7 ) Workers No. Registered Watercraft per 1 ,000 county population h R = .9082° no CO X (41) Regression Coefficients Standard Errors of Regression Coefficients Level of Significance 8,583.984432 48.336752 -48.042538 2,316.674253 16.456685 21.730985 .004 .030 0.047606 -200.578147 -354.804368 0.012992 58.885271 91.255020 <.0005 -122.747538 -84.168886 -171.785598 -228.265170 54.046498 33.744618 59.403892 107.814722 .026 .015 .005 .038 15.84217 17.27205 5.07807 1 .19783 -585.192097 199.322457 .004 1.15084 23.078423 2.246925 <.0005 94.26867 0 R = •8249 aWith 71 degrees of freedom. ^Multiple correlation coefficient. C o e ffic ie n t of multiple determination. Standard error of estimate. .001 <.0005 H Suy = 794.7133° * y Mean 23.48193 2.96663 9,594.77952 12.13711 6.07036 176 Ceteris paribus, the higher the proportion o f m in o rity races in a county population, the lower the aggregate p a r t ic ip a tio n ra te in boating which w i l l be generated by t h a t county. Total county surface water acreage {x-|-|)* as defined in th is study, was p o s it iv e ly c o rrela te d w ith the aggregate boating p a r tic ip a tio n ra te shown by th a t county. The r e l a t i v e a v a i l a b i l i t y of boatable surface water resources in a county does appear to have a p o s itiv e (but small) association w ith boating p a r t ic ip a t io n . However, boat launching f a c i l i ­ t ie s ; s u b s titu te le is u r e time amusement-recreation services; h o te ls , motels, t o u r is t co u rts, and camps; and public and commercial camp­ grounds did not appear to have a s ig n if ic a n t influence upon the ra te of boating p a r t ic ip a tio n shown by county populations. Occupations of county labor force s i g n i f i c a n t l y influenced the ra te o f boating p a r tic ip a t io n in the State o f Michigan equation; Professional occupations U -jg )* sales workers ( x ^ ) , craftsmen ( x-|g) * operatives ( x 2 q)» laborers ( x23^ * workers ( x27) ’ were ^ariT1 laborers ( x25) ’ anc* household n eg atively c o rrela te d w ith county boating p a r tic ip a tio n ra te s . The measure used fo r th is v a ria b le was the per­ centage o f a county's employed labor force represented by various occupation categories. Number o f registered w a te rc ra ft per 1,000 county population was p o s itiv e ly and s i g n i f i c a n t l y c o rrela te d with the aggregate boating p a rtic ip a tio n r a te . C eteris parib us, the higher the incidence o f registered w a te rc ra ft ownership shown by a county population, the higher w i l l be th at county's boating p a r tic ip a tio n ra te . 177 Several o f the independent variables which were deleted from the f in a l regression equation appear to be highly correlated with some of those variables retained. The "high income" variable (xc ) , fo r b example, exhibited a p o s itive c o rre la tio n with va ria b le x2- - t r a v e l distance, which was deleted from the fin a l equation. Part o f the e ff e c t o f the deleted va ria b le (x2 ) is thus retained in the equation. The high income v a ria b le (x5 ) was also p o s itiv e ly correlated with aggre­ gate disposible income (Xg). These in te rc o rre la tio n s among the inde­ pendent variables make the computed regression c o e ffic ie n ts less r e lia b le estimators i f the model is u t il i z e d as a forecasting to o l. A strongly negative association was also present between the "high income" va ria b le (Xg) and the "low income" va ria b le (x ^ ). was not retained in the fin a l regression equation. However, A co rre la tio n matrix is exhibited in Appendix E. Top 30 Origin Counties The aggregate p a rtic ip a tio n model could not be estimated fo r the f iv e study regions id e n tifie d in Chapter I I I because o f a lack o f s u ffic ie n t degrees o f freedom. A decision was made, th e re fo re , to estimate the equation fo r the "top" and "bottom" t h i r t y counties of o rig in o f the s ta te . In performing th is operation, a rank-ordered l i s t was f i r s t prepared. All 83 counties were ranked according to the to ta l e s t i ­ mated (aggregate) number of boating a c t i v i t y occasions generated during the study year (1968). This population va ria b le is not the same as th at used fo r the dependent variable in the regression model. The 178 dependent v a ria b le consisted o f the estimated number o f aggregate boating a c t i v i t y occasions per 1,000 county population (see Table 9, page 9 7 ). On the basis o f the l i s t o f rank-ordered counties, the follow ing 30 counties were selected as the top o rig in areas in the State o f Michigan;^ (82 Wayne (81 Washtenaw (63 Oakland (14 Cass (50 Macomb (58 Monroe (41 Kent (78 S t. Joseph (25 Geneisee (08 Barry (33 Ingham (09 Bay (61 Muskegon (46 Lenawee (13 Calhoun (80 Van Buren (38 Jackson (1 2 Branch (70 Ottawa (03 A1legan (77 St. C la ir (04 Alpena (11 Berrien (52 Marquette (39 Kalamazoo (17 Chippewa (73 Saginaw (30 H ills d a le (28 Grand Traverse (47 Livingston S t a t is t ic s from the i n i t i a l Appendix F. regression equation are shown in Variables which were retained in the f in a l regression equation follow ing s a tis fa c tio n o f the specified stopping c r i t e r i o n are shown in Table 36 below. ^Numbers which appear in parentheses before each county are county i d e n t if ic a t io n numbers. Ind ividu al counties are arrayed in order o f descending rank as o rig in areas in the State o f Michigan during 1968. TABLE 3 6 .- - S t a t is t ic s from the Final Regression Equation, Top 30 Michigan Counties o f O rig in . Regression Coefficients Variable Intercept No. of Registered Watercraft per 1 ,000 county population Standard Errors of Regression Coefficients (a) 544.646554 302.367966 (X?fi) 20.917046 3.587544 R = .7405b aWith 28 degrees of freedom. ^Multiple correlation coefficient. C o e ffic ie n t of multiple determination. Standard error of estimate. 2 R = .5mc syx Level of Significance <.0005 = 759.3992d Mean 74.90000 180 The only variable retained in the f in a l equation was number of registered w ate rcraft per 1,000 county population (Xgg). There was a strong p o s itive co rrela tio n between boating p a rtic ip a tio n rate and the incidence o f registered w ate rcraft ownership per county, as might be expected. Bottom 30 Counties of Origin A rank-ordered l i s t was also prepared in order to determine the "bottom" 30 counties o f o rig in in Michigan. Counties were again ranked on the basis of the aggregate number of boating a c t i v i t y occasions generated by each county during the study year (1968). On the basis of th is operation, the following l i s t o f counties were selected as the "bottom t h i r t y . " As noted previously, the numbers in parentheses which precede each county r e f e r to the county's id e n tific a tio n number. Counties are ranked in order of ascending rank as o rig in areas in the State of Michigan. (40) Kalkaska (60) Montmorency (43) Lake (07) Baraga (67) Osceola (74) Sanilac ( 6 8 ) Oscoda (55) Menominee (57) Missaukee (27) Gogebic (58) Arenac (65) Ogemaw (48) Luce (79) Tuscola (01) Alcona (02) Alger ( 6 6 ) Ontonagon (37) Isabella (69) Otsego (44) Lapeer 181 (18) Clare (71) Presque Is le (20) Crawford (64) Oceana (75) Schoolcraft (54) Mecosta (32) Huron (10) Benzie (26) Gladwin (36) Iron Least squares estimators from the i n i t i a l regression equation fo r the "bottom t h ir t y " counties are shown in Appendix F. Table 37 shows the re su lts obtained follow ing s a tis fa c tio n o f the computer program stopping c r it e r io n . Both "high income" (x,-) and "low income" (x^) variables were highly s ig n ific a n t in the f in a l i t e r a t i o n . Both variables had a p o s itiv e e ffe c t upon boating a c t i v i t y occasions fo r th is group o f 30 counties. There was also a strong in te rc o r re la tio n between the high income and low income variables. Distance from a Michigan Great Lake (x7 ) was negatively correlated with boating a c t i v i t y occasions in the f in a l equation. Proportion o f m inority races (x^) was also retained in the f in a l regression equation, and was n egatively correlated with boating p a rtic ip a tio n rate fo r th is group o f counties. Public and p rivate campsites ( x -jq) was negatively co rrelated with boating p a rtic ip a tio n ra te . Ceteris paribus, as the number o f public and p riv a te campsites (having boat-launching f a c i l i t i e s ) increases w ith in a county, the rate of boating p a rtic ip a tio n decreases. Surface water acreage o f county ( ) with boating p a rtic ip a tio n ra te . was p o s itiv e ly correlated As the acreage o f boatable surface water increases (among th is group o f counties) so too does the boating p a rtic ip a tio n ra te . Number of public boat-launching site s in county TABLE 3 7 .— S ta tis tic s from Final Regression Equati Regression Coefficients Variable , Bottom 30 Countries o f O rig in . Standard Errors of Regression Coefficients (a) (x4 ) -11,207.498550 195.639884 ,509.851132 58.355302 (X5) 174.447884 (X7) / (X8) Intercept Households with Less than $3,000 annual cash income Households with Greater than $10,000 annual cash income Distance from a Great Lake Proportion of minority races in county popu­ lation Public and private campsites in county Surface water acreage of county Public boat-launching sites in county Occupation-Professional, Technical & Kindred workers Occupation-Managers and Administrators (except farm) Occupation-Sales workers (V Occupation-Clerical and Kindred workers Level of Significance Mean .008 25.46667 30.039930 <.0005 18.86667 -38.689514 6.293840 <.0005 28.80000 -316.976168 33.883101 <.0005 1.80800 -2.484757 0.517980 .001 (X „ ) 0.144861 0.022212 <.0005 (Xi2) 48.438188 16.527460 .017 9.53333 -1,296.822480 141.400906 <.0005 11.42800 -409.845991 71.360625 <.0005 7.03333 (x17) -1,051.257845 165.594912 <.0005 5.61633 (Xig) -484.560733 98.638268 .001 11.60367 I V 353.20000 8,527.08000 TABLE 37.— Continued. Standard Errors of Regression Coefficients Regression Coefficients Variable (x19) 131.142229 <.0005 15.96567 -737.767922 103.394451 <.0005 17.10800 (x23) -810.847255 115.097971 <.0005 6.04533 (x24) -403.454656 132.045609 .014 3.90567 -856.514299 127.076978 <.0005 1.61567 (x26) -464.648508 133.533825 .007 13.67333 (x27) -2,201.197764 189.162799 <.0005 1.17433 ( x 2g ) 12.695381 3.343728 .004 97.40000 (X2g) -1,127.762766 161.627179 <.0005 4.47767 o X -884.884763 h R = .9922° aWith 8 Mean ro Qccupation-Craftsmen, Foremen & Kindred Workers Occupati on-Operati ves (except transport) Occupation-Laborer (except farm) Occupation-Farmers and Farm Managers Occupation-Farm Laborers and Farm Foremen Occupation-Service Workers (except private household] Occupation-Private Household Workers No. of Registered Water­ c ra ft per 1,000 County Population Lccupation-Transport Equipment Operatives Level of Significance degrees of freedom. ^Multiple correlation coefficient. cCoefficient of multiple determination. Standard error of estimate. n r 2 = .9845 A Suy = 319.650 yx 184 (x12) was strongly p o s itive in i t s e f f e c t upon boating p a rtic ip a tio n ra te . For the "bottom t h ir t y " counties, the population's boating p a rtic ip a tio n ra te would be expected to increase with the construction of additional boat launching f a c i l i t i e s . The occupation variables were a l l highly negative in t h e ir e ff e c t upon boating p a rtic ip a tio n rate fo r the "bottom t h i r t y " counties. Professional, tec h n ica l, and kindred workers (x-jg); managers and administra to rs --e x c e p t farm (x-jg); sales workers ( x ^ h c le r ic a l and kindred workers (x-jg); craftsmen, foremen, and kindred workers (x^g); operativesexcept transport Cx2 0 )* l aborers""GXcept farm ( x23)* ^armers and farm managers ( x ^ ) ; farm laborers and farm foremen ( x25) ’ service workers — except p riv a te household (x 2 g ); p riv a te household workers (x^?); and transport equipment operatives (x2g) a l l were negatively correlated with boating p a rtic ip a tio n ra te . Number o f registered w ate rcraft per 1,000 county population (x28) was p o s itiv e ly correlated with boating p a rtic ip a tio n rate in the "bottom t h ir t y " counties. w ate rcraft per 1 ,0 0 0 Ceteris paribus, as the number of registered population increases in a county, so too w il l th at county's aggregate p a rtic ip a tio n rate in boating. O u t-o f-S tate Boating The f i r s t major objective o f th is study was to . . obtain an estimate o f the to ta l level o f recreational boating undertaken in Michigan during 1968*, i t s d is trib u tio n in various geographic regions in the state . . . ." o bjective: There were two sub-parts involved in th is (a) to estimate boating a c t i v i t i e s undertaken in Michigan 185 by residents o f other states or (Canadian) Provinces, and (b) re c re ­ a tio n a l boating undertaken in other states or (Canadian) Provinces by Michigan residents. I t was not possible to f u l f i l l these two sub­ objectives* F i r s t , i t was not possible to obtain estimates o f to ta l boating a c t i v i t y which was undertaken in Michigan by sampled non-residents since there was no way o f computing expansion fa c to rs . Residents o f other states who re g is tere d t h e i r w a te rc r a ft w ith the Michigan Secretary o f S tate Department were included in the o rig in a l sample involved. However, w hile i t was possible to determine the o r ig in state and obtain an estimate o f the to t a l number o f powered w a te rc r a ft owned by non­ residents coming from other s ta te s . I t was, th e re fo r e , impossible to c a lc u la te expansion factors f o r o u t - o f - s t a t e o r ig in counties without undertaking an ad d itio n al survey o f appropriate s ta te agencies in a number o f other states and Canadian Provinces. This type o f research seems b e tte r suited to a regional ( i n t e r - s t a t e ) approach w ith b e tte r funding than the present study. The second sub-objective was to obtain an estimate o f the to ta l amount o f boating which was undertaken in other states or Canadian Provinces by registered Michigan w a te rc ra ft owners. Due to funding lim it a t io n s in the study, th is information was not coded, and was thus not a v a ila b le fo r use in th is d is s e rta tio n . Conceptually, one approach to making such estimates would be to determine: (a ) the number o f a c t i v i t y occasions, and (b) the state or province o f o u t - o f -s t a te boating a c t i v i t y undertaken by sampled Michigan w a te rc ra ft owners. would then be possible to determine the r a t i o between the number o f It 186 sampled w ate rcraft (which were used o u t-o f-s ta te during the study period) and the to ta l number o f registered w atercraft in each county o f Michigan. I t would then be possible to determine expansion factors f o r each Michigan county, and to use these factors in estimating to ta l boating a c t i v i t y occasions fo r each destination state or Canadian Province. This is another study which might be best approached as an in tern ation al consortium. CHAPTER V SUMMARY, CONCLUSIONS, LIMITATIONS, AND RECOMMENDATIONS FOR FURTHER RESEARCH This chapter w il l be divided into four parts: ( 1 ) a summary of p rincipal study findings; ( 2 ) conclusions suggested by the data analysis; (3) lim ita tio n s of the research methods employed; and (4) recommendations fo r fu rth e r research. Summary Modified User C haracteristics Model Study hypothesis number one states th a t the level o f p a r t i c i ­ pation in recreational boating by a household u n it is not s i g n i f i ­ cantly influenced by: (a) Family income ( b) Family size (c) Occupation of household head (d) Age o f household head (e) Education level of household head ( f ) Place o f storage o f w a te rc ra ft (during boating season) (g) Number of w ate rcraft owned (h) Length of sampled w ate rcraft ( i ) Horsepower ra tin g of w ate rcraft motor 137 188 ( j ) Type o f power system of w ate rcraft (k) Transportation of sampled w a te rc ra ft Family Income Ordinary le a s t squares was u t i l i z e d to te s t the re la tio n s h ip between boating p a rtic ip a tio n and fam ily income o f sampled w ate rcraft owners. The results of the s t a t i s t i c a l analysis is inconclusive with respect to th is v a ria b le . While s ig n ific a n t re lation sh ips were noted in several study regions, th is re s u lt must be discounted since the income variables (x-jg, x ^ , and x^g) were subject to s t a t i s t i c a l bias stemming from the procedure followed in model s p e c ific a tio n . In order to adequately te s t the hypothesized re la tio n s h ip with the data collected in this study, dummy variables would have to be u t i l i z e d . An a lte r n a tiv e approach (and one most basic to the conceptualization o f th is study) would have been to a l t e r the procedure u t i l i z e d in gathering data in the f i e l d . Raw {ungrouped) fam ily income values might have been obtained from sampled respondents through household interviews. On the basis o f the contingency tables constructed fo r the study regions, a weak re la tio n s h ip appears to e x is t between fam ily income and frequency o f boating. However, an open-ended frequency d is trib u tio n on fam ily income (with unequal in te rv a ls between classes) was u t il i z e d in the tables presented. Family Size S ig n ific a n t relation sh ips between frequency of boating par­ tic ip a tio n and family size were found to e x is t in two study regions, 189 as well as fo r the to ta l sample. The stated study hypothesis is thus rejected fo r fam ily size on the basis of th is sample o f registered w a te rc ra ft owners. Within the range o f values obtained, boating p a rtic ip a tio n tends to increase p o s itiv e ly with fam ily size. Occupation o f Household Head Occupation o f household head had a s ig n if ic a n t e f f e c t upon boating p a rtic ip a tio n in four o f the f i v e study regions examined. In Region 1, the "professional" occupation U-jg) had a s ig n ific a n t (but negative) e f f e c t upon boating p a r t ic ip a tio n . In Region 7C, service workers ( x27) ^acl a s ig n if ic a n t e f fe c t upon boating p a r t i c i ­ pation. Other factory workers ( * 3 5 ) was the only occupation va ria b le which was s ig n ific a n t in Region 12— Marquette-Iron Mountain. The hypothesized re la tio n s h ip is thus rejected fo r these three regions. The hypothesis is accepted fo r Region 10— Traverse Bay, Region 6 —Lansing, this sample. and fo r the state o f Michigan equation on the basis of None o f the occupation classes exhibited a s ig n ific a n t influence upon boating p a rtic ip a tio n in these three equations. The hypothesis is re je c te d , however, fo r Region 1— D e t r o it , Region 7C-Saginaw Bay, and Region 12—Marquette-Iron Mountain. Age of Family Head Age o f family head was s ig n if ic a n t ly correlated with boating p a rtic ip a tio n in three study regions: Region 1— D e t r o it , Region 10-- Traverse Bay, and Region 12A—Marquette-Iron Mountain. In Region 10, age of fam ily head was p o s itiv e ly correlated with boating p a r t i c i ­ pation. However, the computed regression c o e ffic ie n ts had negative 190 signs in both Region 1 and Region 12A. is rejected The hypothesized re la tio n s h ip fo r Regions 1, 10 and 12A; andaccepted fo r Regions 6 and 7C, and fo r the State of Michigan. Age o f fam ily head squared was s ig n if ic a n t ly correlated with boating p a rtic ip a tio n in Region 10 and fo r the State of Michigan. In both cases, the computed regression c o e ffic ie n ts had negative signs. For these two regions, age may have a non-linear re la tio n s h ip with boating p a rtic ip a tio n . Educational Level of Household Head The study hypothesis is accepted fo r this v a ria b le . No s ig ­ n if ic a n t re latio n sh ip was found between education of household head and boating p a rtic ip a tio n in any of the study regions examined. Further study of th is re la tio n s h ip should be undertaken, however, as the education va ria b le was subjected to possible bias due to the wording of the question re la tin g to education in the survey instrument. the wording and structure o f the survey question (question 20) F ir s t, was such th at a respondent had no way o f answering i f he had received zero years o f education, i . e . , no box was provided. Also, the question was structured ambiguously over the high bound o f the range considered. Years o f education completed could range between one and seventeen years, as seventeen boxes were provided. However, an eighteenth box was provided for the use of respondents whose education exceeded seventeen years. F in a lly , there is a p o s s ib ilit y th at respondents may have been confused about the wording o f the survey question. Non­ c re d it short courses, and in -s e rv ic e tra in in g could have been counted in a rriv in g at a response to the question as worded. 191 Place o f Storage o f W atercraft Respondents were asked where they usually stored sampled w atercraft during the boating season (question 4 ) . There were seven "place o f storage" categories provided: 1. At my permanent home, which is not on alake or 2. At waterfrontage located a t my permanent home l o t . 3. At a commercial marina-berth. 4. At a summer cottage. 5. At a pub!icly-owned marina, 6. At a boat or yacht club. 7. Other (s p e c ify ). riv e r. Category seven was suppressed in order to obtain a determinate solution to the problem. in the model. However, six o f the categories were retained Category one (RESIDS) was s t a t i s t i c a l l y s ig n ific a n t at less than .0005 in Region 1. sign. The calculated c o e ffic ie n t had a negative Both category one (RESIDS) and category two (WATFRNT) were s t a t i s t i c a l l y s ig n ific a n t in Region 6. The calculated c o e ffic ie n ts fo r both categories had negative signs, however. In Region 10, two of the categorical classes were s i g n i f i ­ cantly correlated with boating p a rtic ip a tio n : WATFRNT (x?). COMMAR (*g)» and In the State of Michigan Equation, one categorical class (RESIDS) was s t a t i s t i c a l l y s ig n if ic a n t . c o e ffic ie n t again had a negative sign. The calculated The in te rp re ta tio n o f these results is th a t the s ig n ific a n t categorical classes would have a negative e ffe c t upon the inte rc ep t in the equation. The stated study hypothesis re la tin g to th is class of variables is rejected in 192 p a rt. Place o f storage did have a s ig n if ic a n t influence upon boating p a r tic ip a tio n in three o f the f i v e study regions, as well as in the State o f Michigan Equation. Number o f W atercraft Owned M u ltip le boat ownership was p o s itiv e ly co rrelated with boating p a rtic ip a tio n in four o f the f i v e study regions, as well as in the State o f Michigan Equation. The calculated regression c o e ffic ie n ts a l l had p o s itiv e signs except fo r region 7C--Saginaw Bay. However, the m u ltip i e-boat ownership v a ria b le lacked s ig n ific a n c e in the equa­ tion estimated f o r th at region. The s t a t i s t i c a l analysis indicates th at number o f boats owned by sampled w a te rc ra ft owners is highly s ig n if ic a n t as an in d ic a to r of boating p a r t ic ip a t io n , and the study hypothesis is thus re jec te d . Length o f Sampled W atercraft Boat length (>^ 4 ) was p o s itiv e ly (and s i g n i f i c a n t l y ) co rrelated with boating p a r tic ip a tio n in Region 1. For th is region, owning la rg e r w a te rc ra ft was strongly associated with boating p a r t ic ip a t io n . This v a ria b le was also p o s itiv e ly co rrelated with p a r t ic ip a tio n in the State o f Michigan Equation. However, the v a ria b le lacked s ta ­ t i s t i c a l sig n ifica n c e in a l l other study regions. sis is rejected in p a rt. The study hypothe­ I t is re jec te d fo r Region 1, and fo r the State o f Michigan as a whole, but i t is accepted fo r the four other delineated study regions. I t is possible th a t other study regions could be id e n t if ie d w ithin the s ta te where boat length assumed g rea ter 193 importance in view o f the fa c t th a t i t was s t a t i s t i c a l l y s ig n if ic a n t in the S tate o f Michigan Equation. Horsepower Rating o f W atercraft Motor Horsepower o f sampled w a te rc ra ft motor was s i g n i f i c a n t l y correlated with boating p a r t ic ip a tio n in only the S tate o f Michigan Equation. regions. I t lacked s t a t i s t i c a l s ig n ific a n c e in a l l other study I t is conceivable th a t th is v a ria b le would have a g rea ter influence upon boating p a r tic ip a tio n in some other region w ith in the s ta te , however. For the s ta te as a whole, the in te r p r e ta tio n o f th is find in g would be th a t boating p a r t ic ip a tio n tends to increase posi­ t i v e l y with la rg e r and more powerful w a te r c r a ft. Since powered w ater­ c r a f t re q u ire more sophisticated launching, maintenance, and storage f a c i l i t i e s than non-power w a te r c r a ft, i t is l i k e l y th at demands fo r marina f a c i l i t i e s w i l l be received from w a te rc ra ft owners having the la rg e s t w a te rc ra ft engines. The study hypothesis is re jec te d fo r the State o f Michigan as a whole, but accepted f o r the f i v e study regions. Further research of th is nature should concentrate on v e rify in g or r e je c tin g th is fin d in g , and should perhaps concentrate upon te s tin g the observed re la tio n s h ip in ad d itio n al study regions. Type o f Power System of W atercraft There were f iv e classes of va ria b les r e la tin g to power system o f sampled w a te rc ra ft in the i n i t i a l modified u s e r-c h a ra c te ris tic s model: 1. W atercraft with outboard motor 2. Sailboat w ith motor 194 3. Watercraft with inboard motor 4. Watercraft with inboard-outboard motor 5. Other (w rite in) Variable was suppressed in the f in a l equation in order to obtain a determinate solution. fo r classes 1-4. Dummy (zero-one) values were entered In the State o f Michigan Equation, a l l four classes were s ig n ific a n t a t less than the .05 le v e l. In a l l cases, the power system variables had a p o s itive e f f e c t upon the dependent v a ria b le. The hypothesis is rejected in p a rt. Type o f power system was s ig n if ic a n t ly correlated with boating p a rtic ip a tio n in the state o f Michigan equation. However, a d if f e r e n t selection o f study regions might re s u lt in additional areas o f the state where these classes of variables s ig n ific a n tly influenced boating p a rtic ip a tio n . Transportation o f Sampled Watercraft Sampled boat owners were asked whether or not they transported t h e ir w ate rcraft " . . . from your house or other location to par­ t i c u la r launching sites during the past boating season(calendar 1968}." Since a yes or no answer was obtained, boat transportation was entered as a "zero-one" v a ria b le. year Boat transportation was posi­ t iv e ly correlated with boating p a rtic ip a tio n in the State o f Michigan Equation at the .002 le v e l. However, i t was not s ig n ific a n t in any o f the f iv e delineated study regions. in some instances. In f a c t , i t had a negative sign The hypothesis is rejected fo r the State of Michigan as a whole, but accepted fo r the fiv e study regions examined. Because of its significance in the State of Michigan Equation, i t may 195 be possible to estimate the equation f o r other regions where boat transportation would be more important as an explanatory v a ria b le . I t may also be relevan t to obtain a b e tte r response to the transportation questions by u t i l i z i n g personal interview s, and by interviewing during the actual boating season. Aggregate P a rtic ip a tio n Model Study hypothesis number two states th a t the ra te o f p a r t i c i ­ pation in recreational boating by a regional population is not sig­ n if ic a n t ly influenced by: (a Travel distance (b Aggregate disposable income (c Percent o f households with incomes under $3,000 (d Percent of households with incomes over $10,000 (e Population density (f Distance from a Great Lake (9 Percent o f population composed of m inority races (h Location with respect to an SMSA (i Number of commercial and public campgrounds in county (j Surface water acreage o f county (k Number of public boat launching s ite s in county (1 Number o f h otels, motels, t o u r is t courts, and camps in county (m Number o f amusement and recreation service firms in county (n Number o f registered recreational w a te rcraft in county (o Occupations of county residents 196 Travel Distance The measure used fo r th is va ria b le was the estimated weighted average one-way tra ve l distance between o rig in and d estination counties in the State o f Michigan. Information on the actual number o f boating trip s taken by sampled w ate rcraft owners was not obtained in the survey instrument; thus, a major assumption had to be made in order to calcu late an average one-way travel distance fo r each Michigan County. An assumption was made th a t the number o f boating t r ip s taken by registered w a te rc ra ft owners between individual o rig in and d e s ti­ nation counties was d ir e c t ly proportional to the percentage o f to ta l boating a c t i v i t y occasions estimated fo r the destination county during the survey year. No s ig n ific a n t re la tio n s h ip was found between travel distance and the ra te of boating p a rtic ip a tio n undertaken by county popu­ la tio n s . The hypothesized re la tio n s h ip is thus accepted fo r th is variable. An a lte r n a tiv e formulation might have resulted in a sig­ n if ic a n t re la tio n s h ip . Determination of the actual number of boating trip s taken by sampled w a te rc ra ft owners (as opposed to the number o f a c t i v i t y occasions) might represent a more r e a l i s t i c formulation o f this variable. Aggregate Disposable Income The measure used fo r th is variable corresponds closely with "disposable personal income" per county. I t consisted o f the net E ffec tiv e Buying Income (EBI) in thousands of d o llars fo r each Michigan County in 1968. There was no s ig n ific a n t relation sh ip 197 between th is variable and county boating p a rtic ip a tio n ra te . The hypothesized re la tio n s h ip is accepted. Percent o f Households with Incomes under $3,000 This va ria b le consisted o f the percentage o f households with net cash incomes of less than $3,000 fo r the calendar year 1968* by Michigan County. The low income va ria b le (x^) was p o s itiv e ly cor­ re lated with the dependent va ria b le (county boating p a rtic ip a tio n ra te ) among the "bottom t h ir t y " Michigan o rig in counties; and the computed regression c o e ffic ie n t was s ig n ific a n t a t the .008 level of p ro b a b ility . There was no s ig n ific a n t re la tio n s h ip between th is fa c to r and the dependent v a ria b le in e ith e r the Statewide or "top t h ir t y " o rig in counties equations. The hypothesis concerning th is variable is thus rejected in p a r t, and accepted fo r the State o f Michigan and "top t h ir t y " o rig in counties equations. Percent of Households with Incomes over $ 1 0 , 0 0 0 The value used fo r th is v a ria b le consisted o f the percentage o f households w ithin a county which had net cash incomes which were equal to or greater than $10,000 fo r the calendar year 1968. The high income v a ria b le (x^) was s ig n ific a n t in both the State o f Michigan and the "bottom t h ir t y " counties o f o rig in equations. In both in ­ stances, the high income va ria b le was p o s itiv e ly correlated with the dependent v a ria b le . The study hypothesis concerning the re latio n sh ip betv/een high income and the dependent va ria b le is rejected fo r the 198 State o f Michigan and "bottom th irty '* o rig in counties equations, but is accepted fo r the "top t h ir t y " o rig in counties equation. Population Density This v a ria b le consisted o f the estimated number o f persons per square mile fo r each Michigan County. No s ig n ific a n t r e la t io n ­ ship was found between population density (x^) and the dependent v a ria b le. A p o s itive re latio n sh ip was noted in both the State of Michigan and "top t h ir t y " counties o f o rig in equations, w hile a negative c o rre la tio n was found in the "bottom t h ir t y " o rig in counties equation. However, the calculated sig nificance p ro b a b ilitie s of the regression c o e ffic ie n ts was greater than .05 in a l l cases. The study hypothesis is accepted fo r th is v a ria b le . Distance from a Great Lake The measure used fo r th is va ria b le was the shortest one-way highway distance (in miles) between the county seat in each Michigan county, and the closest point of boating access on a Michigan Great Lake. The distance from a Great Lake va ria b le (x^) was found to be strongly negative in it s influence upon boating p a rtic ip a tio n in the "bottom t h ir t y " counties o f o rig in equation. In th at equation, the calculated significance p ro b a b ility o f the regression c o e ffic ie n t was s ig n ific a n t a t less than the .0005 le v e l. A p o s itive relation sh ip existed between distance from a Great Lake (Xy) and the dependent variable in both the State o f Michigan and "top t h ir t y " counties of o rig in equations. However, the computed regression c o e ffic ie n ts lacked sig nificance. The hypothesis is rejected fo r the "bottom 199 t h i r t y " o r ig in counties, and accepted f o r the State o f Michigan and "top t h ir t y " o rig in counties equations. Proportion o f M in o rity Races in Population The measure used f o r th is v a ria b le consisted o f the to ta l number o f persons in each c la s s ifie d m in o rity race in a county (In d ia n , Japanese, Chinese, F i l i p i n o , Negro, and a l l o ther) divided by the to ta l estimated 1970 population. Parameter values calculated for th is v a ria b le may be biased in unknown d ire c tio n s since 1970 census data were used; w hile the survey data on boating p a rtic ip a tio n was c o lle c te d during 1968. An assumption was made, however, th a t the percentage o f m inority races which existed in each Michigan County held constant between the survey year (calendar 1968) and A pril 1, 1970. The m inority races v a ria b le (Xg) was highly s ig n if ic a n t in the S tate of Michigan Equation and the "bottom t h i r t y " o rig in counties equations. In both cases, there was a negative c o rre la tio n between the percentage o f m in o rity races and the dependent v a ria b le . In both equations, the computed sig n ifica n c e p ro b a b ility o f the regression c o e ffic ie n ts was less than .0005. The study hypothesis is re je c te d , th erefo re, f o r these two regions, and accepted f o r the "top t h i r t y " o rig in counties equation. Distance from an SMSA— Size-Distance The measure used fo r th is v a ria b le consisted of a series o f scale values, based upon each Michigan county's location with respect to an SMSA. Both population and distance were used as c r i t e r i a . 200 A fte r assigning scale values to a l l SMSA counties in the s ta te , a distance decay p rin c ip le was followed in determining scale values fo r a l l other counties in the S tate. Counties located less than 50 miles from the central c i t y of an SMSA were assigned a value which was four less than the value calculated fo r the SMSA county, etc. The size distance va ria b le (Xg) lacked sig nificance in a l l three equations: the State of Michigan, the "top t h ir t y " o rig in counties, and the "bottom t h ir t y " o rig in counties. sis is thus accepted fo r th is v a ria b le . The study hypothe­ I t should be noted that a r b itr a r y re s tra in ts were used in specifying th is v a ria b le. A lte r­ native approaches might be used in formulating th is va ria b le which might lead to a d if fe r e n t re s u lt. Number o f Commercial and Public Campgrounds The value used fo r this variable consisted o f the number of individual campsites (a t both commercial and public areas) which had the services of constructed boat-launching f a c i l i t i e s w ithin the campground. Only campgrounds which a c tu a lly provided boat-launching f a c i l i t i e s during 1968 were selected fo r inclusion in the county to ta ls . This variable was s ig n ific a n t a t the .001 level in the "bottom th ir t y " o rig in counties equation. The computed regression c o e ffic ie n t was negatively correlated with the county boating p a rtic ip a tio n ra te. The hypothesized relation sh ip is thus rejected fo r the "bottom t h ir t y " o rigin counties; and accepted fo r the State of Michigan and "top th ir ty " o rig in counties equations. 201 Surface Water Acreage o f County Values entered f o r th is va ria b le consisted of the to ta l surface water area (in acres) contained in each county in selected surface water categories: ( 1 ) natural lakes and ponds, ( 2 ) natural lakes with a dam, (3) a r t i f i c i a l lakes, (4) a r t i f i c i a l ponds, (5) hydro­ e le c t r ic rese rv o irs , voirs. ( 6 ) small lakes, and (7) flood control reser- Only water bodies containing a t le a s t four acres were included in the tabulations fo r each county. Surface water acreage was p o s itiv e ly correlated with boating p a rtic ip a tio n in a l l three equations. The computed regression c o e ffic ie n t was s ig n ific a n t a t less than .0005 in the State o f Michigan and "bottom t h ir t y " o rig in counties equations. Surface water was not s ig n ific a n t at the .05 level in the "top t h ir t y " o rig in counties i n i t i a l equation, and was not retained in the f in a l it e r a t io n . The hypothesized re latio n sh ip is , th ere fo re, rejected fo r this variable in part. Public Boat-Launching Sites The measure used fo r th is variable consisted o f the number of pub!icly-constructed boat-launching sites on inland lakes and ponds and Great Lakes during 1968 fo r each Michigan county. Values represent, insofar as possible, only constructed public-access s ite s during 1968 which were not located at a public or p riva te campground fa c ility . This variable was negatively correlated with the aggregate boating p a rtic ip a tio n ra te in both the State of Michigan and "top 202 t h ir t y " o rig in counties equations. However, in both cases, the regression c o e ffic ie n t lacked sig n ifica n c e. The computed regression c o e ffic ie n t was s ig n if ic a n t a t the ,017 level in the "bottom t h ir t y " o rig in counties equation; and the c o e ff ic ie n t had a p o s itive e ff e c t upon the dependent v a ria b le . The hypothesized re la tio n s h ip is thus accepted fo r the State o f Michigan and "top t h i r t y " o rig in counties equations; but i t is rejected fo r the "bottom t h i r t y " counties equation. Number o f Hotels, Motels, Tourist Courts, and Camps The value entered fo r th is va ria b le was the aggregate number of commercial motels, h o te ls , to u r is t homes, t r a i l e r parks, and sporting and recreational camps present and in operation in each Michigan county as of July 1, 1967. Precise data was not a v a ila b le for calendar year 1968; and values entered were assumed to hold constant during the study year. There was a negative c o rre la tio n between th is v a ria b le C x^) and the aggregate rate of boating p a rtic ip a tio n . However, the computed regression c o e ff ic ie n t lacked significance in a l l three equations estimated. The study hypothesis re la te d to th is v a ria b le is accepted. Number of Amusement and Recreation Service firms This v a ria b le was entered in order to te s t the hypothesized s t a t i s t i c a l re la tio n s h ip between aggregate boating p a rtic ip a tio n rates and the a v a i l a b i l i t y of su b stitu te le is u re time amusement and recreation service firms in operation w ith in Michigan Counties. No precise data were a v a ila b le fo r th is v a ria b le during 1968; and values 203 entered consisted of the number o f commercial amusement-recreation service firms which were in operation as o f A pril 1, 1967. The computed regression c o e ffic ie n ts fo r th is va ria b le {*-( 4 ) lacked sig nificance in a l l three equations estimated. The hypothesized re la tio n s h ip is thus accepted in th is instance. Number of Registered W atercraft per County The value used fo r th is v a ria b le U 28) consisted o f the to ta l number o f registered w ate rcraft per 1,000 county population fo r each Michigan county during 1968. The computed regression c o e ffic ie n ts were highly s ig n ific a n t in a l l three equations estimated: they were s ig n ific a n t a t less than the .0005 level in the State o f Michigan and "top t h ir t y " o rig in counties equations; and the c o e ffic ie n t computed was s ig n ific a n t a t the .004 level in the "bottom t h ir t y " o rig in counties equation. In a l l cases, the v a ria b le was p o s itiv e ly co rrelated with the dependent v a ria b le. The hypothesized re la tio n s h ip is rejected fo r th is v a ria b le . Occupations o f County Residents The values entered for these variables consisted of the percentage of a county's employed labor force accounted fo r by twelve occupational classes. Percentages were calculated separately for each occupational cla ss , based upon data presented in the 1970 Census of Population. Precise data on these variables were not a v a ila b le fo r 1968, and calculated percentages were assumed to hold constant between 1970 and the study year. 204 In the State o f Michigan Equation, seven o f the computed regression c o e ffic ie n ts were s ig n if ic a n t a t less than the .05 le v e l: Professional, technical and kindred workers ( x - j ^ ; sales workers ( x ^ J ; craftsmen, foremen and kindred workers ( x ^ ) ; operatives— except transport (x 2 q ); laborer— except farm ( * 2 3 ) ’ ^arm laborers and farm foremen (Xgjj); and Pr iv a te household workers (x27) . In a l l cases, the regression c o e ffic ie n ts had negative signs. None o f the regression c o e ffic ie n ts were s t a t i s t i c a l l y sig ­ n if ic a n t in the "top t h ir t y " o rig in counties equation. However, a l l twelve occupational classes had s ig n ific a n t regression c o e ffic ie n ts (a t less than the .05 le v e l) in the "bottom t h ir t y " counties equation. As was the case in the State o f Michigan Equation, the computed regression c o e ffic ie n ts were a l l negatively correlated with the dependent va ria b le in the "bottom t h i r t y " counties equation. The hypothesized re la tio n s h ip is rejected fo r the State o f Michigan and "bottom t h ir t y " counties, but is accepted fo r the "top t h ir t y " o rig in counties. Conclusions Considerable v a ria tio n in the rate of recreational boating p a rtic ip a tio n was found to e x is t among sampled registered w ate rcraft owners in the State o f Michigan. Excluding Kalkaska County (where the rate o f p a rtic ip a tio n was estimated to be z e ro ), the estimated number of a c t i v i t y occasions ranged from a high of 10,161 boat days per 1,000 population in Roscommon County to a low of 286 boat days per 1,000 population in Osceola County. The highest rates o f boating 205 p a rtic ip a tio n were found to e x is t in non-metropolitan areas of the state. While s ig n ific a n t relationships were noted between fam ily income o f respondents and boating p a r tic ip a tio n , these results should be regarded as inconclusive since the data collected on fam ily income were inadequate to provide a basis fo r a rigorous te s t o f th is r e la ­ tionship. Contingency tables between fam ily income and boating p a rtic ip a tio n suggest th a t a non-linear re la tio n s h ip e x is ts . Further research w i l l be required in order to te s t the re la tio n s h ip between these variables more s a t is f a c t o r ily . Among socio-economic variables analyzed in th is study, fam ily s iz e , occupation o f fam ily head, and age of fam ily head were s ig ­ n if ic a n t ly correlated with boating p a rtic ip a tio n in one or more study regions. Boating p a rtic ip a tio n increased p o s itiv e ly with fam ily size in two of the study regions examined. was also noted fo r the Statewide sample. A p o s itiv e re latio n sh ip This finding indicates that boating tends to be a family a c t i v i t y ; and th a t the highest rates o f boating p a rtic ip a tio n tend to e x is t among larg e r fam ilies who own registered w ate rcraft. S ig n ific a n t relationships were found between occupational class and boating p a rtic ip a tio n in four o f the study regions examined. Occupation appears to be correlated with boating p a r t i c i ­ pation most closely in the metropolitan regions of the s ta te . This may be due to the fa c t th at c e rta in occupations (which are most common in urban regions) have more le is u re time. Occupation may well be in te rc o rre la te d with family income to a substantial degree. Because 206 o f the manner in which the income variables were sp e cifie d , however, no conclusive finding is possible in th is study. Age o f fam ily head was s ig n ific a n t ly correlated with boating p a rtic ip a tio n in three o f the study regions examined. However, computed regression c o e ffic ie n ts had negative signs in two o f these regions {Region 1 and Region 12A). In Region 10, age of fam ily head was p o s itiv e ly correlated with boating p a rtic ip a tio n . Previous research has shown th at age is in te rc o rre la te d with fam ily income, i . e . , boating p a rtic ip a tio n varies a t d if f e r e n t combinations o f income and age. Lim itations in the income va ria b le did not permit a d e f i n i ­ tiv e finding on this re lation sh ip in the present study, however. Age o f family head squared did e x h ib it a s ig n ific a n t influence upon boating p a rtic ip a tio n in two o f the study regions examined (the statewide sample and the Region 10 are a ). In both cases, the regression coef­ fic ie n ts had negative signs, suggesting th at the re la tio n s h ip between age o f fam ily head and boating p a rtic ip a tio n is c u rv ilin e a r. In addition to variables pertaining to socio-economic charac­ t e r is t ic s of the sampled w a te rcraft owners (or t h e i r immediate fa m ilie s ) the modified u se r-ch arac teris tic s model contained independ­ ent variables which related to sampled w a te rc ra ft. Certain p la c e -o f- storage variables were s ig n if ic a n t ly correlated with the dependent variable (boating p a r tic ip a tio n ). Place-of-storage o f w ate rcraft a t home residence during the boating season was negatively correlated with boating p a rtic ip a tio n in the two metropolitan study regions (Region 1 and Region 10). This finding suggests th at registered w atercraft owners who store t h e ir w ate rcraft a t home during the 207 boating season, and transpo rt i t on in d ivid u al boating t r i p s , as a class, p a r tic ip a te less than boat owners who store t h e i r w a te rc ra ft a t o ther locations in these two regions. A s im ila r r e s u lt was noted when the equation was estimated f o r the to ta l (statew ide) sample. In Region 10 (one o f the re s o rt areas o f the s ta t e ) p la ce -o f-s to ra g e variables were also important. In the Traverse Bay Region, p la c e -o f- storage a t a commercial boat marina, or a t permanent residence (located on w aterfrontage) were both p o s it iv e ly c o rre la te d with boating par­ t i c i p a t io n . Boat owners in these two categ o rical classes were found to p a r tic ip a te s i g n i f i c a n t l y more than boat owners who stored t h e i r w a te rc ra ft a t other locations during the boating season. M u ltip le boat ownership appears, on the basis o f th is study, to be strongly associated w ith boating p a r t ic ip a t io n . In four of the f iv e study regions examined, as well as in the S tate o f Michigan Equation, m u ltip le boat ownership was s i g n i f i c a n t l y co rrela te d with p a r tic ip a tio n . C eteris parib us, as the number o f w a te rc ra ft owned increases (w ith in the re lev an t range examined), so too does boating p a r tic ip a t io n . In regions where the incidence o f m u ltip le boat ownership is high, ind ividu al p a r tic ip a tio n in boating should also be high among th a t segment o f the population which owns registered w a te rc ra ft. Boat length was v a ria b le in i t s e f f e c t upon boating p a r t i c i ­ pation. This v a ria b le was s ig n if ic a n t in Region 1, as well as the State o f Michigan Equation. other study regions. However, i t lacked s ig n ific a n c e in a l l This fa c to r assumes importance, however, in public p olicy concerning the construction o f p ublic boat marinas 208 and other f a c i l i t i e s , since la rg e r w a te rc ra ft usually require more elaborate care and handling equipment than smaller boats. Therefore, this v a ria b le , while not s t a t i s t i c a l l y s ig n ific a n t in four o f the study regions, may be more important then a s t r i c t in te rp re ta tio n o f study results may in d icate. F i r s t , Region 1 (containing the C ity of D e tro it and Wayne County) generates more to ta l boating a c t i v i t y occasions than any other region in the s ta te . was s ig n ific a n t in the to ta l Also, th is va ria b le (statewide) sample. The dilemma faced here, though, is re lated to the id e n tific a tio n problem, i . e . , is a high level o f boating p a rtic ip a tio n the re s u lt o f demand factors or supply factors in the destination counties? There is no easy answer re a d ily a v a ila b le to th is question since both supply and demand factors should lo g ic a lly be considered when analyzing boating p a rtic ip a tio n . Closely related to the discussion above is another study finding concerning w atercraft c h a ra c te ris tic s . Horsepower ra tin g of w ate rcraft motor was s ig n if ic a n tly correlated with boating p a r t i c i ­ pation in only the State o f Michigan (statewide) Equation. Ceteris paribus, fo r the statewide sample as a whole, boating p a rtic ip a tio n tends to increase with greater horsepower ratings of sampled water­ c r a f t motors. One may ask whether or not th is find in g is the re s u lt o f boating p a rtic ip a tio n being induced by the construction o f public and p rivate boat marina f a c i l i t i e s ? I t is extremely doubtful that the la rg e r horsepower engines would be as re a d ily purchased were i t not fo r public and p riva te docking f a c i l i t i e s provided which are capable of accommodating la rg e r w a te rc ra ft. 209 The type-of-power-system classes were extremely va ria b le in t h e ir e f f e c t upon boating p a r tic ip a tio n . In Region 1— D e t r o it , sampled w atercraft owners who reported owning boats with outboard motors, as a class, exhibited a s ig n ific a n t influence upon the dependent v a ria b le . In Region 6 — Lansing, sampled w a te rc ra ft owners having sailboats with motors, as a class, exhibited a s ig n ific a n t influence upon boating p a rtic ip a tio n . In the State of Michigan Equation, a l l four categorical classes were s ig n if ic a n t ly correlated with the dependent v a ria b le . The implications o f th is finding are unclear. While this class of variables was s ig n ific a n t in explaining part o f the v a ria tio n in the dependent v a ria b le , l i t t l e was gained, apparently, by entering sub-class e ffe c ts in the regression equation. The e ffe c ts o f transportation upon w a te rc ra ft use are not cle a r as a re s u lt of th is analysis. Because o f the nature o f the wording and structure of the questions on transpo rtatio n in the survey in s tru ­ ment, this fa c to r was entered as a dummy (zero-one) v a ria b le . More­ over, the transportation v a ria b le exhibited a s ig n ific a n t influence upon boating p a rtic ip a tio n in the State o f Michigan Equation. ever, one is s t i l l How­ l e f t unclear about the implications fo r public p olicy, given th is r e s u lt. I t would be more important to know "how many" individual boating trip s were taken by respondents, and to what destinations. Given such inform ation, one would be in a b e tte r position to assign costs to each t r i p , and to construct economic demand curves. Cross-section data could thus be used to construct a market demand curve fo r an individual study region. V a riatio n in tra n s fe r costs 210 between o rig in regions and d estination counties would ensure v a r ia ­ b i l i t y in the price o f boating t r i p s even though cross-sectional data were used. 2 Computed R values were quite low fo r the various study regions u t il i z e d ; ranging from a low value o f .1048 in the State o f Michigan Equation to a high of .2130 in Region 6 — Lansing. These re su lts indicate th a t the selected socio-economic fa c to r s , together with water­ c r a f t c h a ra c te ris tic variables represent only a p a r t ia l explanation of the v a ria tio n found to e x is t in boating p a rtic ip a tio n rates reported by sampled w a te rc ra ft owners. Furthermore, in order to use such variables as an aid to forecasting boating p a rtic ip a tio n rates of registered w a te rc ra ft owners, an additional assumption has to be made: i t would be necessary to assume th a t the class e ffe c ts o f the various categorical variables used (the a j ) are a d d itiv e . c lear th a t such is the case. I t is not Combining w a te rc ra ft c h a ra c te ris tic s with socio-economic e ffe c ts does not appear to be wholly j u s t i f i a b l e . Also, v a ria tio n in the socio-economic factors used in the model (and therefore the computed regression c o e ffic ie n ts ) may be expected to take place over time, raising serious questions concerning the v a l i d i t y o f forecasting fu tu re boating p a rtic ip a tio n rates with the c o e f f i ­ cients obtained in th is study. In the aggregate p a rtic ip a tio n model, a conscious e f f o r t was directed a t the inclusion o f "supply" variables in the s t a t i s t i c a l equation. In th is equation, aggregate boating p a rtic ip a tio n rates o f county populations were specified as a function o f socio-economic fa c to rs , supply fa c to rs , complementary boating f a c i l i t i e s , and 211 su b stitu te le is u re time a c t i v i t i e s . 2 R e la tiv e ly high R values were obtained fo r th is model in each region where the equation was e s t i ­ mated. However, th is s t a t i s t i c is an unsatisfactory estimator of the c o e ff ic ie n t o f m u ltip le determination in the county populations concerned, since i t was computed using grouped data. In the "top t h ir t y " o rig in counties equation, number o f registered w a te rc ra ft per 1,000 county population was s ig n ific a n t ly correlated with boating p a rtic ip a tio n . This single v a ria b le was retained in the fin a l regression equation, and explained more than 54 percent o f the v a ria tio n in the dependent v a ria b le . variables were retained in the model. No other Surface water acreage, and complementary boating f a c i l i t i e s v a ria b le s , were deleted from the equation in the fin a l i t e r a t i o n . These factors are thus judged to be r e l a t i v e l y unimportant in explaining variatio n s in boating p a r t i c i ­ pation rates in the top o rig in counties o f the s ta te . Since the model was estimated separately fo r the "top t h ir t y " o rig in counties o f the s ta te , i t must be concluded th a t other factors account fo r v a ria tio n in boating p a rtic ip a tio n rates in these counties. In the "bottom t h ir t y " o rig in counties equation, a very high 2 R value was obtained. Independent variables retained in the fin a l equation accounted fo r an estimated 98 percent o f the v a ria tio n in the dependent v a ria b le. All twelve of the occupation variables were retained in the f in a l it e r a t io n . retained. Both income variables were also In the t h i r t y counties where boating p a rtic ip a tio n rates were lowest, both high income (households with annual incomes o f $ 1 0 , 0 0 0 and above) and low income (households with annual incomes 212 less than $3,000) were important in explaining v a ria tio n in boating p a rtic ip a tio n . A county's location with respect to a Great Lake (mileage) was negatively correlated with boating p a rtic ip a tio n . A one-unit increase in the travel distance to a Great Lake would be accompanied by a negative e ff e c t upon the aggregate boating p a r t i c i ­ pation ra te o f th at county. Likewise, the number of public and p rivate campsites (with access to boat launching f a c i l i t i e s ) was negatively correlated with boating p a rtic ip a tio n in the "bottom t h ir t y " o rig in counties. Ceteris paribus, as the number o f such campsites increases w ithin a county, boating p a rtic ip a tio n would be expected to decrease on the basis o f th is study. This may be a re s u lt of over-crowding and over-use a t water areas serviced by public and p riva te campsites having boat-launching f a c i l i t i e s . Surface water acreage was p o s itiv e ly correlated with boating p a rtic ip a tio n in the "bottom t h ir t y " o rig in counties equation. Ceteris paribus, among the lowest aggregate boating p a rtic ip a tio n counties, the p a rtic ip a tio n ra te would be expected to increase d ir e c t ly with the a v a i l a b i l i t y of surface water acreage. Closely related to this v a ria b le , was the finding regarding the public boat-launching s i t e v a ria b le. A p ositive co rrela tio n was found to e x is t between a county's boating p a rtic ip a tio n rate and the number of public boat-launching sites in th a t county. Among the "bottom t h ir t y " counties o f o r ig in , boating p a rtic ip a tio n may be expected to increase d ir e c t ly with the number o f constructed public boat-launching site s provided. This seems to indicate th a t boat-launching f a c i l i t i e s represent a d e f in it e policy va ria b le which can be used by public natural resources 213 adm inistrators. I t would be extremely d i f f i c u l t to a l t e r socio­ economic c h a ra c te ris tic s over time. However, boat-launching f a c i l i ­ tie s represent a v a lid tool which may have income d i s t r i b u t i v e e ffe c ts i f constructed in close proxim ity to those segments o f the population which one wishes to provide re crea tio n b en efits as a matter o f public p o licy . Additions to the boatable surface water acreage o f a county might represent another valuable p o lic y to o l. A rtific ia l lakes and ponds, when constructed in close proxim ity to the population to receive primary re crea tio n b e n e fits , can also be regarded as an income d is t r i b u t i v e p o lic y . Development o f e x is tin g natural surface water resources may or may not serve the same purpose, since tra n s fe r costs may be p r o h ib itiv e to many segments o f the p o te n tia l boating population. L im itatio n s One o f the primary lim ita tio n s o f th is study is re la te d to the methods used in preparing and d is t r ib u t in g the survey question­ n a ire . In a l l lik e lih o o d , s i g n if ic a n t memory bias was introduced in the survey data co lle cte d since respondents were requested to re c a ll s p e c ific d e ta ils about boating undertaken over a period o f time equivalent to one calendar year (19 68 ). Further, the survey in s tr u ­ ment was not d is trib u te d u n til A p ril and Hay o f 1969. I t is probable th a t many respondents had begun boating during the calendar year 1969 a t the time the survey instrument fo r th is study was received. is highly probable th a t the a c t i v i t y occasions data gathered is biased in unknown d ire c tio n s . It 214 Another question may be raised regarding the response ra te obtained to the mail survey. Approximately 30 percent of the question­ naires mailed were a c tu a lly completed and returned by respondents. Thus questions may be raised about the ra te o f boating p a r tic ip a tio n exhibited by survey non-respondents. A post card follow -up was under­ taken in three control counties, re s u ltin g in a s l i g h t l y higher response to the survey. Also, follow -u p interview s were completed among non-respondents in these three counties (Ingham, Leelanau, and Grand Traverse). However, follow -u p interview s were not completed u n til July o f 1969. An independent analysis o f survey respondents was undertaken in a companion study. No s i g n if ic a n t d iffe re n c e s were found between survey respondents and non-respondents, but the la t e date o f the fo llow -up interviews make these re s u lts highly suspect. Another l im it a t io n involves the sampling plan fo r th is study. Further research in t h is area should be d irected toward reducing the sample s ize . The data co lle cte d in th is study should provide a basis f o r c a lc u la tin g an adequate sample s iz e . The systematic random sample drawn in th is study has the e f f e c t of c lu s te rin g the sample in the large urban counties where the g rea tes t number o f registered water­ c r a f t e x is t . The time horizon used in th is study as a basis fo r c o lle c tin g data on boating a c t i v i t y severely l im it s the usefulness o f the survey. Registered boat owners were asked to supply boating use information fo r one calendar y e a r. A shorter time period would be p re fe ra b le . Compressing the base period to peak use periods during the summer 215 months (June, Ju ly, or August) would s im p lify the data c o lle c tio n process since respondents would be in a b e tte r position to answer sp e cific questions about boating a c t i v i t y undertaken. By reducing the sample s iz e , sampling from a select group of study regions, and reducing the time horizon base period, the data collected should be much more usefu l. Personal interviews would be a b e tte r data c o lle c tio n procedure. The data used as measures fo r independent variables had sources of s t a t is t i c a l b ias, stemming la rg e ly from the fa c t th at they were collected a t points o f time other than the study base period (1968). Also, the dependent va ria b le (boating a c t i v i t y oc­ casions) suffered from the same d i f f i c u l t y in both of the s t a t is t i c a l models used. I t was necessary to assume, fo r example, th a t the number o f boating a c t i v i t y occasions was constant during a l l points in time during the study year, and th a t the number o f registered water­ c r a f t in the State o f Michigan was in v a ria n t during the study year, i . e . , the number o f registered w a te rc ra ft a t the end of the calendar year was constant during 1968. A fu rth e r lim it a t io n in the dependent va ria b le used (in both models) has to do with the nature of boating a c t i v i t y occasions. It is not c le a r, as a re s u lt o f th is study, what "boat days" means, i . e . , there is a problem o f interpersonal d e fin it io n o f boating a c t i v i t y occasions. A "boat day" was defined, fo r purposes of th is study, as ". . . the number o f days th at a boat was a c tu a lly in the water under power or s a i l . " Each part day of boating was counted as a f u l l day. Respondents were also asked to l i s t the number o f boat days spent on 216 p a r tic u la r boating a c t i v i t i e s , e . g . , trout/salmon fis h in g , other fis h in g , hunting, water s k iin g , c ru is in g , or "other." Because of memory b ias, the data on the number of boat days spent on p a r tic u la r a c t i v i t i e s was ignored. This deficiency lim it s the usefulness o f the study. It would have been in te re s tin g , fo r example, to examine the e ffe c ts o f a c t i v i t y s p e c ia liz a tio n , and the im plications th a t th is may have upon boating use in various d estination counties o f the s ta te . Separate equations might then be estimated f o r the various categories of a c t i v i t y s p e c ia liz a tio n . F in a lly , the data on boat use collected in th is study does not represent a v a lid expression o f boating demand. There is good evidence to suggest th at the prices charged a t public boating f a c i l i ­ tie s in the state are nominal (or z e r o ), and do not r e f l e c t actual supply costs. This means th a t attendance or user s t a t is t i c s r e f l e c t current market rules governing public provision o f boating f a c i l i t i e s . Under such conditions, i t is erroneous to consider user s t a t is t i c s as e ith e r demand (or supply) estimates. A d if f e r e n t set o f prices charged might s ig n if ic a n tly a l t e r observed attendance s t a t is t i c s . Under current conditions, user s t a t i s t i c s on boating p a r t i c i ­ pation are a r e fle c tio n o f non-market (or q uasi-) demand. Any attempt to account f o r e x is tin g patterns o f use are a r e fle c t io n of both supply and demand conditions and should be so q u a lifie d . Consideration o f only the demand side o f the p ictu re is tantamount to admitting th at users w i l l be allowed to manipulate the market without sending appro­ p ria te market signals; while consideration o f only supply conditions allows recreation planners to manipulate the market without receiving 217 market signals. Under current market conditions (where high tra n s fe r costs e x is t) supply factors are important and have s ig n if ic a n t w elfare connotations. Supply conditions represent p olicy v a ria b les . I f c e rta in disadvantaged groups are to be granted recreation b enefits as a con­ scious public p o lic y , tra n s fe r costs between o r ig in and destin ation areas should be reduced. This can be done most expeditiously by a lte r in g supply conditions in close proximity to the population class which is to receive recreation b e n e fits , assuming no change in present public pricing p o lic ie s . Recommendations fo r Further Research This study has, fo r the most p a rt, emphasized the e ffe c ts of non-price variables on p a rtic ip a tio n in recreational boating. In f o r ­ mation on the price o f the "whole recreation experience" was not collected in the survey instrument. However, some emphasis was given to estimation of the re la tio n s h ip between boating p a rtic ip a tio n and the consumer's level o f income. This analysis did not prove to be e n t ir e ly adequate since the fam ily income data was collected in grouped form, with unequal in te rv a ls between classes. Future research can be more meaningful i f fam ily income data are collected in ungrouped form. Also, information co llected on the number o f boating trip s taken should be co lle cte d . Because o f the unusual nature of the (tra n s fe r ) costs associated with recreational boating, the q u a n tific a tio n o f demand functions is possible when cross-sectional data are used. Using the cost o f the "whole recreation experience" w i l l ensure th a t the price va ria b le takes on a wide range 218 o f values since the supply o f boatable water surface areas is geographi­ c a l ly dispersed over space. Information r e la t in g to the value o f re crea tio n al resources to the using public is becoming in c re as in g ly important to public decision makers. However, obtaining inform ation on the value o f boating waters depends upon knowledge o f the demand function fo r re creatio n al boating. Future research should concentrate upon pro­ viding th is type o f inform ation. Future research could also be helpful by concentrating on the re la tio n s h ip between re crea tio n al boating and the level o f consumer income. By c o lle c tin g data on boating t r ip s and consumers' incomes, information on income e l a s t i c i t i e s could be obtained. Boating t r ip s could be segregated by type o f a c t i v i t y , e . g . , fis h in g , hunting, c ru is in g , water s k iin g , e tc . Such inform ation could then be used to estimate c r o s s - e l a s t i c it i e s between various boating a c t i v i t i e s . The data c o lle c te d in th is study were obtained well a f t e r the peak boating season had ended. Furthermore, when questionnaires were d is t r ib u t e d , many sampled boat owners had probably begun boating during the 1969 boating season. Future research should concentrate upon a much shorter period o f time f o r which data is c o lle c te d — perhaps 1-3 months during the period o f peak boating a c t i v i t y (Ju ly through August). Also, much b e t t e r control should be exercised over the c o lle c tio n o f data. Household interviews would be the preferred method o f data c o lle c t io n . However, i f t h is is not possible, c a r e f u lly d is trib u te d mail questionnaires could be used i f they were received 219 by sampled w a te rc r a ft owners on a monthly basis during the actual time th a t boating was being undertaken. The sample frame used in th is study represents a continuing source o f inform ation which may be used by fu tu re researchers. How­ ever, i t is r e s t r ic t e d to households which own powered w a te rc r a ft. In order to be t r u l y re p re s e n ta tiv e o f the re crea tio n al boating f l e e t in the s t a t e , some e f f o r t should be made to include households owning non-powered w a te rc r a ft (canoes, rowboats, e t c . ) in the sample. The survey questionnaire developed f o r use in th is study proved to be q u ite lengthy and complex to adm inister and in t e r p r e t. Information co lle cte d on number o f boating a c t i v i t y occasions under­ taken by sampled w a te rc ra ft owners may contain considerable e rro r due to memory bias and the complexity o f the questions posed in the survey instrument. Future research could b e n e fit by rewording the questions on boating a c t i v i t y occasions on (a) Great Lakes, and ( b) inland lakes and streams. APPENDICES APPENDIX A MAIL SURVEY QUESTIONNAIRE 221 STATE OF MICHIGAN W ATUW AY1 COMMISSION HATUtAL ■ K O U tC Il C O M M IlflO M C A IL T. JOHNSON A. son* Omlmw* CM AIUS H A W H. WHdTEICr GEORGE ROMNEY, Governor DEPARTMENT OF NATURAL RESOURCES C. M. LA ITALA ■AlAH A . MAC MULLAH, Director ■O IEIT C. McLAUOHlIN YOLMA* j . M lllt t V k> C M im LtO N A ID H. THOMSON lO IIS T r. KINO io u u , j* . mofiiCK o. AUGUST SCHOUt SO SEAT J. FUI10NO J t r n r i T. Moron tu lld n g Urn tin g , M khfeon 40*16 J T S U li r J Dear Boat Owner: At th is time o f y e a r, when boats are out o f the w ater, the Waterways Com­ m ission, lik e everyone e ls e , 1s making plans fo r the coming season and seasons ahead. We want to make sure th a t the riv e rs and lakes o f Michigan, Including the Great Lakes, o ffe r safe and accessible recreation to a ll who love the w ater. To help us In our jo b , we need your assistance In fin d in g out more about the kinds o f f a c i l i t i e s you and other boaters re q u ire . I f there are shortages 1n c ertain areas, we would H k e to know about them. We a re , th e re fo re , sending you th is questionnaire w ith the request th a t you take a few moments to f i l l 1t out and send 1 t back to us. This study 1s one o f several research projects being undertaken f o r the Waterways D ivision by the Recreation Research and Planning Unit a t Michigan State U n iv e rs ity . Your name was taken a t random from the l i s t o f boat re g is tra n ts , and your reply need not be signed. I t w ill be used w ith a ll the other re p lie s to show us the pattern of boating 1n Michigan and In d ic a te where we should be providing new or improved f a c i l i t i e s . Simply place your completed questionnaire 1n the stamped, pre-addressed envelope and mall 1t back to us a t your convenience. Thank you very much fo r your help. With best wishes fo r a good season 1n 1969. Keith Wilson D ire cto r f KW:jaw Enclosures 222 < 223 FOR YOUR ASSISTANCE: A COUNTY AND HIGHWAY MAP OF MICHIGAN ttc ttt I ALCOM "i'lan *'* HTI I I 9 ^ 1t!^_L _l___ I oicou. I 'OICOM. I ioico I L1 U ItU tfl. I .................. u) !fc L ' -, 'MONTCtlM 1 -1L K IT f- ClCOL, non >*•<« Hami l»r*ctii ro *r . X " " .. _ i iLtiM . r»M.t : , *i ■ ttr o T Q ! „K_ —"Jt* ^ ^ m r o ., tfitftOtt _ .A L ...!._ r L X T ‘ A*«UM« 'l/LA U ir.' r . t «rtii» ! JACIjOK VAIflTKMAV i pjMCrta* l MM I'-WI™iffABCN ^MlLllOAU L|HAW|f atTMfftr UUl*bC 0 601* 4 224 M IC H IG A N R E C R E A T IO N A L B O A T IN G N E E D S Q U E S T IO N N A IR E — — — — ■■ ■" PLEASE ANSWER QUESTIONS,fTHROLIGH13 F dfi TtfE BOAT ID E N TIFIED BY THE REGISTRATION tftiAlBER AND BOAT LENGTH WHICH .1 APPEAR UNDER YOUR AODRESS ON PAG E l J rC , 1 WHAT TYPE OF POWER SYSTEM DOES THIS BOAT HAVE? (Check one) CD Outboard m otor n 2 Sailboat w ith m otor O Inboard motor CD Other [write ltd CD Inboard motor w ith outboard drive WHAT IS THE HORSEPOWER RATING OF THE PRIMARY MOTOR (OR MOTORS) USED ON THIS BOAT? Hp. „Hp. Indicate horsepower o f any other motor* used on th ii b o a t:________, — __ 3 WHAT COUNTY IS THIS BOAT REGISTERED IN?______________________________________________ County 4 WHERE DO YOU USUALLY KEEP THIS BOAT DURING THE BOATING SEASON? (Check one) CD A t my permanent home, which i* not on a take or river. CD A t waterfrontage located at my permanent home lot, □ CD CD CD CD 5 A t a commercial marina-berth. A t a tummer cottage. A t a publicly-owned marina. A t a boat or yacht club. Other (specify)______________________________________________________________ WAS THIS BOAT TRANSPORTED FROM YOUR HOME OR OTHER LOCATION TO PARTICULAR LAUNCH­ ING SITES DURING THE PAST BOATING SEASON (calendar year 16601? CD YES O NO If "N O " akip over questions 6, 7, and 8 , and proceed w ith question 9. 6 WAS THIS BOAT TRANSPORTED BY: CD trailer CD ear-top carrier 7 PLEASE INDICATE THE TOTAL NUMBER OF TIMES YOU TRANSPORTED THIS BOAT FROM THE PLACE OF STORAGE OR MOORING TO THE PLACE OF USE. Number o f time*____________________________________ 8 IN THE TABLE BELOW, NAME THE COUNTIES WHERE YOU MOST OFTEN LAUNCHED THIS BOAT; AND INDICATE THE NUMBER OF TIMES THE BOAT WAS LAUNCHED AT EACH BOATING ACCESS POINT. Number o l Time* Th h Boat Launched e t County (Write In) Publlc Marina or Ramp City. County or Towmhip M o il Launcher: ™ ?ntl mott Launcher ™ All other Launch**: ™ Slate Facllltie* Commercial Marina Federal I Private property or othrr 225 9 DID YOU USE TH]§ BOAT ON A N Y OF THE MICHIGAN SECTIONS OF THE GREAT LAKES, OR CONNECT­ ING WATERS*, DURING THE PAST BOATING SEASON (calendar year 1068)? "(Greet Lakes and connecting water* ere Lakes Huron, Superior, Erie, Michigan, end St. CJelr; St. Mary's River, St. Clair River, and Detroit River.) O □ 10 NO ——— If "N O ", please proceed to question 11. YES ——— If "Y E S " please continue w ith question 10. IN THE TABLE BELOW, NAME THE THREE GREAT LAKES OR CONNECTING WATERS COUNTIES WHERE THIS BOAT WAS USED DURING THE PAST BOATING SEASON. Give the number o f days that the boat was actually In the water under power or sail In each county; and give the number of boating days spent on particular activities. (See map on page 2.) USE OF THIS BOAT ON GREAT LAKES AND CONNECTING WATERS ONLY Note: Count each part day spent b olting as a fu ll day. The number o f days spent on specific boating activities may not equal the total number o f days shown in the left-hand column. Count each part day spent on a particular boating activity as a fu ll day for that activity, \ Boating Activities No. days you used this boat for— Davs of County (Writa in) Soaring 17 YVlCLn^itptti-County of moat use: 4 * County of 2nd most use: “► 4" County of 3rd most use: * 11 ^ O th tr fishing (No. Days) Dm) z 0 11 (No. Hunting Water skiing Cruising Other (No. Days) (No. Days) (No. Daya) 9 S 0 ► 4f ■ 4 Trout/Salmon fishing If Tout Boating in "A ll ^ Other" Counties: ► ► DID YOU USE THIS BOAT ON ANY INLAND LAKES OR STREAMS IN MICHIGAN DURING THE PAST BOATING SEASON (calendar year 1960)? Cl N O U YES — II "N O " please proceed to question 13. H "Y ES " please continue w ith question no. 12. 226 12 IN THE TABLE BELOW, NAME THE THREE MICHIGAN COUNTIES WHERE THIS BOAT WAS USED MOST ON INLAND LAKES AND STREAMS DURING THE PAST BOATING SEASON' Give the number of deyithatthlgboei wet actually in the water tinder power or sail in each of these count lei; and give the number of boating dayt tpent on varlout activities. (See map on page 2.) USE OF THIS BOAT ON INLAND LAKES A STREAMS Note: Count each part day tpent boating at a full day. The number of dayt spent on specific boating aeiivitlm may not equal the total number of days shown in the left-hand column. County (Write in) 4 * 4 * 13 Trout/Stlnnon fhhing Other tithing Hunting W iltf lining Cruising Othar (No. Day it (No, Daytl (NO. Daytl (No. Daytl (No Davs) (No. Daytl 2 It 4 I Boating Activities No , d ays you used th ii boat fo r- Total Day* ol Boating EXAMPLE Count each part day tpent on a particular boating activity at a full day for that activity. /f' J Z o o County of molt u h ; County of 2nd m oix u*t. Courtly of 3rd moTtuw ■ * ► ^ Boating in "A ll m ► Other" Couniiei. ......... DID YOU USE THIS BOAT IN ANY CANADIAN PROVINCE OR A STATE OTHER THAN MICHIGAN DURING THE PAST BOATING SEASON (calendar year 196017 □ N O LJ Y E S I f ' ’NO", skip over the remainder of this question end proceed with question 14. If "YES," please complete the table below. Other States: Give the Number of Days Boat was In tha Water Under Power or Sail County or noarest city (if known) * County o l most use: *■ County of In d motl ino: «M County of Jrd most use: « Name of State or Canadian Province * tf unknown, please consult a highway map. **(N O T£: count each part day o l boating at a fu ll day). Number of boating days** 227 THE FOLLOWING QUESTION CONCERNS OTHER RECREATIONAL BOATS OWNED IN ADDITION TO THE ONE IDENTIFIED B YTH E REGISTRATION NUMBER ON PAGE 1. (Not*: If you own no other boats, plans check her* [U and skip over to quart Ion 15) 14 IN THE TABLE BELOW. GIVE THE NUMBER OF OTHER REGISTERED AND UNREGISTERED BOATS OWNED BY YOU, AND BY THE MEMBERS OF YOUR IMMEDIATE FAM ILY RESIDING WITH YOU. Also, give the boat length and horsepower rating o f the motor uied on it. Type of boat* Length HortrpowAr riling of the motor 'Include other inboards, outboards, sailboats, canoes. Inboard-outboards, rowboats, etc. IN ORDER TO FORECAST THE FUTURE DEMAND FOR BOATING FACILITIES IN MICHIGAN, IT IS NECESSARY FOR US TO BE ABLE TO TIE IN FAM ILY CHARACTERISTICS WITH BOATING USE PATTERNS. PLEASE ASSIST US BY ANSWERING THE QUESTIONS IN THE FOLLOWING SECTION. 15 PLEASE GIVE YOUR COUNTY AND STATE OF PERMANENT RESIDENCE. AND WRITE IN YOUR POSTAL ZIP CODE. County name-----------------------------------------------------State___________ _________ Postal Zip Code___________ 16 WHAT IS THE AGE AND SEX OF THE "HEAD OF YOUR FAM ILY?" Age:___ years 17 Sex: Male O Female GIVE THE AGE AND SEX OF EACH MEMBER OF YOUR FAMILY RESIDING WITH YOU (excluding the "head of household” ) Male: ages:____ 18 O Female: ages:________ ___ ________________ WHAT IS THE OCCUPATION OF THE "HEAD OF YOUR FAM ILY?" (Please indicate the type of job that you hold, NOT the organirotion tor which you work), (Write ini 19 PLEASE ESTIMATE YOUR TOTAL FAM ILY INCOME FOR 1968 BY CHECKING THE PROPER BOX BELOW. (Check only one box). □ □ Under $3,000 $3,000 to 55,999 □ P S6.Q00 to $7,993 $8,000 to S9.999 P $10,000 to $14,999 □ $15,000 to 524,999 P $ZS,000 and over 228 2 0 WHICH OF THE ANSWERS BELOW BEST INDICATES THE TOTAL YEARS OF EDUCATION COMPLETED BY THE "HEAD OF YOUR FAMILY?" I Chock one box) □1 □ □3 □4 □5 □6 □7 □ B 2 21 □ 10□ □11 □12 9 □ □14 □15 □1B □17 □or more 13 IN THE SPACE BELOW. PLEASE INDICATE A N Y SPECIAL BOATING PROBLEMS YOU MAY HAVE: THANKS FOR YOUR HELP t II you accidently m ilpiace the return envelope provided, plena mall to: Recreation Retaarth and Planning Unit Room 312 Natural Resource* Building Michigan State Unhranlty Eait Laming, Michigan 48923 APPENDIX B CODE NUMBERS FOR MICHIGAN COUNTIES, TOTAL NUMBER OF REGISTERED WATERCRAFT, NUMBER OF QUESTIONNAIRE RESPONSES USED IN ANALYSIS, AND EXPANSION FACTORS CALCULATED FOR USE IN ESTIMATING TOTAL BOATING ACTIVITY OCCASIONS, BY MICHIGAN ORIGIN COUNTY 229 CODE NUMBERS FOR MICHIGAN COUNTIES 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 Alcona Alger Allegan A1pena Antrim Arenac Baraga Barry Bay Benzie Berrien Branch Calhoun Cass Charlevoix Cheboygan Chippewa Clare Clinton Crawford Delta Dickinson Eaton Emmet Genesee Gladwin Gogebic Grand Traverse G ra tio t H ills d a le Houghton Huron Ingham Ionia Iosco Iron Isa b e lla Jackson Kalamazoo Kalkaska Kent 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 230 Keweenaw Lake Lapeer Leelanau Lenawee Livingston Luce Mackinac Macomb Manistee Marquette Mason Mecosta Menominee Midland Missaukee Monroe Montcalm Montmorency Muskegon Newago Oakland Oceana Ogemaw Ontonagon Osceola Oscoda Otsego Ottawa Presque Is le Roscommon Saginaw Sanilac Schoolcraft Shiawassee S t. C la ir S t. Joseph Tuscola Van Buren Washtenaw Wayne Wexford NUMBER OF REGISTERED WATERCRAFT AND NUMBER OF RETURNED QUESTIONNAIRES USED, BY MICHIGAN ORIGIN COUNTY No. o f R egistered W a te rcra ft^ ui jy No. o f Returned Q u e stio nn a ire s Used L .A p a ild iU II h i County 1-A lcona 2 -A Ig e r 3 -A lle g a n 4-Alpena 5 -A ntrim 6-Arenac 7-Baraga 8- B arry 9 - Bay 10- Benzie 11-B e rrie n 12- Branch 13-Calhoun 14-Cass 1 5-C ha rlevo ix 16-Cheboygan 17-Chippewa 1 8-C lare 1 9 -C lin to n 20-Crawford 21-D e lta 22-D ickinson 23-Eaton 24-Emmet 25-Genesse 26-Gladwin 27-Gogebic 28-Gd. Traverse 2 9 -G ra tio t 3 0 - H ills d a le 31-Houghton 32-Huron 20 f t . o r Less 705 870 4,255 3,178 2,305 590 678 3,593 5,204 1,607 8,442 5,122 8,295 6,651 1,914 2,512 3,007 1,378 2,531 526 1,774 1,626 3,538 2,133 22,660 1,127 1,896 4,681 2,078 2,674 1,907 1,340 Over 20 f t . T o tal 8 713 16 126 886 100 67 18 11 98 337 32 356 121 238 194 180 109 135 27 56 28 53 9 97 127 763 24 39 167 37 58 93 73 4,381 3,278 2,372 608 689 3,691 5,541 1,639 8,798 5,243 8,533 6,845 2,094 2,621 3,142 1,405 2,587 554 1,827 1,635 3,635 2,260 23,423 1,151 1,935 4,848 2,115 2,732 2,000 1,413 20 f t . o r Less 17 9 53 35 36 10 10 53 65 18 102 61 100 62 30 28 24 20 33 5 34 25 62 33 297 15 19 58 14 26 31 15 Over 20 f t . 1 0 4 4 0 0 1 4 6 0 12 1 6 4 4 0 2 1 0 1 0 0 0 5 20 1 2 6 2 3 4 3 T o ta l 18 9 57 39 36 10 11 57 71 18 114 62 106 66 34 28 26 21 33 6 34 25 62 38 317 16 21 64 16 29 35 18 F a ctor 39.611 98.444 76.860 84.051 65.889 60.800 62.636 64.754 78.042 91.056 77.175 84.565 80.500 103.712 61.588 93.607 120.846 66.905 78.394 92.333 53.735 65.400 58.629 59.474 73.889 71.938 92.143 75.750 132.188 94.207 57.143 78.500 No. o f R egistered W a te rcra ft^ u n g in County o r Less 12,960 2,757 2,102 1,941 1,698 9,993 11,395 703 23,102 183 640 1,905 1,801 5,354 3,500 759 1,975 18,510 2,097 3,266 2,237 1,967 1,215 4,232 613 4,801 3,192 839 8,505 2,531 34,686 1,191 1,045 659 Over 20 f t . 391 55 35 13 34 287 398 16 985 12 3 32 96 168 83 7 156 3,769 70 76 66 43 57 130 9 431 43 21 377 34 2,306 21 10 18 T o tal 13,351 2,812 2,137 1,954 1,732 10,280 11,793 719 24,087 195 643 1,937 1,897 5,522 3,583 766 2,131 22,279 2,167 3,342 2,303 210 2,010 24 1,272 4,362 622 5,232 3,235 860 8,882 2,565 36,992 37 25 22 29 111 162 5 253 4 11 27 31 58 50 10 23 154 14 49 22 12 1 0 0 1 10 8 0 17 0 0 1 4 5 7 1 6 77 3 2 1 1 11 3 52 7 47 38 8 1 13 3 12 111 1 0 1,212 36 429 15 1,055 677 22 20 7 60 2 1 2 222 38 25 22 30 121 170 5 270 4 11 28 35 63 57 11 29 231 17 51 23 25 14 60 3 60 41 13 118 36 489 17 23 22 Expansion F a cto r 60.140 74.000 85.480 88.818 57.733 84.958 69.371 143.800 89.211 48.750 58.455 69.179 54.200 87.651 62.860 69.636 73.483 96.446 127.471 65.529 100.130 80.400 90.857 72.700 77.750 87.200 78.902 66.154 75.271 71.250 75.648 71.294 45.870 30.773 232 3 3 -Ingham 3 4 -Io n ia 3 5 -Iosco 3 6 -Iro n 37- Is a b e lla 38-Jackson 3 9 -Kalamazoo 40-Kalkaska 41-K ent 42-Keewenaw 43-Lake 44-Lapeer 45-Leelanau 46-Lenawee 4 7 -L iv in g s to n 48-Luce 49-Mackinac 50-Macomb 51-M anistee 52-M arquette 53-Mason 54-Mecosta 55-Menominee 56-Midland 57-Missaukee 58-Monroe 59-Montcalm 60-Montmorency 61-Muskegon 62-Newaygo 63-0akland 64-0ceana 65-0gemaw 66-0ntonagon 20 f t . No. o f Returned Q u e stio nn a ire s Used --------------------------------------------------------------------20 f t . o r Less Over 20 f t . T o ta l No. o f Registered W atercraft! No. o f Returned Questionnaires Used 20 f t . o r Less . 67-0sceola 68-0scoda 69-0tsego 70-0ttawa 71-Presque Is le 72-Rosconron 73-Saginaw 74-SaniIac 75-Schoolcraft 76-Shiawassee 77-St. C la ir 78-St. Joseph 79-Tuscola 80-Van Buren 81-Washtenaw 82-Wayne 83-Wexford 956 402 1,108 6,599 1,300 2,976 9,766 885 1,259 3,116 5,827 5,557 1,828 4,554 7,869 61,553 1,884 13 3 24 495 13 139 342 29 13 67 895 124 64 61 267 6,352 35 969 405 1,132 7,094 1,313 3,115 10,108 914 1,272 3,183 6.722 5,681 1,892 4,615 8,136 68,405 1,919 402,590 23,485 426,075 Total Mean 4,850.482 Over 20 f t . 282.952 Total 5,133.434 20 f t . o r Less 20 6 Over 20 f t . Total 1 0 1 21 6 10 25 9 98 13 38 140 17 13 49 53 77 28 58 116 520 9 118 21 2 123 14 41 155 18 13 50 83 84 30 59 125 638 23 4,807 572 5,379 57.916 1 3 15 1 0 1 30 7 2 1 6.891 64.810 Expansion Factor 46.143 67.500 113.200 57.675 93.786 75.976 65.213 50.778 97.846 63.660 80.987 67.630 63.067 78.220 65.088 107.218 83.435 — — ^Taken from S i 2e and Type o f Registered Boats in Michigan Counties, unpublished S t a t is t ic s , Michigan Department o f S tate, December 1968. 233 O rig in County APPENDIX C OPTICAL SCAN SHEETS USED IN CODING MAIL SURVEY RESPONSES 234 ^ g S S S 2 S 2 S S 2 ; ■; »; i n X . .f X " " " tt .|X : |X tt n i’ .SSigi!ii!B!iSSSBS52o;S2^ »i *■ l> jj * jiQ* jj ljft|j » ip « - * »1 ii :| •> i S fSi i I i i i • “i l i i l i ' i i i l T£ H i n f n n i l U H H l U H H n i ' ' Hi •: c 235 a s S g n S S S K S S S S iiS S ^ S ii •t 8 SKSt!8 s ; ; s S o » » M 4*H i ii ii ii ii ii ii ii ii 41 u i i n i: u H i n ii v t; X *r ** f* n H ** ^ - ii n M H i H ^ 4!it I ii1! :r ii ii ii i: i :! :i § i: ii Mi H HH H H ii ii kii i ii ii ii * ii ii ii *l !• i : :i ii :i * ii ii * i ii I ii I t ^ I I ii 1411 ii !! I I H m 11 I H si 3 i: ii !i fi fi a a fi ii ii !! S 1 ?«! I ^ «« ii I Ui *t M n u n n i H f l i ^ ii :: 4 4 H 4 N N !! ii ii 4 ii I: i! ii I I H I ii I i! I i l l 236 1 :n-: 3 7 9 I.D. Number "1 " =-r-: 1:1:; -.:rz County where launched meet ::t: City, county, twp. 11 :a-.: :-.h: State 13 :a=i ::t:z ::*= Federal IS ■! ;: r ; Commercljl marine 17 ;4 : ::t: :3:: :A : :: * i r:3c= : : i : r:*= S^:; :.-V: z r f. : Private property, other -3>:: :•i :j County —2nd meet launchet 21 =:*^ 19 23 :»■: : ; r : :'T.i City, county, twp. 25 :a- r- - r--. " * = State 27 -~J> Federal 29 i ■i :■*: Commercial marina 31 • m :: ': r : r’* Private property, other 33 i i l ;t -.r: T-si: County —all other launches 35 ::*r 37 E t; ::±: City, county, twp. 39 Z&-- "1 " r-vrr State 41 : W . f •" 43 !»■ ;;»■ . rt Commercial marina 45 : i.i ■ -r;- ■ * ■ ■*■ Private property, other c :t t > * 2 4 ;:js :rt= :a :: DECK 2 Question 8 r*- fi" :*:r --T-J :;j;S 6 :3:r in;: :c : 14 16 IB :-*=r ::i: ; i: "ft:: ::T:; ::tt; :: b : ::r: ::tt: ,;7“ t:jT2 nk: ::ft: ::5c: :.* r :itk; :b : v* : ::ft ■. ::C-: litz - v.. .-ft: r ■ft ::ft * ,.8;; ,B : ::tt; ::ft: V t ■I! =tl:= ::::: :« :s :»5 :v: : M W :^ir * : r* : r::;: ::t:= " j: ::rs tifti s :? : rv = ::t:z :ft:: ::St: ::t: ::M: 26 28 :« ■ r:i:: ::2: ;ra: ;t 8 ; :;U : r1 ;: . ‘.ft: ta' ::t: fp: ::t. :.i: ::l. _ _ _ _ ““ ::l:? .’ft:: :ti.z f :.tf: : ft.- f i: : ftT it: t r:l:r ::t: ::1: ::::i ::::: := ':2 :.ft: 42 44 :0 " ;:t:; i.ttr :‘ft: fi : .i: 46 48 -'ft ’ . 1 ::i: :*r ■ ““ z+t * , ;:lis —“ : ■ « : ■ -:a■ : : tri :6 ' .4 :‘ft, ■ 4 S i .. 4 ^ : . b: ::i:: o -i *4: e. ..i ■ . ft-. e. ;:1■ * . :a.: ..ft- ::3: 36 38 40 X: — :v.r 30 32 34 :3.: • a :.* -:c: ::a: = V = _ _ w im e .ft-: ::t: f3-‘ t :::i :ft,: ::3: 20 22 :r: ::r: 24 :X : Z 7 J .Z :.t: : r-tti ;:t: ::* i :■>: :: i: :'C: t:*r; t :::: :5t: ::3: ::^ = 12 :x : :’ i : : i: : C; ::::= : :n = V 10 :A : :i: :t: Z 3 - 0 : : i : :«ri ::tT ::y; ■ ft” f. ft r b . 1 ■ ft - ' _ ». ** »- ■ ft ■ » 237 DECK 3 GREAT LAKES I. D. Number I 2 1 4 ..D ^.G reat.Lakn... 7 9 ..T outrilv*:;;: ..County n u ttu w l.. 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 49 51 S3 55 57 59 61 63 65 67 69 71 73 75 77 79 ..Trout/»imaq ffthJng ..Ottwr.fithJrisL ;::i: ..Hunting ..... ..... ^Wtwrikilnft, T:::; Cruising ..... ..OUiw.. ..... ..... ..... .J o tA i^ m .... ..... ..CouritY-.&?alrrl9 (3 fishing Olhtfllthlr^L .... „ Hunting Waterikiing.......... Cruising Other _ Total day* County —3rd used Trout/salmon fishing Other fishing Hunting Water skiing Cruising Other total days All other counties trout/salmon fishing Other fishing Hunting Water skiirig" "Cruising Other.......... tfS 6 8 10 12 14 16 IB 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 238 INLAND LAKES AND STREAMS 2 *W* z*ii rn=s 4 :w : 1.0. Number i: ( ii " f : ;:t=i s:»:i 7 r:* t Total day* :^c: ;:r= •■r- - -fi Wjf! U,?4: I 3 ;» : ZZfLZ. ::|i: OthmrfWilgM 19"*=Hunting ”S :::t: Other tithing 53 r:a : ::r: "it: ■■A■ Hunting 5 5 ;;tt: ::f: Water tkiing ::rt; 57 i u : ::a : Cruliino 59::U: ::it: ;;rt: Other 61 ::a: " it: ::Hr Total dayi 63 " i f t t r t ! ::;t: All other counties 65 :::tr ::st: ::it: .;A : 6 7 ::lt: TT7== ;:s : ::r: ::ti : : r : ;:z; ttnt rrrt: 12 ZZKZ ::r: t:ii: s:tts 51 77 : 79 ;:cs DECK 4 :s«i: •‘X ■ ::^= ==TS= ;:C: ::::: ::::: ''X ' 6 z:K. zz.-.z ::::: e 10 ZZItZ ZZZZZ 14 "X= ::s : ::rt: ::=" ::ft: =r^s :x : 4 9 73 : 75 =” == ::::: ::::: ::t= ZZJZZ trtzz ;^ = :x : 31 ::tx: ::ci ::x: ::u= Trout/tetmon tithing 33 "ill : n : use: Other fi thing :;ii: 35 Hunting 37 "«= ==*= «*= Water skiing 3 9 ‘ U: " i : ::a: Cntliing 4 1 - ttr Other 71 "S : Cruising Other 25 :: : ; e : Total daya :,T2 7 ::rc: " ,:I -:;tCounty — 2nd uaad 69 : : W6 irv= SS|f- ::Jt= ::::: "J” ::n : ::rr: :: :r : f :t::: ::::r :tl:= ::;:t 111111! f 11111111E11111111111111111111111II1111111111 I if ii I-. ii I il 1! if II § I S I ? ii ii $ ii $ ii I! ?i I I i!.;l ii i ii ii I ii if H if * * n ** ii «« i« n n ii >i m ii if m ri i« ii «i »i ii 1 i* ii m ii H if I ii u ii § tl II u li ii ii ii ii ii ii f< h ii fi ii ii ll ti II * If 4i If ff •ti 4} 4i 41 4; 4; ii II 4: II ii 41 »f ■' II II II H II 41 fi fi to r« a 1 it ftt ?tt F*J rfc fig m E tc '* O * P F ¥ tt *4 n tl* ft I "HiS tt II ii * tl 2itT ~ fi »* |9 R If 4 i4 ! R >*0 iiUJ ii dt ttt a: tt: i- D tf) N i- n ft n o « r» S * * * APPENDIX D ORIGIN-DISTINATION MATRIX AND TABLE SHOWING PROCEDURE FOLLOWED IN CALCULATING THE ONE-WAY TRAVEL DISTANCE, BY MICHIGAN ORIGIN COUNTY 240 Appendix T a b le Estimated Total Boat Days by O rigin County and D is tr ib u tio n by D estination County, S tate o f Michigan, 1968 Destination County o f O rigin Alcona O rigin County Code : D estination County Code 1 1 10 4 35 53 48 12,200 1,981 198 1,386 158 197 16,120 2 2 17 21 52 72 75 23,134 98 4,824 98 197 2,166 30,517 3 2 3 384 72,710 15,679 769 154 307 3,920 231 4,612 3,920 769 3,074 3,074 4,842 114,445 Total Alger Total Allegan 8 17 28 39 43 49 51 53 59 61 62 80 Total Alpena Number. o f Boat Days1 4 1 4 10 16 17 48 241 3,194 92,456 2,522 336 1,777 132 242 Alpena (c o n 't) 49 51 60 68 71 72 75 Total Antrim 5 10 15 21 25 28 40 51 54 75 Total Arenac 6 16 35 63 82 Total Baraga 7 31 32 42 48 52 66 70 Total Barry 3 8 16 17 40 49 51 52 53 54 59 62 67 672 336 1,681 84 5,211 588 252 108,641 77,222 988 1,647 3,329 1,450 659 1,450 66 791 198 87,800 8,208 243 790 2,614 182 12,039 18,853 1,127 376 626 3,886 626 63 2,819 28,376 259 121,448 907 907 1,619 194 2,397 324 389 842 2,526 1,490 389 243 Barry (c o n 't ) 70 72 80 389 648 777 135,501 1 4 3,746 7,726 4,683 54,942 1,873 1,717 6,946 1,483 1,093 312 10,458 2,029 1,093 12,564 2,341 234 4,214 1 ,639 234 468 2,263 78 4,917 1,561 780 5,385 78 780 1,873 137,510 Total Bay 9 6 9 10 15 16 17 18 24 26 28 32 35 40 45 51 52 53 56 60 62 65 69 71 72 73 79 83 Total Benzie 10 10 28 72 39,245 911 637 40,793 11 2 3 7 77 8,952 154 232 9,107 118,232 10,959 849 1,080 154 Total Berrien 8 10 11 14 15 16 24 244 Berrien ( c o n 't) 28 36 39 41 42 43 49 51 52 53 54 61 62 64 70 75 78 80 83 3,704 849 77 77 2,315 1.003 1.003 13,660 386 3,087 1,158 154 9,415 7,795 2,701 1,080 1,080 22,689 540 222,569 2 8 2,114 5,074 99,195 1,691 507 1,776 169 85 592 254 677 507 85 677 113,403 Total Branch 12 12 13 15 20 27 61 63 65 66 68 71 78 Total Calhoun 13 2 3 8 10 n 12 13 15 16 17 18 19 20 21 402 2,495 42,665 10,062 322 10,384 112,619 1,851 966 3,864 403 403 725 403 i 245 / Calhoun (con t ) 23 27 28 34 36 38 39 40 43 45 51 53 54 55 57 60 61 62 64 67 68 69 70 72 75 77 78 80 83 Total 14 Cass 11 12 14 17 27 48 51 62 75 78 80 83 Total Charlevoix ir 10 5 10 15 17 21 24 7,970 322 805 3,301 402 402 15,697 2,737 6,037 1.288 4,025 1*047 3,542 1.449 242 80 5 1.208 483 805 1,127 1,208 5,877 4,508 8,291 2,415 644 2,334 3,059 483 270,077 1,556 1,245 142,500 311 207 616 3,734 2,593 ?33 3,734 14,416 519, 172,364 862 308 52,781 123 123 3,942 246 Charlevoix ( c o n ' t ) 28 35 308 739 59,186 15 16 24 48 49 281 75,354 468 604 187 1,404 78,298 Total Cheboygan 16 72 Total Chippewa 17 17 49 96,435 2,296 98,731 18 10 16 18 26 37 40 49 51 53 57 67 72 67 134 12,578 669 1,338 134 335 803 134 201 67 803 17,263 19 10 16 17 18 19 20 24 28 29 33 34 37 38 40 43 49 51 53 59 61 62 78 470 4,312 7,683 3,214 157 1 ,489 6,428 1,098 314 784 10,426 1 ,254 627 4,704 862 314 706 5,644 157 3,136 Total Clare Total Clinton 247 Clinton (c o n 't ) 67 72 75 83 1,803 6,585 470 549 63,264 20 16,435 923 17,358 Total Crawford 20 40 Total Delta 21 2 21 22 23 27 47 49 52 55 75 Total Dickinson 22 7 21 22 31 32 36 53 66 Total Eaton 23 3,439 38,367 752 1,773 376 376 376 3,600 806 7,792 57,657 1,046 4,120 31,065 1,373 262 5,690 785 262 44,603 23 25 28 32 33 469 293 2,345 2,638 11,667 1,524 469 18,820 117 654 176 704 176 3,635 2,345 654 1,935 351 34 997 1 2 5 6 8 10 12 13 15 16 17 18 20 248 35 37 38 40 43 48 49 51 53 Eaton (c o n 't) 54 59 62 69 72 77 Total Emmet 24 15 16 17 24 45 48 57 83 Total Genesee 704 1,759 469 704 117 714 1,231 1,173 5,511 3,635 13,954 117 3,694 5,218 235 8 9 » 204 3,152 6,245 335 61 ,318 1,130 2,954 119 238 7 6 >978 25 1 I 7 - 99} 4 5 6 7 9 1,625 10,560 5,612 738 6,277 5,686 2,732 15,730 3,101 24,443 222 2,954 517 5,338 158,693 59,962 369 13,809 2,954 11 ,446 517 33,452 10 15 16 17 18 19 20 21 24 25 26 27 28 31 32 34 35 249 36 38 40 43 44 45 47 49 50 51 52 53 54 55 57 60 61 62 63 64 65 Genesee (c o n 't) 66 67 68 69 70 71 72 73 74 75 76 77 78 79 83 Total Gladwin 26 9 16 17 20 21 26 35 43 51 56 63 72 T o tal 591 295 3,323 1,034 24,960 6,055 14,400 1,920 148 17,206 591 1,108 2,215 443 1,698 4,135 738 222 7,532 443 14,695 738 2,142 4,431 2,511 222 5,981 50,141 2,363 3,101 3,766 1,920 1,772 7,311 14,991 443 590,340 216 144 360 1,655 360 8,417 72 360 2,446 2,878 4,316 288 21,511 250 Gogebic 27 27 31 66 Total Gd. Traverse 28 5 10 15 16 24 28 40 45 51 83 8,100 7,797 1,060 303 454 158,219 757 5,375 4,542 151 186,758 29 1 9 18 20 29 35 37 51 54 59 61 72 4,759 1,322 3,305 3,966 793 4,759 3,966 1,718 13,351 2,247 264 16.259 56,709 30 11 12 13 28 30 38 46 49 51 54 57 58 60 61 283 6,406 471 754 75,083 2,920 1,884 188 1,507 4,992 188 942 377 377 1,970 98,342 Total Gra tiot Total H ills d a le 68 Total Houghton 21,746 92 4.054 25,892 31 7 30 6,971 629 251 Houghton ( c o n 't ) 31 42 Total Huron 32 1 6 17 32 51 72 Total Ingham 33 3 4 5 6 8 9 10 11 13 15 16 17 18 19 20 23 26 27 28 29 31 33 34 35 36 37 38 39 40 41 45 47 49 50 51 53 54 55 57 59 40,172 17,200 64,972 942 2,198 157 19,154 157 236 22,844 842 1,804 3,488 361 15,516 421 11,667 722 4,811 11,366 8,720 5,032 24,718 3,368 5,052 3,308 4,511 481 7,698 241 120 34,941 8,600 1 ,804 4,511 7,217 5,473 180 4,029 7,758 361 10,464 3,608 2,225 14,975 1,624 33,378 2,526 2,706 17,320 252 60 61 62 63 67 Ingham (c o n 't) 68 69 70 71 72 75 76 77 78 81 82 83 Total Ionia 34 2 8 12 20 23 29 34 40 41 43 51 53 54 57 59 67 72 Total Iosco 222 2,960 74 1,924 1,628 1,480 26,492 666 7,326 518 1,036 296 4,292 444 4,588 74 1,036 55,056 24 35 256 74,710 74,966 36 36 41.389 41.389 1 173 231 635 3,464 231 520 464 Total Isabella 1,0 2 2 3,608 46,067 361 1,443 4,511 301 4,630 301 7,578 360,760 35 Total Iron 1,924 1,263 2,406 722 3,308 1,804 1,564 37 5 10 16 17 18 20 253 I s a b e lla ( c o n ' t ) 27 35 37 51 54 56 59 63 65 69 71 72 83 Total Jackson 38 4 5 8 10 12 13 16 18 26 28 30 33 38 39 46 48 49 51 52 53 60 62 67 68 69 70 71 72 75 81 Total Kalamazoo 39 3 5 8 9 10 346 58 9,237 404 4,388 346 1,732 1,732 1,155 1,386 346 4,388 520 31,754 5,098 5,607 1,020 1,529 85 4,333 8,411 8,496 7,731 10,620 1 ,274 1,104 156,069 850 2,039 1,399 340 2,889 1,359 935 255 3,549 14,613 1,189 1,189 850 510 6,882 1,189 4,928 256,302 9,355 694 29,691 1,526 1,804 254 11 14 16 23 28 30 38 39 40 43 49 51 52 54 57 60 61 62 64 Kalamazoo ( c o n ' t ) 66 70 75 78 80 83 Total Kalkaska Total 40 Kent 41 - 971 2,775 416 139 624 832 139 92,541 347 7,631 277 14,013 971 139 139 277 486 4,509 208 208 1,596 1,318 7,006 30,038 971 211,641 0 0 1 3 5 6 7 8 10 15 16 17 20 21 22 26 27 28 33 34 37 39 40 41 178 44,516 8,653 535 446 41,483 9,724 4,282 2,855 624 2,409 1,695 892 357 3,122 13,203 89 2,944 892 1,695 1 ,249 188,057 255 Kent (c o n 't) 42 43 44 48 49 51 52 53 54 55 59 60 61 62 64 67 70 72 75 80 82 83 1,071 19,002 268 1,071 13,917 33,633 892 9,813 34,882 535 32,027 1,338 20,162 84,750 8,029 9,813 70,209 2,052 981 357 89 11,419 6 8 6 ,2 1 0 Total Keewenaw Total 42 2,194 2,194 Lake 9 16 43 49 51 53 233 175 2,806 585 468 292 4,559 1 20 533 415 553 277 692 415 484 23,106 208 415 208 692 553 208 277 1,176 Total Lapeer 25 31 32 35 36 44 49 50 51 60 63 66 69 72 256 Lapeer (c o n 't) 74 77 79 69 899 138 31,318 10 5,799 2,873 38,807 867 54 48,400 Total Leelanau 45 28 45 46 47 Total Lenawee 46 1 5 6 10 12 15 16 17 30 31 36 38 41 46 49 52 57 58 59 64 67 72 77 79 81 82 Total Livingston 47 1 15 17 18 26 28 32 33 47 55 63 1,315 1,052 2,630 526 1,139 2,454 7,450 363 3,418 614 614 3,681 351 81,077 3,367 526 263 18,494 263 1,315 1,841 263 175 526 1,928 351 135,996 2,074 189 3,897 1,119 1 ,8 8 6 1,257 189 691 81,027 440 629 257 Livnigston (c o n 't ) 68 81 Total Luce 48 7 48 49 Total Mackinac 49 16 49 75 Total Macomb 50 1 4 6 9 10 15 16 17 18 21 24 25 26 28 32 35 38 40 44 46 47 48 49 50 51 57 58 59 60 63 65 68 69 70 71 72 74 440 4,463 98,301 347 9,724 2,361 12,432 2,058 59,521 147 61,726 8,487 3,086 1,350 96 772 1,640 7,041 5,690 579 482 1,061 1,157 1 ,736 2,797 6,365 2,893 386 1,157 2,700 2,508 4,340 193 5,015 426,098 5,980 4,822 772 772 1,543 25,462 4,244 4,437 37,421 96 675 4,822 193 258 75 77 79 82 83 Macomb (c o n 't) Total Manistee 51 10 28 45 51 53 Total Marquette 52 2 7 21 22 25 36 49 52 Total Mason 53 3 10 28 43 51 53 57 64 54 5 10 16 17 37 45 49 51 53 54 60 62 64 Total Menominee 112,360 1,543 28,644 964 724,501 1,530 255 8,413 59,911 1,657 71,766 5,963 6,684 1,442 131 655 852 655 86,171 102,553 200 1 ,0 0 1 401 2,103 4,706 42,655 200 1,0 0 1 52,267 Total Mecosta 2 ,1 2 2 55 7 52 241 322 161 161 402 804 563 1,930 161 32,964 161 2,412 161 40,443 454 727 259 Menominee ( c o n 't ) 55 75 23,805 636 25,622 6 1,309 13,813 945 4,144 1,309 291 2,617 364 145 291 13,886 2,254 727 1,745 436 2,181 1,091 2,399 22,901 1,309 291 436 2,181 2,908 8,070 1,018 654 654 90,369 Total Midland 9 10 15 16 17 18 20 24 25 26 28 35 40 43 45 51 54 56 57 61 62 67 71 72 73 75 83 Total Missaukee 17 22 36 57 Total Monroe 1 4 7 12 17 21 28 30 31 38 43 78 1,244 233 5,831 7,386 2,616 262 610 1,918 5,494 3,662 262 2,965 872 16,481 1,744 260 46 47 Monroe ( c o n 't ) 50 51 54 57 58 60 62 67 68 71 75 81 82 Total Montcalm 50 4 5 10 15 16 17 18 21 04 28 40 41 43 45 51 52 54 59 61 62 66 69 72 75 83 Total Montmorency fin ou 204 50 60 67 Total t 13,865 1,308 959 M 2,616 174 92,781 1’I II 1 *744 4,366 2,616 3,924 1,046 872 -7^412 73.933 552 1,105 473 158 1*578 79 473 868 4,736 158 1 *9 ?® 473 3,551 4,103 79 5,444 38,583 789 789 316 2,209 3,235 Z89 73.933 132 132 662 23,220 463 24,60¥ 261 Muskegon 61 3 452 10 11 15 16 21 27 28 40 41 43 45 48 49 51 53 56 57 58 59 61 62 64 70 72 76 83 6,398 4,516 1,807 3,086 903 2,258 3,839 75 7,602 6,473 2,258 151 1.581 17,087 16,334 1,957 151 75 2,258 185,787 2,032 11,893 9,635 1,581 301 1,129 Total Newaygo 2 9 1 »770 62 7 10 28 43 48 49 51 52 53 220 54 61 62 67 440 879 66,151 1,465 75,895 Total Oakland 63 513 366 733 513 293 806 3,223 293 1 2 4 5 6 7 17,702 3,253 10,818 13,541 7,414 3,345 262 Oakland ( c o n 't ) 9 10 n 12 13 15 16 17 18 20 21 22 23 24 25 26 27 28 30 31 32 35 36 37 38 40 42 43 44 45 47 48 49 50 51 53 54 56 57 58 59 60 61 63 64 65 67 68 69 70 71 72 76 12,785 378 1,059 605 6,203 16,945 2,194 15,508 6,052 1,362 303 530 3,555 13,238 18,004 530 2,950 5,901 2,648 20,955 33,436 756 530 3,404 1 ,362 7,565 1 ,2 1 0 2,194 11,498 21,938 1,135 5,598 109,311 4,615 983 756 6,884 9,229 5,371 454 15,886 1 ,2 1 0 466,597 378 7,262 6,960 11,045 4,236 2,799 8,019 24,888 263 74 75 77 79 81 82 83 3,404 983 64,906 303 6,657 25,418 2,345 1,069,379 64 10 51 53 64 82 428 2,139 1,283 25,310 285 29,445 65 5 6 35 49 51 61 63 65 72 2,752 688 734 138 734 642 7,058 24,816 550 38,112 66 7 27 31 66 431 677 154 13,017 14,279 67 7 18 67 83 554 1,800 1,246 554 4.154 68 16 35 60 68 1,350 337 743 4,725 7.155 69 5 16 40 69 113 2,264 3,396 11,546 Oakland ( c o n ' t ) Total Oceana Total Ogemaw Total Ontonagon Total Osceola Total Oscoda Total Otsego T o ta l 17 ,31 9 264 Ottawa 70 2 3 5 7 8 9 10 15 16 18 24 28 35 40 42 44 46 47 48 51 53 54 59 61 62 64 67 70 83 Total Presque I s l e 71 16 71 938 39,015 39,953 72 4 10 21 40 72 76 304 532 152 80,231 81,295 73 1 2 3,065 848 196 456 717 16,108 24,194 1,696 4,043 Total Roscommon Total Saginaw 231 23,935 346 1,038 1,327 115 2,422 1,730 2,711 1,154 1,442 807 692 807 2,480 2,480 1,557 750 173 6,517 3,460 346 58 5,710 20,821 9,170 4,845 143,841 1,038 242,003 3 4 5 6 9 10 16 265 Saginaw ( c o n 't ) 17 18 20 24 26 27 28 29 31 32 35 36 37 40 45 49 51 52 56 57 59 60 65 67 68 69 71 72 73 74 75 77 79 83 Total Sanilac T o tal 74 1 9 28 35 40 50 60 65 71 74 77 79 1,109 17,868 522 1,304 25,303 130 7,239 130 978 2,087 11,999 652 1,369 456 6,326 1,304 1,043 652 6,913 1,696 7,434 326 5,152 2,087 587 4,369 2,348 31,302 12,064 391 913 1,369 456 11,151 220,352 254 203 355 3,504 1,066 102 2,234 152 2,031 14,218 1,066 152 2 5 ,33 7 266 Schoolcraft 75 21 48 52 75 391 587 489 17,221 18,688 76 5 10 16 17 18 25 26 28 35 40 41 42 127 2,483 764 828 1,146 1,401 1,591 5,093 64 6,366 955 509 191 68,310 Total Shiawassee 49 Total St. C l a i r 77 1 16 17 24 28 32 35 44 48 50 58 72 74 75 77 82 Total St. Joseph 78 8 10 11 12 14 16 17 28 36 43 48 71 78 243 1,701 121 405 3,401 801 1,620 810 1,215 17,169 567 1,620 4,697 81 191 ,446 2,268 228, 174 609 68 406 1,758 9,333 473 135 2,367 1,150 2,097 812 338 132,149 267 St. Joseph ( c o n ' t ) 80 83 6,695 947 159,337 7 9 126 4,730 631 2,523 883 1 ,261 4,162 4,352 126 2,144 9,649 30,587 Total Tuscola 10 16 18 26 32 35 51 68 79 Total Van Buren 3 4 10 11 14 16 30 35 42 43 51 54 57 70 80 82 83 Total Washtenaw 4 5 9 10 13 15 16 17 18 21 24 25 26 28 33 1,643 4,146 469 235 391 4,693 235 78 1,095 626 626 156 235 156 104,424 1,799 704 121,711 65 3,189 521 846 65 1,497 781 2,083 1 ,041 325 1,172 260 781 3,319 65 268 Washtenaw ( c o n ' t ) Total Wayne 82 38 40 43 45 46 47 48 49 50 51 53 58 60 61 63 68 69 71 72 81 82 3,059 651 3,905 195 2,408 41,005 651 2,994 2,148 3,580 65 5,923 781 130 846 2,734 130 911 716 79,342 10,089 178,273 1 30,235 4,396 5,039 16,083 5,575 858 18,656 107 9,864 858 2,680 19,192 74,731 18,763 21,980 5,897 2,037 8,470 5,683 21,229 1,072 13,188 10,507 2,252 35,918 12,973 751 34,846 9,542 2 4 5 6 7 8 9 10 11 14 15 16 17 18 20 21 24 25 26 27 28 30 31 32 35 36 38 40 269 Wayne ( c o n 't ) 41 42 43 44 45 46 47 48 49 50 51 53 54 57 58 60 61 62 63 64 65 66 67 68 69 70 71 72 74 75 76 77 79 81 82 83 Total Wexford 83 429 4,289 4,182 14,903 6,326 8,256 88,777 3,109 3,002 213,793 28,091 9,328 5,683 3,002 54,038 27,877 2,095 17,584 124,909 214 9,221 6,433 1,394 4,074 16,726 9,650 10,829 27,769 10,400 5,683 3,753 190,741 322 69,370 641,056 1,715 2,023,200 5 334 7 9 10 16 28 43 45 51 53 54 57 167 250 2,670 167 417 417 83 834 167 417 1,335 270 Wexford ( c o n 't ) Total T o t a l , All Origins 58 59 62 67 83 334 1,168 1,252 334 32,873 43,219 11,700,274 V o r percentage d i s t r i b u t i o n o f boat days see Table which-follows. 271 Travel Distances From Origin Counties to a l l Boating Destination Counties, Percent o f Total Boat Days Taken a t Destination Counties, and Calculation o f Average Travel Distance For Each Origin County, Michigan, 196B Destination County Travel Distance (miles) Origin County Alcona A1 ger (1) (2) t 1! (4) (10) (35) (48) (53) (2 ) (17) (21) (52) (72) (75) 18 35 175 39 210 Per­ cent of Total Boat Days .7568 .1229 .0123 .0860 .0098 235 .0 1 2 2 1 .0 0 0 0 16 128 63 44 261 47 .7581 .0032 .1581 .0032 .0064 .0710 75.68(18)+12.29(35)+1.23(175) . . . +8 .60(39)+.98(210 ) + l .22 . . . (235)=2,835.54+100= . . . 28.35 miles 75 .81 (16)+ .3 2(1 28 )+ !5.81 (63 )+ . . . .32 (44)+ .6 4(261) + 7 , 10 . . . (4 7 ) = 2 ,765.70+100=27.66 . . .m ile s 1 .0 0 0 0 Allegan (3) (2 ) (3) (8 ) (17) (28) (39 (43) (49) (51) (53) (59) (61) (62) (80) 428 16 51 368 183 28 117 316 144 118 76 60 84 39 .0034 .6353 .1370 .0067 .0014 .0027 .0342 34(428)+63.53(16)+13.70(51)+ . .67(368)+.14(183)+.27 . (28 )+3.42(117)+.20(316) . +4.03(144)+3.42(118)+,67 . ( 7 6 )+2.6 9(60 )+2.69(84)+ . 4 . 2 3 (39 )=4,190.91+100= . 41.90 miles .0 0 2 0 .0403 .0342 .0067 .0269 .0269 .0423 1 .0 0 0 0 Alpena (4) (1) (4) ( 10) 35 14 173 .0294 .8510 .0232 2 . 9 4 ( 3 5 )+85.10 (14) + 2 .32(173)+ . . . .31 (80 )+ !.0 8(1 83)+ .1 2(2 02 ) . . . + .62 (1 30)+.31(194)+!. 55 272 (16) (17) (48) (49) (51) (60) ( 68) (71) (72) (75) A1pena ( c o n 't ) Antrim (5) (5) ( 10) (15) ( 21) (25) (28) (40) (51) (54) (75) 80 183 .0031 .0108 202 .0 0 1 2 130 194 44 58 41 114 213 .0062 .0031 .0155 .0008 .0480 .0054 .0023 1 . 0000“ 12 78 34 255 179 41 17 99 94 202 .8795 .0113 .0188 .0379 .0165 .0075 .0165 .0007 .0090 .0023 ( 4 4 ) + . 08(58)+4.8 0 ( 4 1 )+.54 (114)+.23(213 ) = 2 , 463.22+ 100=24,63 miles 8 7 . 9 5 (12 )+1.1 3(78 )+1.88(34)+ . 3 . 7 9 ( 2 5 5 ) + l .65(179)+ . . 7 5 ( 4 1 )+ ! .6 5 ( 1 7 ) + .0 7 . (99)+.90(9 4)+ .2 3(202)= . 2,666.05+100-26.66 miles 1 .0 0 0 0 Arenac (6 ) (6 ) (16) (35) (63) (82) 10 .6819 140 40 109 136 .0 2 0 2 .0656 .2172 .0151 6 8 . 19 (10)+2.02(140)+6.56(40)+ . . . 21 .72(109)+!.51(1 36)= . . . 3,799.94+100=37.99 miles 1 .0 0 0 0 Baraga (7) (7) (31) (32) (42) (48) (52) (66) (70) 10 36 497 77 182 72 63 523 .6644 .0397 .0133 .0221 .1369 66.4 4 (1 0 ) + 3 .97(36)+ 1 .33(497)+2.21 (77)+13.69 (18 2)+2.21(72)+.22(63) + 9 . 93(523)=9,496.45+100= 94.96 miles .0221 .0 0 2 2 .0993 1 .0 0 0 0 Barry (8) (3) (8 ) (16) (17) (40) (49) (51) (52) (53) (54) (59) 51 16 244 339 157 287 154 441 134 92 57 .0019 .8963 .0067 .0067 .0119 .0014 .0177 .0024 .0029 .0062 .0186 19(51)+8 9.63(16)+.67(339)+ . 1 . 1 9 ( 1 5 7 ) + . 14(287)+1 .77 . (154)+.24(44 1)+.29(134)+ . . 6 2 ( 9 2 ) + ! . 8 6 ( 5 7 ) + l .10(82) . +.29 (10 5)+.29 (58 )+.4 8 . (156)+.57(74)=2,732.78+ . 100=27.33 miles 273 (62) (67) (70 (72) (80) Barry ( c o n 't ) 82 105 58 156 74 .0 1 1 0 .0029 .0029 .0048 .0057 1 .0 0 0 0 Bay (9) ( 1) (4) (6 ) (9) ( 10) (15) (16) (17) (18) (24) (26) (28) (321 (35) (40) (45) (51) (52) (53) (56) (60) (62) (65) (69) (71) (72) (73) (79) (83) 102 129 31 12 150 166 169 267 54 159 54 146 61 68 124 173 144 369 144 22 118 122 58 124 153 83 14 32 100 .0272 .0562 .0341 .3995 .0136 .0125 .0505 .0108 .0079 .0023 .0760 .0148 .0079 .0914 ,0170 .0017 .0306 .0119 .0017 .0034 .0165 .0006 .0358 .0113 .0057 .0392 .0006 .0057 .0136 2.72(102)+5.62(129)+3.41 ( 3 1 )+39.95 (12 )+ !.36 (150)+1.25(166)+5.05 (169)+1.08(276)+.79 ( 5 4 ) + . 23{159)+7.60(54) +1 .48(146 )+.79(61)+ 9 . 14(68)+1.70(124)+ .17 (173)+3.06(144)+ 1.19(369)+.17(144 )+ .3 4 (2 2 )+ !.6 5 (1 1 8 )+ .06 (1 22)+3.58(58)+ 1.13(124)+.57(153 )+ 3 .9 2(8 3)+.06 (14 )+ .5 7 (32)+1.36(100)=6,785,61 +100=67.86 miles 1 .0 0 0 0 Benzie ( 10) ( 10) (28) (72) 8 40 87 .9621 .0223 .0156 9 6 .21( 8 ) + 2 . 23(4 0 )+!.56(8 7)= . . . 994.60+100=9.95 miles 1 .0 0 0 0 Berrien ( 11) (2 ) (3) (7 (8 ) ( 10) (11) (14 (15) (16) 464 58 518 .0004 .0402 .0007 88 .0 0 1 0 206 14 36 266 309 .0409 .5312 .0492 .0038 .0049 04(46 4)+4 .02(58)+.07(518)+ . . .10(88)+4.09(206)+53.12 . . ( 1 4 ) + 4 . 92(36)+.38(266)+ . . .49(309)+.07 (271) + l .66 . . (218)+.38(47 6)+.04(54)+ . . .04 (80 )+ !.0 4 (5 8 8 )+ .4 5 . . (1 5 2 )+ .45 (351)+6.14(173) . . +.1 7 (4 8 8 )+ 1 .39(146)+.52 . . (1 4 2 )+ .0 7 (89 )+4.23(112)+ 274 (24) (28) (36) (39) (41) (42) (43) (49) (51) (52) (53) 54) (61) (62) (64) (70) (75) (78) (80) (83) Berrien (co n 't) 271 218 476 54 80 588 152 351 173 488 146 142 89 112 115 54 434 71 25 184 .0007 .0166 .0038 .0004 .0004 .0104 .0045 .0045 .0614 .0017 .0139 .0052 .0007 .0423 .0350 3.50(1 15)+ 1. 2 1 (54J+.49 (43 4)+.49(71)+10.19(25)+ . 24 (1 84)=5,113.49+100= 51.13 miles .0121 .0049 .0049 .1019 .0024 1 .0 0 0 0 Branch ( 12) (2) (8 ) (1 2 (13) (15) ( 20) (27) (61) (63) 65) (66) ( 68) (71) (78) 440 63 14 38 248 210 606 136 122 203 601 238 298 26 .0186 .0447 .8747 .0149 .0045 .0157 .0015 .0008 .0052 1.86(440)+4.47(63)+8 7.47(14)+ . . 1.49(38)+.45(248)+ . . 1.57(210)+.15(606)+ . . .08(136)+-52(122)+.22 . . (203)+.60(601)+.45(238)+ . . .07(298)+.60(26)= . . 3,536.55+100=35.36 miles .0 0 2 2 .0060 .0045 .0007 .0060 1 .0 0 0 0 Calhoun (13) (2) (3) (8 ) ( 10) (11 ( 12) 13 (15) 16) (17) (18) (19) (20 ( 21) 414 44 27 196 74 38 22 217 259 354 132 67 191 437 .0015 .0092 .1580 .0372 .0 0 1 2 .0384 .4170 .0068 .0036 .0143 .0015 .0015 .0027 .0015 15 (414)+.9 2 ( 4 4 ) + l 5.80(27)+ 3.72(196)+.12(74)+3 .84 (38J+41.70(22)+.68(217)+ .36(259)+!.43(354)+.15 (13 2)+.15(67)+.27(191)+ .1 5(437 )+2.95(28)+.12 (6 0 1 ) + .30(192)+1.22(50)+ . 15 (534)+.15(44 )+5.81 (26 )+1.0 1(172)+ 2.23(134)+ .48(219)4-1.49(180) + . 39 (157)+1.31(117)+.54(454)+ .09(146)+.30(244)+.45 (99)+.18(107)+.30(125)+ .42(131)+.45 (2 1 9 )+ 2 .18 275 28 601 192 50 534 44 26 172 134 219 180 157 117 454 146 244 99 107 125 131 219 211 65 171 385 163 48 64 146 .0295 .0012 .0030 .0122 .0015 .0015 .0581 .0101 .0223 .0048 .0149 .0039 .0131 .0054 .0009 .0030 .0045 .0018 .0030 .0042 .0045 .0218 .0167 .0307 .0089 .0024 .0086 .0113 .0018 1.0000 . . . . (14) (17 (27) (48) (51) (62) (75) (78) (80) (83) 36 67 17 414 551 434 187 126 445 48 39 195 .0090 .0072 .8267 .0018 .0012 .0036 .0217 .0150 .0054 .0217 .0837 .0030 1.0000 . 9 0 ( 3 6 ) + . 7 2 ( 6 7 ) + 8 2 .67(17)+ . . . .1 8 ( 41 4)+.12 (55 1)+.36 . . . ( 4 3 4 ) + 2 . 1 7 ( 1 8 7 ) + l .50 . . . ( 1 2 6 ) + . 5 4 (44 5)+ 2 .17(48)+ . . . 8.3 7(3 9 )+ .3 0 (1 9 5 )= . . . 3,107.09+100=31.07 miles 5) ( 10) (15) (17) ( 21 ) (24) 34 89 11 186 269 18 .0146 .0052 .8918 .0021 .0021 .0666 1 . 4 5 ( 3 4 ) + . 52 (89 )+89 .18(11)+ . . . .2 1 ( 1 8 6 ) + . 2 1 (2 6 9 ) + 6 .66 . . . ( 1 8 ) + . 5 2 ( 5 2 ) + l .25(150)= . . . 1,506.53+100=15.06 miles (23) (27) (28) (34) (36) (38) (39) (40) (43) (45) (51) (53) (54) (55) (57) (60) (61) (62) (64) (67) Calhoun (con‘ t ) ( 68) (69) (70) (72) 1$ (78) (80) (83) Cass Charlevoix (14) (15) ( 11) (12) . . . . . . . . ( 2 1 1 ) + 1 . 6 7 (6 5 ) + 3 . 07(171) . 8 9 (3 8 5 )+ .2 4 (1 6 3 )+ .8 6 ( 4 8 ) + l . 13 (64)+.18(1 46)= 6,997.46+100=69.97 miles 276 Charlevoix ( c o n 't ) (28) (35) 52 150 .0052 .0125 1.0000 Cheboygan (16) (15) (16) (24) (48 (49) (72) 91 13 85 123 52 106 .0036 .9624 .0060 .0077 .0024 .0179 1.0000 .3 6 ( 9 1 )+ 9 6 . 24 (1 3 )+ .6 0 (8 5 )+ . . . . 7 7 ( 1 2 3 ) + . 2 4 ( 5 2 ) + ! .7 9 . . . (106) =1 ,631.81*100= . . . 16.32 miles Chippewa (17) (17) (49) 10 58 .9800 .0200 1.0000 9 8 . 0 0 ( 1 0 ) + 2 . 0 0 ( 5 8 ) = ! ,096 t . . . 100=10.96 miles Clare (18) (10) (16) (18) (26) (37) (40 (49 (51 (53) (57) (67) (72) 102 139 16 30 19 78 181 96 96 52 46 45 .0039 .0078 .7286 .0387 .0775 .0078 .0194 .0465 .0078 .0116 .0039 .0465 1.0000 Cl inton (19) (10) (16) (17) (18) (19) (20) (24) (28) (29) (33) (34) (37) (38) (40) (43) (49) (51) (53) (59) (61 (62) (67) 164 201 295 68 15 126 188 160 34 20 29 51 57 140 123 243 158 156 50 101 106 106 .0012 .0074 .0682 .1214 .0508 .0025 .0235 .1016 .0174 .0050 .0124 .1648 .0198 .0099 .0743 .0136 .0050 .0112 .0892 .0025 .0496 .0285 3 9 ( 1 0 2 ) + . 78 (139)+ 72.86(16)+ . 3 . 8 7 ( 3 0 ) + 7 .7 5 ( 1 9 ) + . 7 8 . ( 7 8 ) + l .94 (18 1) + 4 . 65(96)+ . .78(96)+!.16(52)+.39(46)+ . 4 . 6 5 ( 4 5 ) = 2 , 798.08*100= . 27.98 miles 12 (16 4)+.7 4(20 1) + 6 . 82(295)+ 1 2 .1 4 ( 6 8 ) + 5 . 0 8 (15J+.25 (126)+2 .35(188 )+10.16 (1 6 0 ) + 1 .7 4 ( 3 4 )+ .5 0 (2 0 )+ 1 .2 4 ( 2 9 ) + 1 6 .48 (5 1 ) + l .98 ( 5 7 ) + . 9 9 (14 0)+7 .43(123)+ 1 .3 6 ( 2 4 3 )+ .50 (15 8)+l .12 (15 6)+8 .92 (50 )+ .25 (1 01 )+ 4 . 96 (10 6)+ 2 .85(106)+ 10 .41(107)+.74(326)+ . 8 7 ( 1 14)=10 , 6 2 9 . 55-H 00= 106.29 miles 277 Clinton (c o n 't) (72) (75) (83) 107 326 114 .1041 .0074 .0087 1.0000 Crawford ( 20) (20) (40) 9 27 .9500 .0500 1.0000 95(9)+5(27)=990+100=9.90 miles Delta ( 21 ) (2) (21) (22) (23) (27) (47) (49) <52 (55) (75) 63 6 53 417 181 431 144 68 40 55 .0597 .6654 .0130 .0308 .0065 .0065 .0065 .0625 .0140 .1351 1.0000 5 . 9 7 ( 6 3 ) + 6 6 . 5 4 ( 6 ) + l .30(53)+ . . . 3.08(417)+ .65(181 )+.65 . . . (4 3 1 ) + .65(144)+6 .25(68)+ . . . 1.40(40)+13.51(55)= . . . 3,843.38+100=38.43 miles Dickinson ( 22) (7) (21) (22) (31) (32) (36) (53) (66) 86 53 6 115 461 47 426 125 .0234 .0924 .6965 .0308 .0059 .1275 .0176 .0059 1.0000 2.34(86)+9.24(53)+69.65 . . . ( 6 ) + 3 . 08(115)+.59(61)+ . . . 12 .75(47)+!.76(426)+ . . . .59(125)=2,921.81+100= . . . 29.22 miles Eaton (23) (1) (2) (5) (6) (8) (10) (12) (13) (15) (16) (17) (18) (20) (23) (25 (28) (32) (33) (34) (35) 200 394 170 130 29 181 47 28 202 239 333 106 164 6 70 177 155 20 35 167 .0052 .0033 .0263 .0296 .1308 .0171 .0052 .2110 .0013 .0073 .0020 .0079 .0020 .0410 .0263 .0073 .0217 .0039 .0112 .0079 .5 2 ( 2 0 0 ) + .33(394)+2.63(170)+ . . . 2.9 6(130)+ !3 .08(2 9)+ . . . 1 .7 1 ( 1 8 1 ) + . 52(47)+21.10 . . . (28)+.13(202)+.73(239)+ . . . .20(333)+.79(106)+.20 . . . (1 6 4)+4 .10 (6 )+2.63(70)+ . . . .73 (177)+2.17(155)+.39 . . . ( 2 0 ) + l . 12(35)+.79(167)+ . . . 1.9 7(89)+.52(38)+ .7 9 . . . (157)+.13(132)+.80(353)+ . . . 1 . 3 8 ( 2 8 1 ) + ! . 3 1 (175)+6.18 . . . (158)+15.64(57)+.13(106) . . . +4.14(191) + 5 . 85(145)+ . . . .26(364)+4.07(103)= . . . 8,877.30+100=88.77 miles 278 Eaton ( c o n 't) (37) (38) (40) (43) (48) (49) (51) (53) (59) 62 (69) 72) \m (54) 89 38 157 132 353 281 175 158 57 106 191 145 364 103 .0197 .0052 .0079 .0013 .0080 .0138 .0131 .0618 .1564 .0013 .0414 .0585 .0026 .0407 1.0000 Emmet (24) (10) (15) (16) (17) (24) (45) (48) (57) (83) 106 18 85 179 6 97 198 80 89 .0193 .0409 .0811 .0043 .7966 .0147 .0384 .0016 .0031 1.0000 1 . 9 3 ( 1 0 6 ) + 4 . 0 9 ( 1 8 ) + 8 . 11(85)+ . . . . 4 3 ( 1 7 9 ) + 7 9 . 6 6 ( 6 ) + l .47 . . . ( 9 7 ) + 3 . 8 4 ( 1 9 8 )+ .1 6 (8 0 )+ . . . .3 1 ( 8 9 ) = 2 , 465.78+100= . . . 24.66 miles Genesee (25) (1) (2) (4) (5) (6) (7) (9) (10) (15) (16) (17) (18) (19) (20) (21) (24) (25) (26) (27) (28) (31) (32) (34) (35) (36) 146 371 173 179 75 482 46 190 210 213 311 93 46 141 394 203 12 93 557 186 511 88 74 112 491 .0296 .0009 .0028 .0179 .0095 .0012 .0106 .0096 .0046 .0266 .0053 .0414 .0004 .0050 .0009 .0090 .2688 .1016 .0006 .0234 .0050 .0194 .0009 .0567 .0010 2 . 9 6 ( 1 4 6 ) + .0 9 ( 3 7 1 )+ .2 8 ( 1 7 3 ) + . . . 1 .7 9 ( 1 7 9 ) + .9 5 ( 7 5 ) + .1 2 . . . (4Q2)+1.06 (46 )+ .96 (1 90 )+ . . . . 4 6 ( 2 1 0 ) + 2 .66(213)+.53 . . . (311) + 4 . 1 4 ( 9 3 )+ .0 4 (4 6 )+ . . . .50 (14 1)+ .0 9 (3 9 4 )+ .9 0 . . . ( 2 0 3 ) + 2 6 . 8 8 ( l 2 ) + 1 0 . 16 . . . ( 9 3 ) + . 0 6 ( 5 5 7 ) + 2 .34(186)+ . . . .5 0 ( 5 1 1 ) + ! . 9 4 ( 8 8 ) + .0 9 . . . ( 7 4 ) + 5 . 67 (112)+ .1 0(491)+ . . . . 0 5 ( 8 8 )+ .5 6 (1 6 6 )+ .1 8 . . . (1 5 1 ) + 4 .2 3 (2 1 j + 1 .03 . . . (2 1 3 )+ 2 .44 (45 )+.33 (2 58 )+ . . . . 0 2 ( 6 2 ) + 2 . 91(184)+.10 . . . ( 4 1 3 )+ .1 9(18 4)+ .3 8(1 29)+ . . . .07 (43 2)+ .2 9 (1 4 0 )+ .7 0 . . . ( 1 6 2 )+ .1 2(14 5)+ .0 4(1 44)+ . . . 1 . 2 8 ( 3 7 ) + . 0 7 (17 2)+2 .49 . . . (102)+.1 2(53 5)+.3 6(1 34)+ . . . .75 (13 7)+ .4 3 (1 6 8 )+ .0 4 . . . (132)+1.01(197 )+8.49 . . . ( 1 2 7 ) + . 4 0 ( 3 7 ) + . 5 3 ( 8 0 )+ . . . . 6 4 ( 3 4 1 )+ .3 3 (2 6 )+ .3 0 . . . ( 6 8 ) + l .24 (14 1) + 2 . 54(51)+ . . . .07(140)=9*550.25+100= 279 Genesee (c o n 't) (38) (40) (43) (44) (45) (47) (49) (50) (51) (52) (53) (54) (55) (57) (60 (61) (62) (63) (64) (65) (66) (67) (68) (69) (70) (71) (72) (73) (74) (75) (76) (77) (78) 79) (83) 88 166 151 21 213 45 258 62 184 413 184 129 432 140 162 145 144 37 172 102 535 134 137 168 132 197 127 37 80 341 26 68 141 51 140 .0005 .0056 .0018 .0423 .0103 .0244 .0033 .0002 .0291 .0010 .0019 .0038 .0007 .0029 .0070 .0012 .0004 .0128 .0007 .0249 .0012 .0036 .0075 .0043 .0004 .0101 .0849 .0040 .0053 .0064 .0033 .0030 .0124 .0254 .0007 1.0000 Gladwin (26) (9) (16) (17) (20) (21) (26) (35) (43) (51) (56) (63) (72) 54 134 229 60 312 9 65 87 103 37 127 36 .0100 .0067 .0167 .0769 .0167 .3913 .0034 .0167 .1137 .1338 .2007 .0134 1.0000 Gogebic (27) (27) 20 .8399 . . 95.50 miles 1.00(54)4-.67(134)+! .67(229)+ . 7.69(60)4-1 .67(312)4. 39.13(9)4-.34(65)4-1.67 . (87)4-11.37(103)4-13.38 . (37)4-20.07(127)4-1.34 . ( 3 6 ) = 6 ,291.51+100= . 62.91 miles 83.99(20)4-. 35(110)4*15.66(65) = 280 Gogebic (con't) Gd. Traverse (28) (31) (66) 110 65 .0035 .1566 1.0000 . . . 2,736.20*100=27.36 miles (5 ) 41 40 52 115 69 13 30 31 63 51 .0434 .0417 .0057 .0016 .0024 .8472 .0041 .0288 .0243 .0008 1.0000 4 . 3 4 ( 4 1 )+ 4 .1 7 ( 4 0 ) + .5 7 ( 5 2 ) + . . . .16 (11 5)+.24 (69 }+ . . . 8 4 .7 2 ( 1 3 ) + .4 1 ( 3 0 ) + . . . 2 . 8 8 ( 3 1 ) + 2 .43 (63 )+.08 . . . ( 5 1 ) = 1 ,769.45+100= . . . 17.69 miles 149 53 36 95 13 116 19 127 61 49 97 75 .0839 .0233 .0583 .0699 .0140 .0839 .0699 .0303 .2354 .0396 .0047 .2868 1.0000 8.3 9 (1 4 9 ) + 2 .3 3 ( 5 3 )+ 6 .9 9 ( 9 5 ) + . . . 1 .40 (13)+ 8.39(116)+6.9 9 . . . (19)+3.03(127)+23.54 . . . ( 6 1 ) + 3 . 96 (49 )+.47 (9 7)+ . . . 28.68(75)=7,373.28+ . . . 100-73.73 miles fill .0029 .0651 .0048 .0077 .7635 .0297 .0192 .0019 .0153 .0508 .0019 .0096 .0038 .0038 .0200 1.0000 .2 9 (11 8)+ 6 - 51 (2 4 )+ .4 8 (5 5 )+ .7 7 . . . (23 8)+76.35(14) + 2 . 97 . . . ( 4 1 ) + l .92(35) + .19(331 )+ . . . 1 . 5 3 ( 2 3 3 ) + 5 .08(164)+.19 . . . ( 1 9 2 )+ .9 6 (7 4 )+ .3 8 (2 6 6 )+ . . . .38(153)+2.00(241)= . . . 3,659.23+100=36.59 miles (51) (54) (57) (58) (60 (61) ( 68) 118 24 55 238 14 41 35 331 233 164 192 74 266 153 241 (7 ) (30) (31 (42) 36 583 11 42 ,1073 .0097 .6183 .2647 1.0000 1 0 . 7 3 ( 3 6 ) + . 97(583)+6 1.83(11)+ . . . 2 6 . 4 7 ( 4 2 ) = 2 , 743.66+100= . . . 27.44 miles (10 ( 15) (16) (24) (28) (40) (45 (51) (83) Gratiot (29) ( 1) (9 ) (18) ( 20 ) (29) (35) (37) (51) (54) (59) (61) (72) Hillsdale Houghton (30) (31) ( 11) ( 12) (13) (28) (30) (38) 281 Huron (32) (1) (6) (17) (32) (51) (72) 161 90 326 10 204 143 .0412 .0962 .0069 .8385 .0069 .0103 1.0000 Ingham (33) (3) (4) !5! (6) (8) (9) (10) (11) (13) (15) (16) (17) (18) (19) (20) (23) (26) (27) (28) (29) (31) (33) (34) (35) (36) (37) (38) (39) (40) (41) (45) (47) (49) (50) (51) (53) (54) (55) (57) (59) (60) (61) (62) (63) 89 208 172 110 47 83 183 120 47 204 219 314 86 20 145 20 110 561 179 52 514 12 39 148 494 69 38 72 159 66 206 36 262 96 177 163 107 436 133 62 197 106 111 70 .0023 .0050 .0097 .0010 .0430 .0012 .0324 .0020 .0133 .0315 .0242 .0140 .0685 .0093 .0140 .0092 .0125 .0013 .0214 .0007 .0003 .0969 .0238 .0050 .0125 .0200 .0152 .0005 .0112 .0215 .0010 .0290 .0100 .0062 .0415 .0045 .0925 .0070 .0075 .0480 .0053 .0035 .0067 .0020 4 . 1 2 ( 1 6 1 ) + 9 . 62 (90)+.69(3 26)+ . . . 83 .85 (1 0 )+ .6 9 (2 0 4 )+ . . . 1.03(143)=2,880.6H . . . 100=28.81 miles .2 3 (8 9 )+ .5 0 (2 0 8 )+ .9 7 (1 7 2 )+ . . . . 1 0 ( H 0 ) + 4 . 30(47) + . 12(83)+ . . . 3 . 2 3 ( 1 8 3 ) + . 20 (120)+1.33 . . . (4 7 ) + 3 .1 5 ( 2 0 4 ) + 2 .42(219)+ . . . 1 .40 (31 4)+6 .85 (8 6)+.93 . . . ( 2 0 ) + l . 40 (14 5)+.9 2(20 )+ . . . 1 .2 5 ( 1 1 0 ) + .1 3 ( 5 6 1 ) + 2 .13 . . . (17 9 )+ .0 7 (5 2 )+ .0 3 (5 1 4 )+ . . . 9 .6 8 (1 2 ) + 2 .3 8 ( 3 9 ) + .5 0 . . . (14 8)+ 1 .2 5 (4 9 4 )+ 2 .00(69)+ . . . 1 . 5 2 ( 3 8 ) + . 0 5 ( 7 2 ) + l . 12 . . . (1 5 9 ) + 2 .15(66)+.10(2 06)+ . . . 2 . 9 0 ( 3 6 ) + l .00(26 2)+.62 . . . ( 9 6 ) + 4 . 15 (177)+.45(163)+ . . . 9.2 5(1 07)+ .7 0 (4 3 6 )+ .7 5 . . . (1 3 3 )+ 4 .80 (62)+.53(1 97)+ . . . .35 (10 6)+.67 (11 1)+.20 . . . ( 7 0 ) + .92 (121 )+.50 (17 2)+ . . . ,43 (171) + . 2 8 ( 8 9 ) + l . 00 . . . (232)+12.77(125)+.10 . . . ( 3 4 4 ) + .4 0 ( 3 2 ) + !.2 5 (1 1 7 ) + . . . .0 8 ( 9 1 ) + l .28(65)+ . . . . 0 8 ( 8 9 ) + 2 . 10(133)= . . . 11,534.80*100=115.35 miles 4 282 Ingham (c o n 't) (67) (68) (69) (70) (71) (72) (75) (76) (77) (78) (81) (82) (83) 121 172 171 89 232 125 344 32 117 91 65 89 133 .0092 .0050 .0043 .0028 .0100 .1277 .0010 .0040 .0125 .0008 .0128 .0008 .0210 1.0000 Ionia (34) (2) (8) (12) (20) (23 (29) (34) (40) (41) (43) (51) (53) (54) (57) (59) (67) (72) 365 35 81 141 35 53 12 123 34 100 141 131 69 97 23 82 122 .0040 .0538 .0013 .0349 .0296 .0269 .4812 .0121 .1331 .0094 .0188 .0054 .0780 .0081 .0833 .0013 .0188 1.0000 Isabella (37) (1) (5) (10) (16) (17) CIS) (20) (27) (35) (37) (51) (54) (56) (59) (63) (65) (69) 141 106 116 153 247 19 78 494 108 20 110 43 30 55 122 77 105 .0054 .0073 .0200 .1091 .0073 .0164 .0146 .0109 .0018 .2909 .0127 .1382 .0109 .0545 .0545 .0364 .0436 40(365)+5.38(35)+.13(81)+ 3.49(141) + 2 . 96(35)+ 2.69(53)+48.12(12)+ 1.21(123)+13.31(34)+ .94(100 +1.88 141)+ .54(131)+7.80(69)+.81 (9 7 )+ 8 .33(23)+.13(82)+ 1.88(122)=3,740.10+ 100-37.40 miles 54(141)+.73(106)+ 2.00(116)+ . . 10.91(153)+.73(247)+ . . 1.6 4(1 9)+1 .4 6(7 8)+!.09 . . (494)+.18(108)+29.09 . . (20)+1.27(110)+13.82 . . (43)+ 1.09(30)+5.45(55)+ . . 5.45(122)+3.64(77)+ . . 4.36(105)+!.09(176)+ . . 13 .8 2 ( 5 8 ) + l .64(66)= . . 7 , 0 9 0 . 8 3 n 00=70.91 miles 283 I s a b e lla (con't) (71) (72) (83) 176 58 66 .0109 .1382 .0164 1.0000 Iosco (35) (24) (35) 143 15 .0034 .9966 1.0000 .3 4 ( 14 3)+ 9 9.66 (15 )= 1,543.527 . . . 100=15.43 miles Iron (36) (36) 16 1.0000 100(16)=1,600*100=16.00 miles Jackson (38) (4) (5) (8) (10) (12) (13) (16) (18) (26) (28) (30) (33) (38) (39) (46) (48) (49) (51) (52) (53) (60) (62) (67) (68) (69) (70) (71) (72) (75) (81) 245 207 65 218 47 44 257 123 148 213 41 38 16 66 39 370 299 211 454 194 234 142 153 210 209 108 270 162 382 37 .0199 .0219 .0040 .0060 .0003 .0169 .0328 .0332 .0302 .0414 .0050 .0043 .6089 .0033 .0079 .0055 .0013 .0113 .0053 .0037 .0010 .0138 .0570 .0046 .0046 .0033 .0020 .0268 .0046 .0192 1.0000 ii) 28 205 36 153 193 54 46 279 .0442 .0033 .1403 .0072 .0085 .0046 .0131 .0020 Kalamazoo (39) (8) (9) (10) (11) (14) (16) 1 . 9 9 ( 2 4 5 ) + 2 . 19(207)+.40(65 )+ .6 0 ( 2 1 8 ) + . 0 3 ( 4 7 )+ ! .6 9 ( 4 4 ) + 3 .2 8 ( 2 5 7 ) + 3 .32(123)+ 3 . 0 2 ( 148)+4.14(213)+-50 (41) + . 4 3 ( 3 8 ) + 6 0 . 89(16)+ . 3 3 ( 6 6 )+ .7 9 ( 3 9 ) + . 5 5 ( 3 7 0 ) + . 1 3 ( 2 9 9 ) + 1 . 13(211)+.53 (454)+.3 7(19 4)+.1 0(2 34)+ 1 . 3 8 ( 1 4 2 ) + 5 . 70(153)+.46 (210)+.4 6(20 9)+.3 3(1 08)+ .2 0 ( 2 7 0 ) + 2 .68(162)+.46 (38 2)+ l.9 2 (3 7 )= 7 ,6 6 5 .1 8 + 100=76.65 miles 1 .3 1 (4 6 ) + .2 0 ( 2 7 9 ) + .0 7 ( 5 2 ) + . . . . 2 9 ( 1 9 0 ) + .3 9 ( 7 7 )+ .0 7 ( 6 6 ) + . . . 43.72(15)+.16(192 )+3.61 . . . ( 1 2 4)+ .1 3(32 1) + 6 . 62(168)+ . . . .46 (47 6)+ .07 (11 4)+ .07 (16 5)+ . . . . 1 3 ( 2 6 6 ) + . 2 3 ( 8 4 ) + 2 . 13(97)+ . . . . 1 0 ( 1 1 0 ) + . 10(583)+.75 . . . ( 5 0 ) + . 62(404)+3 .31(49)+ 284 Kalamazoo (co n 't) (23) (28) (30) (38) (39) (40) (43) (49) (51) (52) (54) (57) (60) (61) (62) (64) (66) (70) (75) (78) (80) (83) 52 190 77 66 15 192 124 321 168 476 114 165 266 84 97 110 583 50 404 49 40 156 .0007 .0029 .0039 .0007 .4372 .0016 .0361 .0013 .0662 .0046 .0007 .0007 .0013 .0023 .0213 .0010 .0010 .0075 .0062 .0331 .1419 .0046 1.0000 Kalkaska (40) 0 0 0 Kent (41) (1) (3) (5) (6) (7) (8) (10) (15) (16) (17) (20) (21) (22) (26) (27) (28) (33) (34) (37) (39) (40) (41) (42) (43) (44) (48) 226 44 158 156 498 37 144 190 232 327 166 410 461 132 573 142 66 34 90 52 145 18 568 75 126 346 .0003 .0649 .0126 .0008 .0007 .0604 .0142 .0062 .0042 .0009 .0035 .0025 .0013 .0005 .0045 .0192 .0001 .0043 .0013 .0025 .0018 .2741 .0016 .0277 .0004 .0016 . . . 14.19(40)+.46(156 )= . . . 4,155.33+100=41.55 miles ,03 (2 2 6 )+ 6 .49 (44 )+!.26(158)+ . . . .0 8 ( 1 56)+.07(498)+6.04 . . . ( 3 7 ) + l . 42(144)+.62(190)+ . . . .42(23 2)+.09 (327)+.35 . . . (166)+.25(41 0)+.13(461)+ . . . .0 5 ( 1 3 2 ) + .4 5 ( 5 7 3 ) + l .92 . . . (1 4 2 ) + .0 1 ( 6 6 ) + .43(34)+ . . . .13 (90 )+ .2 5(5 2)+.18 (14 5)+ . . . 27.4 1 (18)+ .1 6(5 68) + 2 . 77 . . . (75)+.04(126)+.16(3 46)+ . . . 2.03(274)+ 4.90 (121)+.13 . . . (429)+1.43(100)+5.08 . . . ( 6 6 ) + . 08(448)+4 .67(35)+ . . . ,19(219)+2.94(43)+12.35 . . . ( 4 9 ) + 1 . 1 7 ( 6 9 ) + l .43(79)+ . . . 10.23(28)+.30(146 )+.14 . . . (357)+.04(59)+.01(153)+ . . . 1.6 6(1 0 7 )= 6 ,299.16+100= . . . 62.99 miles 285 Kent (con1t ) (49) (51) (52) (53) (54) (55) (59) (60) (61) (62) (64) (67) (70) (72) (75) (80) (82) (83) 274 121 429 100 66 448 35 219 43 49 69 79 28 146 357 59 153 107 .0203 .0490 .0013 .0143 .0508 .0008 .0467 .0019 .0294 .1235 .0117 .0143 .1023 .0030 .0014 .0005 .0001 .0166 1.0000 Keewenaw (42) (42) 11 1.0000 100(11)=1100 t 100=11.00 miles Lake (43) (9) (16) (43) (49) (51) (53) 111 170 14 213 48 35 .0511 .0384 .6155 .1283 .1027 .0640 1.0000 5 .1 1 (1 1 1 )+3.84(170)+61.55(14)+ . . . 12 .83(312)+1 0.27(48)+ . . . 6.40(35)=5,531.46vl00= . . . 55.31 miles Lapeer (44) (1) (20) (25) (31) (32) (35) (36) (44) (49) (50) (51) (60) (63) (66) (69) (72) (74) (77) (79) 160 156 21 525 68 126 505 16 272 54 199 176 32 549 182 141 60 47 34 .0170 .0132 .0178 ,0088 .0221 .0133 .0154 .7378 .0066 .0133 .0066 .0221 .0177 .0066 .0088 .0376 .0022 .0287 .0044 1 . 7 0 ( 1 6 0 ) + ! . 3 2 ( 1 5 6 ) + l .78(21)+ . . . .88(525)+ 2 .21(68)+1.33 . . . (126)+1.54(505)+73.78 . . . ( 1 6 )+ .6 6 (2 7 2 )+ !.3 3 (5 4 )+ . . . . 66< 199) +2.21(176)+-! .77 . . . (32)+.66 (549 )+.88(182)+ . . . 3.76(141)+.22 (60)+2.87 . . . (4 7 ) + .4 4 ( 3 4 ) = 5 , 297.33 t . . . 100=52.97 miles 1 .0 0 0 0 286 Leelanau (45) (10) (28) (45) (46) (67) 62 31 9 276 105 .1198 .0594 .8018 .0179 .0011 1.0000 11 .9 8 (62 )+5.94(31)+8 0.18(9)+ . . . 1.79(276)+.11(105)= . . .2,154.11+100=21.54 miles Lenawee (46) (1) (5) (6) (10) (12) (15) (16) (17) (30) (31) (36) (38) (41) (46) (49) (52) (57 (58) (59) (64) (67) (72) (77) (79) (81) (82) 236 242 165 253 58 273 292 386 35 587 566 39 132 15 334 489 203 42 129 198 188 198 122 143 42 71 .0097 .0077 .0193 .0039 .0084 .0180 .0548 .0027 .0251 .0045 .0045 .0271 .0026 .5962 .0247 .0039 .0019 .1360 .0019 .0097 .0135 .0019 .0013 .0039 .0142 .0026 1.0000 .97 (23 6)+.77(242)+ !.93(165)+ . . 3 9 (2 5 3 )+ .8 4 { 5 8 ) + l .80 . (273)+ 5.48(2 92)+.27(386)+ . 2.51(35)+.45(5 87)+.45(566)+ . 2 . 7 1 ( 3 9 ) + . 26(132)+59.62(15) . +2.47(334)+.39(489)+.19 . (203)+13.60(42)+.19(129)+ . .97(198)+1.35(188)+.19 . (198)+.13(122)+39(143) + . 1 .4 2 ( 4 2 ) + .2 6 ( 7 1 ) = 7 , 001.07 . +100=70.01 miles Livingston (47) (1) (15) (17) (18) (26) (28) (32) (33) (47) (55) (63) (68) (81) 185 238 348 120 128 213 131 36 11 470 41 176 31 .0211 .0019 .0396 .0114 .0192 .0128 .0019 .0070 .8243 .0045 .0064 .0045 .0454 1.0000 11(1 85)+.19(238)+3.96(348)+ . 1.14(120)+ !.92(128)+ . 1.28(213)+.19(131 )+.70 . (36 )+82 .43(11)+.45(470)+ . .64(41 ) + .4 5 ( 1 7 6 ) + 4 .54(31)= . 3,883.35+100=38.83 miles 287 Luce (48) (7) (48) (49) 182 17 78 .0279 .7822 .1899 1.0000 2.79(182)+78.22(17)+18.99(78)= . . . 3,318.74*100=33.19 miles Mackinac (49) (7) (48) (49) 52 12 91 .0333 .9643 .0024 1.0000 3 . 33{52)+96.43(12)+.24(91)= . . . 1,352.16+100=13.52 miles Macomb (50) (1) 4 (6) (9) (10) (15) (16) 17) 18) 21) 24) 25) 26) 28) 32) 35) 38) 40) 44) 46) 47) 48) 49) 50) 51) 57) 58) 59) 60) 63) 65) 68) 69) 70) 71) 72) 74) 75) 77) 79) 82) 83) 205 232 135 106 250 269 273 370 153 454 263 62 153 245 98 172 92 226 54 86 65 389 318 13 244 200 56 151 222 28 162 197 228 182 257 187 61 401 37 87 24 199 .0117 .0043 .0019 .0001 .0011 .0023 .0097 .0078 .0008 .0007 .0015 .0016 .0024 .0039 .0088 .0040 .0005 .0016 .0037 .0035 .0060 .0003 .0069 ,5881 .0082 .0067 .0011 .0011 .0021 .0351 .0059 .0061 .0516 .0001 .0009 .0067 .0003 .0029 .1551 .0021 .0395 .0013 1.0000 1.17(205)+.43(232 )+.19(135 )+ . . . .01(106)+.11(250)+.23 . . . (26 9)+.97(273)+.78(370)+ . . . .08 (15 3)+.07(454)+.15(263) . . . +.16 (62)+.2 4(153)+.3 9(2 45) . . . +.88 (98 )+.4 0(1 72 )+.0 5(9 2) . . . +.16(2 2 6)+.37 (54 )+ .3 5(8 6) . . . +.60 (65)+ .03(389)+.69(3 18) . . . + 5 8 .81( 1 3 ) + . 8 2 ( 2 4 4 ) + . 67 . . . (200)+.11(56 )+.11(15 1)+ . . . .2 1 (222)+3.51(28)+.59 (162 ) . . . + .6 1 ( 1 9 7 ) + 5 .16(228)+.01 . . . (18 2)+.09(257)+.67(187)+ . . . .03 (61)+ .2 9(401)+15.51(37) . . . + . 2 1 ( 8 7 ) + 3 . 95(24)+.13(199) . . . =5,401.19+100=54.01 miles 288 Manistee (51) (10) (28) (45) (51) (53) 34 63 91 12 32 .0213 .0036 .1172 .8348 .0231 1.0000 2 . 1 3 ( 3 4 ) + . 3 6 ( 6 3 ) + l l .72(91)+ . . . 8 3 .48 (12)+ 2.31(32)= . . . 2,237.30*100=22.37 miles Marquette (52) (2) (7) (21) (22) (25) (36) (49) (52) 44 72 68 82 413 89 163 13 .0581 .0652 .0140 .0013 .0064 .0083 .0064 .8403 1.0000 5 . 8 1 ( 4 4 ) + 6 . 5 2 ( 7 2 ) + l .40(68)+ . . . .13(82)+.64(413 )+.83 . . . ( 8 9 ) + . 64(163)+84.03(13)= . . . 2,365.84+100=23.66 miles Mason (53) (3) (10) (28) (43) (51) (53) (57) (64) 118 65 94 35 32 9 85 37 .0038 .0192 .0077 .0402 .0900 .8161 .0038 .0192 1.0000 .38(11 8)+!.92 (65)+ .7 7(9 4)+ . . . 4 -02(35 )+ 9.00 (32)+81.61 . . . (9 )+ .3 8 ( 8 5 ) + ! .9 2 ( 3 7 ) = . . . 1,508.55+100=15.08 miles Mecosta (54) (5) (10 (16) (17) (37) (45) (49) (51) (53) (54) (60) (62) (64) 94 93 168 262 43 116 210 78 65 11 155 39 69 .0060 .0079 .0040 .0040 .0099 .0199 .0139 .0477 .0040 .8151 .0040 .0596 .0040 1.0000 60(9 4)+.79(93)+.40(168)+ .40 . (2 6 2 )+ .9 9 ( 4 3 ) + l . 99(116)+ . 1.39(210)+ 4.77(78)+.40 . (65)+81.51(11)+.40(155)+ . 5.96(39)+.40 (69)= . 2,483.89+100=24.84 miles Menominee (55) (7) (52) (55) (75) 157 107 12 93 .0177 .0284 .9291 .0248 1.0000 1 .77{157)+2.84(107)+92.91(12)+ . . . 2 . 48 (93)=1,927.33+100= . . . 19.27 miles Midland (56) (6) (9) (10) (15) 46 22 134 154 .0145 .1529 .0105 .0459 1 -45(46)+15-29(22)+1.05(134)+ . . . 4.5 9(1 54)+ !.4 5(16 8)+ .3 2 . . . (263)+2.90(37)+.40(94)+ . . . .1 6 ( 1 5 5 ) + .32(61)+15.37 289 M idland ( c o n 't ) ( 16) (17) (18) ( 20 ) (24) (25) (26) (28) (35) (40) (43) (45) (51) (54) (56) (57) (61) (62) (67 (71) (72) (73) (75) (83) 168 263 37 94 155 61 37 129 84 110 94 157 128 71 12 83 129 106 77 167 72 26 293 83 .0145 .0032 .0290 .0040 .0016 .0032 .1537 .0249 .0080 .0193 ,0048 .0241 .0121 .0266 .2534 .0145 .0032 .0048 .0241 .0322 .0893 .0113 .0072 .0072 1.0000 . . . . . . . . . . . . . . . . . . (37 )+2.49(129)+.80(84)+ 1.9 3(1 10)+ .48 (94)+2.41 (157)+1.21(128)+2.66(71)+ 25.34{12)+1.45(83)+.32 (129)+.48(106)+2.41(77)+ 3 . 2 2 ( 1 6 7 ) + 8 . 9 3 ( 7 2 )+ l .13 . . . (26)+.72(293 )+.72(83)= . . . 5,887.21+100=58.87 miles Missaukee (57) (17) ( 22) (36) (57) 213 348 393 10 .0106 .1684 .0315 .7895 1.0000 1.06(213)+16.84(348)+3.15 . . . (393)+78.95(10)= . . . 8,113.55+100=81.13 miles Monroe (58) ( 1) (4) (7) ( 12) (17) ( 21) (28) (30) (31) (38) (43) (46) (47) (50) (51) (54) (57) (58) (60) (62) 231 258 567 88 396 479 271 74 596 .0152 .0015 .0035 1.52(231)+.15(258)+.35(567)+ . l . l l ( 8 8 ) + 3 . 19(396)+ . 2.13(479 )+.1 5(271)+ !.7 2 . (74 )+.51(596)+9.57(66)+ . 1.01(231) + 8 .0 6 ( 4 2 ) + .76 . (6 9)+.56 (56)+.10(269 )+ . 1 .5 2 (2 0 2 )+ .10(225)+53.90 . (9)+ .8 1 (2 4 7 ) + l .01(205)+ . 2.54(216)+!.52(22 2)+ . 2.28(282)+.61(426)+.51 . (41)+4.31(39)=7,955.16+ . 100=79.55 miles 66 231 42 69 56 269 202 225 9 247 205 .0111 .0319 .0213 .0015 .0172 .0051 .0957 .0101 .0806 .0076 .0056 .0010 .0152 .0010 .5390 .0081 .0101 290 (67) (68 (71) (75) (81) (82) 216 222 282 426 41 39 .0254 .0152 .0228 .0061 .0051 .0431 1.0000 (59) (4) (5) (10) (15) (16) 17) (18) (21) (24) (28) (40) (41) (43 (45) (51) (52) (54) (59) (61) (62) (66) (69) (72) (75) (83) 219 127 137 158 201 295 73 379 163 133 113 35 79 160 125 398 48 13 58 59 519 153 112 326 87 .0075 .0149 .0064 .0021 .0213 .0021 .0011 .0064 .0117 .0641 .0021 .0139 .0064 .0480 .0555 .0011 .0736 .5219 .0107 .0299 .0107 .0043 .0299 .0437 .0107 1.0000 Montmorency (60) (4) (20) (50) (60) (67) 44 63 222 14 144 .0054 .0054 .0269 .9435 .0188 1.0000 , 5 4 ( 4 4 ) + . 5 4 ( 6 3 ) + 2 .69(222) + , . . 9 4 . 3 5 ( 1 4 ) + 1 .88(144)= , . . 2,246.58*100=22.47 miles Muskegon (3) (8) (10) (11) (15) (16) (21) (27) (28) 60 76 122 89 185 233 411 574 136 .0015 .0005 .0219 .0155 .0062 .0106 .0031 .0077 .0132 1 5 ( 6 0 ) + . 0 5 ( 7 6 ) + 2 . 19(122)+ . 1.55(89)+.62(185)+!.06 . (23 3)+.31(411)+.77 . ( 5 7 4 ) + l . 32(136)+.03 . ( 1 4 6 ) + 2 . 6 1 (4 3 ) + 2 . 22(70)+ . .77 (16 4)+ .0 5 (3 4 7 )+ .5 4 . ( 2 7 5 ) + 5 . 8 6 (8 9 ) + 5 . 60(62)+ . .67 (1 2 9)+ .0 5 (1 2 0 )+ .0 3 . ( 1 9 9 ) + . 77 (58)+63.68(10)+ Monroe (con1t ) Montcalm (61) 75 (219)+1.49 (12 7 )+ .6 4 (1 3 7 )+ . , 2 1 ( 1 5 8 ) + 2 . 13(201)+.21 . (29 5 ) + .1 1 ( 7 3 ) + .6 4 ( 3 7 9 ) + . 1 . 1 7 ( 1 6 3 )+ 6 . 41(133)+.21 . (1 1 3 ) + 1 .39 (3 5 )+ .6 4 (7 9 )+ . 4 .8 0(1 60)+ 5.55 (12 5) + . l 1 . ( 3 9 8 ) + 7 . 3 6 (4 8 ) + 5 2 . 19(13)+ . 1 . 0 7 ( 5 8 ) + 2 .9 9 ( 5 9 ) + l .07 . ( 5 1 9 ) + . 4 3 ( 1 5 3 ) + 2 .99(112)+ . 4.37(326)+!.07(87)= . 7,631.34*100=76.31 miles 291 Muskegon ( c a n 't) (40) (41) (43) 45 (48) (49) (51) (53) (56) (57) (58) (59) (61) (62) (64) (70) (72) (76) (83) 146 43 70 164 347 275 89 62 129 120 199 58 10 28 31 37 148 120 108 .0003 .0261 .0222 .0077 .0005 .0054 .0586 .0560 .0067 .0005 .0003 .0077 .6368 .0069 .0408 .0330 .0054 ,0010 .0039 1.0000 Newaygo (62) (7) (10) (28) (43) (48) (49) (51) (52) (53) (54) (61) (62) (67) 471 111 109 42 319 248 88 402 62 39 28 12 53 .0068 .0048 .0096 .0068 .0038 .0106 .0425 .0039 .0029 .0058 .0116 .8716 .0193 1.0000 Oakland (63) P) 2) (4) (5) (6) (7) (9) (10) (11) (12) (13) (15) (16) (17) (18) (20) 179 405 207 213 109 516 80 224 185 122 113 243 247 344 127 175 .0166 .0030 .0101 .0127 .0069 .0031 .0001 .0120 .0003 .0010 .0006 .0058 .0158 .0021 .0145 .0057 . 69(28)+4.08(31) + 3 . 30 (37)+.54(148 )+.10(120)+ . 39( 108)=4 , 143. 20+100= 41.43 miles 68(471)+.4 8(11 1)+.96(10 9)+.68 . (42 )+.38 (319 )+!.06 (2 48 )+ . 4.2 5(8 8)+.39 (40 2)+.29 (62 )+ . . 5 8 ( 3 9 ) + ! . 16(28)+87 .16 . (12)+1,93(53)=2,642.93v . 100=26.43 miles 1 .6 6 ( 1 7 9 ) + .3 0 ( 4 0 5 ) + l .01(207)+ 1.27(213)+.69(109)+.31 (51 6)+.01(80)+1.20(224)+ .03(185)+.10(122)+.06 (1 1 3 ) + . 5 8 ( 2 4 3 ) + l . 58(247)+ . 21(344)+!.45(127)+.57 (175)+.13(428)+.03(479)+ .05 (86 )+ .3 3 (2 3 7 )+ !.2 4 ( 3 7 ) + l . 68(127)+.05(591)+ .28(220)+.55(108)+.25 ( 5 4 5 ) + l .96(99)+3 -13 (146)+.07(524)+.05(122)+ .32(84)+.13(200)+.71 (586)+.11(18 5)+.20(32)+ 1.07{247)+2.05(41)+.12 (364)+.52(29 2)+!0.22 292 Oakland (c o n 1t ) (21) (22) (23) (24) (25) (26) 27) (28) (30) (31) (32) (35) (36) (37) (38) (40) (42) (43) (44) (45) (47) (48) (49) (50) (51) (53) (54) (56) (57) (58) (59) (60) (61) (63) (64) (65) (67) (68) (69) (70) (71) (72) (74) (75) (77) (79) (81) (82) (83) 428 479 86 237 37 127 591 220 108 545 99 146 524 122 84 200 586 185 32 247 41 364 292 28 218 217 163 95 174 54 125 196 173 18 199 136 168 171 202 156 231 161 82 375 59 65 50 30 173 .0013 .0003 .0005 .0033 .0124 .0168 .0005 .0028 .0055 .0025 .0196 .0313 .0007 .0005 .0032 .0013 .0071 .0011 .0020 .0107 .0205 .0012 .0052 .1022 .0043 .0009 .0007 .0064 .0086 .0050 .0004 .0149 .0011 .4363 .0003 .0068 .0065 .0103 .0040 .0026 .0075 .0233 .0032 .0009 .0607 .0003 .0062 .0238 .0022 1 .0 0 0 0 . . . . . . . . . . . . ( 2 8 ) + . 4 3 ( 2 1 8 ) + . 09(217)+ . 0 7 ( 1 6 3 ) + . 6 4 ( 9 5 )+ .8 6 ( 1 7 4 ) + .5 0 ( 5 4 ) + .0 4 ( 1 2 5 ) + 1 . 4 9 ( 1 9 6 ) + . 1 1 ( 1 7 3)+4 3.63 ( 1 8 ) + .0 3 ( 1 9 9 ) + .6 8 ( 1 3 6 ) + .6 5 ( 1 6 8 ) + ! . 0 3 ( 1 7 1 ) + . 4 0 ( 2 0 2 ) + .2 6 (1 5 6 )+ .7 5 (2 3 1 )+ 2 . 3 3 ( 1 6 1 ) + .3 2 ( 8 2 ) + . 0 9 (3 7 5 ) + 6 .0 7 ( 5 9 ) + . 0 3 (6 5 ) + . 6 2 ( 5 0 ) + 2 . 38(30 )+.22 (173)=8,110.51*100= 81.10 miles 293 Oceana (6 4 ) (10) (51) (53) (64) (82) 97 63 37 13 218 .0145 .0726 .0436 .8596 .0097 1.0000 1 .4 5 (9 7 )+ 7 .2 6 (6 3 )+ 4 .36(37)+ . . . 85 .96(13)+.97(218)= . . . 2,088.29+100=20.99 miles Ogemaw (65) (5) (6) (35) (49) 51) (61) (63) (65) (72) 85 30 42 162 116 175 136 20 31 .0722 .0181 .0193 .0036 .0193 .0168 .1852 .6511 .0144 1.0000 7 . 2 2 ( 8 5 ) + l .81 (30) + l .93(42)+ . . . .36(1 62)+!.93(1 16)+ . . . 1.6 8(1 75)+18.52(136)+ . . . 65.1 1 (20)+ !.4 4(31 )= . . . 5,190.82+100=51.91 miles Ontonagon ( 66 ) (7) (27) (31) (66) 63 65 60 16 .0302 .0474 .0108 .9116 1.0000 3 . 0 2 ( 6 3 ) + 4 . 7 4 ( 6 5 ) + l .08(60)+ . . . 91.16 (16 )= 2,02 1.72+ . . . 100=20.22 miles Osceloa (67) (7) (18) (67) (83) 422 46 10 32 .1334 .4333 .2999 .1334 1.0000 13 - 34(422)+43-33(46)+29.99(10)+ . . . 13.34(32)=8,349.44+ . . . 100=83.49 miles Oscoda ( 68) (16) (35) (60) (68) 86 73 35 10 .1887 .0471 .1038 .6604 1.0000 18.87 (86)+4. 7 1 (73 )+10 .38(35)+ . . . 66.04(10 ) = 2 ,9 9 0 .35+ . . . 100=29.90 miles Otsego (69) (5) (16) (40) (69) 29 50 43 12 .0065 .1307 .1961 .6667 1.0000 ■65(29)+13.07(50)+!9.61 (43)+ . . . 66 .67(12 )= 2 , 315.62+ . . . 100=23.16 miles Ottawa (7 0 ) (2) (3 (5) (7) (8) (9) (10) (15) (16) (18) 412 26 183 523 58 155 154 214 257 132 .0009 .0989 .0014 .0043 .0055 .0005 .0100 .0072 .0112 .0048 09(412)+9 .89(26)+.14(183)+ . . .43(5 23)+.55 (58)+.05 . . 155)+1.00(154)+.72 . . (214)+ 1.12(257)+.48 . . (13 2)+.60(219)+.33(167)+ . . . 29 (21 8)+ .33(170)+1.03 . . ( 5 9 3 ) + l .03(151)+.64 . . (143)+.31(123)+.07(371)+ . . 2 . 6 9(1 21)+ !.4 3(94 )+ .14 . . ( 9 0 ) + . 0 2 (60 )+2.36(37)+ 294 Ottawa (con1t ) (24) (28) (35) (40) (42) (44) (46) 47) (48) (51) (53) (54) (59) 61) (62) (64) (67) (70) (83) 219 167 218 170 593 151 143 123 371 121 94 90 60 37 60 63 104 11 132 .0060 .0033 .0029 .0033 .0103 .0103 .0064 .0031 .0007 .0269 .0143 .0014 .0002 .0236 .0860 .0379 .0200 .5944 .0043 1.0000 . . . . . . . . . . . . 8.60(60)+3.7 9(63)+2.0 0 (104)+59.44(11)+.43 (132)=4,705.83+100= 47.06 miles Presque I s l e (71) (16) (71) 45 13 .0235 .9765 1.0000 2 .3 5 ( 4 5 ) + 9 7 . 6 5 ( l3 ) = 1 ,375.20+ . . . 100=13.75 miles Roscommon (72) (4) (10) (21) (40 (72) 114 87 284 50 10 .0009 .0037 .0066 .0019 .9869 1.0000 .09(11 4)+.37 (87 )+.66(284 )+ . . . .19 (50 )+ 98 .69(10)= . . . 1,226.29+100=12.26 miles Saginaw (73) 0) (2) (3) (4) (5) (6) (9) (10 (16) (17) (18) (20) (24) (26) (27) (28) (29) (31) (32) (35) 112 338 158 139 144 42 14 155 180 277 58 108 170 58 524 150 41 478 66 70 .0139 .0038 .0009 .0021 .0033 .0731 .1098 .0077 .0183 .0050 .0811 .0024 .0059 .1148 .0006 .0328 .0006 .0044 .0095 .0544 1 .39(112)+.38(338) + .09(158) + . . . .2 1 ( 1 3 9 ) + .33(144)+7.31 . . . (42)+ 10.98(14)+.77 . . . (155)+ 1.83(180)+.50 . . . ( 27 7)+8 .11(58)+.24(108)+ . . . .59{170)+11.48(58)+.06 . . . (524)+3.28(150)+.06(41)+ . . . . 4 4 (4 7 8 )+ .95(6 6)+5.44 . . . (79)+.30(457)+.62(5 2)+ . . . .21(131)+2.87(178)+.59 . . . (225)+.47(14 8)+.30(380)+ . . . 3.1 4(2 6)+.77 (10 4) + 3 . 37 . . . ( 8 4 ) + . 15(129)+2.34(69)+ . . . . 9 5 ( 9 8 ) + . 27(104)+1.98 . . . (135) + l .07(164)+!4.21 . . . (93)+5.47 (12)+.18(8 6)+ . . . .41(308)+.62(99)+.21 . . . (30)+5.06(104)=8,250.60+ . . . 100=82.51 miles 295 (36) (37) (40) (45) (49) (51) (52) (56 (57) (59) (60) (65) (67) (68) (69) (71) (72) (73) (74) (75) (77) (79) (83) 457 52 131 178 225 148 380 26 104 84 129 69 98 104 135 164 93 12 86 308 99 30 104 .0030 .0062 .0021 .0287 .0059 .0047 .0030 .0314 .0077 .0337 .0015 .0234 .0095 .0027 .0198 .0107 .1421 .0547 .0018 .0041 .0062 .0021 .0506 1.0000 (74) (1) (9) (28) (35) (40) (50) (60) (65) (71) (74) (77) (79) 191 91 235 157 213 61 207 147 242 9 25 63 .0100 .0080 .0140 .1383 .0421 .0040 .0882 .0060 .0802 .5611 .0421 .0060 1.0000 1.00(191)+.8 0(91) + l .40(235)+ . 13.83(157)+4 .21(213)+ . .40 (61) + 8 .82(207)+.60 . (147)+8.02(242)+56.11 . ( 9 ) + 4 . 21(25)+.60(63)= . 8,188.06+100=81.88 miles Schoolcraft (75) (21) (48) (52 (75) 55 70 89 10 .0209 .0314 .0262 .9215 1,0000 2.09(55)+3.14(70)+2.62(89)+ . . . 92.15(10)=!,489.43+ . . . 100=14.89 miles (76) (5) (10) (16) (17) (18) (25) (26) 172 183 218 314 86 26 89 .0019 .0364 .0112 .0121 .0168 .0205 .0233 Saginaw (c o n 1t ) Sanilac Shiawassee 19(172)+3.64(183)+1.12(218)+ . . 1.21(314)+1,68{86)+2.05 . . (26)+2.33(89)+ 7.46(179)+ . . .09 (117)+9 .32(159)+!.40 . . (81)+.74(556)+.28(262)+ . . .28(177)+.37(416)+1.77 . . (111)+.56(56)+.37(108)+ 296 Shiawassee (c o n 1t ) St. C l a i r St. Joseph (77) (78) (28) (35) (40) (41) (42) (49) (51) (52) (54) (56) (58) (59) (60) (65) (68) (69) (72) (76 (83) 179 117 159 81 556 262 177 416 m 56 108 69 167 107 142 171 124 14 133 .0746 .0009 .0932 .0140 .0074 .0028 .0028 .0037 .0177 .0056 .0037 .0559 .0028 .0392 .0186 .0802 .3075 .1258 .0214 1.0000 (1) (16) (17) (24) (28) (32) (35) (44) (48) (50) (58) (72) (74) (75) (77) (82) 206 274 371 264 248 80 173 47 390 37 92 188 25 402 11 60 .0011 .0074 .0005 .0018 .0149 .0036 .0071 .0036 .0053 .0752 .0025 .0071 .0206 .0004 .8390 .0009 1.0000 (8) (10) (11) (12) (14) (16) (17) (28) (36) (43) (48) (71) (78) 73 236 71 26 48 305 400 233 520 167 419 323 12 .0038 .0004 .0026 .0110 .0586 .0030 .0008 .0149 .0072 .0132 .0051 .0021 .8294 5.5 9(6 9)+ .28 (16 7)+ 3 .9 2 (107 +1.86(142)+8.02 (171)+30.75(124)+12.58 ( 1 4 ) + 2 . 14(133)= 12,386.46*100=123.86 miles 11 (206)+.74(2 74)+.05(371)+ .1 8 ( 2 6 4 )+ !.4 9 (2 4 8 )+ .36 (80 )+ .7 1(1 73 )+ .3 6 ( 4 7 ) + . 53 (39 0)+7 .52(37)+ . 2 5 ( 9 2 ) + . 7 1 (188)+2.06 ( 2 5 ) + . 04 (402)+8 3.90(11)+ . 0 9 ( 6 0 ) = 2 , 466.86*100= 24.67 miles 3 8 ( 7 3 ) + .0 4 (2 3 6 ) + .2 6 ( 7 1 ) + l .10 ( 2 6 ) + 5 . 86 (48)+.30(3 05)+ . 0 8 ( 4 0 0 ) + l .49(23 3)+.72 ( 5 2 0 ) + l .32(167)+.51 ( 4 1 9 ) + . 21(323)+8 2.94(12)+ 4.2 0(8 1 )+ .5 9 (1 9 1 )= 3,160.72*100=31.62 miles 297 St. Joseph (con* t ) (80) (83) 81 191 .0420 .0059 1.0000 Tuscola (79) (7) (9) (10) (16) (18) (26) (32) (35) (51) (68) (79) 469 32 181 200 85 85 37 99 175 124 15 .0041 .1546 .0206 .0825 .0289 .0412 .1361 .1423 .0041 .0701 .3155 1.0000 41(469)+15.46(32)+2.06(181)+ . 8.25(200)+ 2.89(85)+4.12 . (85)+13.61(37)+14.23(99)+ . .41 (175)+7.01(124)+31.55 . {15)=6,632 - 30+100= . 66.32 miles Van Buren (80) (3) (4) (10) (11) (14) (16) (30) (35) (42) (43) (51) (54) (57) (70) (80) (82) (83) 39 309 184 25 39 287 115 248 612 130 151 121 174 33 12 177 162 .0135 .0341 .0039 .0019 .0032 .0386 .0019 .0006 .0090 .0051 .0051 .0013 .0019 .0013 .8580 .0148 .0058 1.0000 1.35 {3 9)+3. 4 1(309)+ .39(184) + .19 ( 2 5 ) + . 32 (39)+3.86(287)+ .19(115)+.06(248)+.90 (612)+.51(130) + .51(151) + .13(121)+.19 (174)+.13 (33)+ 8 5 . 80 (12)+1.48(177)+.58 (162)=4,472.59*100= 44.73 miles Washtenaw (81) (4) (5) (9) (10) (13) (15) (16) (17) (18) (21) (24) (25) (26) (28) (33) (33) 223 230 97 240 78 260 263 361 144 444 253 55 144 236 65 37 .0004 .0179 .0029 .0047 .0004 .0084 .0044 .0117 .0058 .0018 .0066 .0015 .0044 .0186 .0004 .0172 0 4 ( 2 2 3 ) + l .79(230)+.29(97)+ . .47(240)+.04 (78)+.84 . (260)+.44(26 3)+!.17 . (361)+.58(144)+.18(444)+ . 1.8 6(2 36)+ .0 4(6 5)+!.72 . ( 3 7 ) + . 36(21 6)+2 .19(200)+ . .11 (263)+l.3 5(4 2)+2 3.00 . ( 3 1 ) + . 3 6 { 3 8 0 ) + l . 68(309)+ . 1 .21(58)+2.01(234)+,04 . {226)+*3.32(41) + .44(212) + . .07(168)+.47(50)+ !.5 3 . (187)+.07(218)+.51(247)+ . .40(177)+44.51(19)+5.66 . (42)=6,457.82*100= . 64.58 miles 298 Washtenaw (con1t ) (40) (43) (45) (46) (47) (48) (49) (50) (51) (53) (58) (60) (61) (62) (68) (69) (71) (72) (81) (82) 216 200 263 42 31 380 309 58 234 226 41 212 168 50 187 218 247 177 19 42 .0036 .0219 .0011 .0135 .2300 .0036 .0168 .0121 .0201 .0004 .0332 .0044 .0007 .0047 .0153 .0007 .0051 .0040 .4451 .0566 1.0000 Wayne (1) (2) (4) (5) (6) (7) (8) (9) (10) (11) (14) (15) (16) (17) (18) (20) (21) (24) (25) (26) (27) (28) (30) (31) ( 32) (35) (36) (38) (40) (-111 207 432 234 241 136 543 133 107 251 187 177 271 274 372 155 203 455 264 64 155 619 247 98 572 111 174 552 77 227 153 .0149 .0022 .0025 .0079 .0028 .0004 .0092 .0001 .0049 .0004 .0013 .0095 .0369 .0093 .0109 .0029 .0010 .0042 .0028 .0105 .0005 .0065 .0052 .0011 .0178 .0064 .0004 .0172 .0047 .0002 1.49(207)+.22(432)+.25(234)+ . . . .79(241)+.28(136)+.04 . . . (543)+.92(133)+.01(107)+ . . . .49(251 ) + .04(187)+.13 . . . (17 7)+.95(27 1) + 3 .69(274)+ . . . . 9 3 { 3 7 2 ) + l. 09(155)+.29 . . . (203)+.10(455)+.42(264)+ . . . . 2 8 ( 6 4 ) + l .05(155)+.05 . . . (61 9)+.65(247)+.52(98)+ . . . .11(57 2)+!.78(111 )+.64 . . . (1 7 4 )+ .0 4 ( 5 5 2 ) + l . 72(77)+ . . . .47(227)+.02(153)+.21 . . . (61 4)+.21(212)+.74(59)+ . . . .31 (274)+.41(7 1)+4-39 . . . (55 )+.15(391)+.15(320)+ . . . 10 .57(24)+!.39(245)+.4 6 . . . (245)+.28(191)+.15(201)+ . . . 2.67(39)+1.38(223)+.14 . . . (1 9 2 )+ .87 (198)+6.17(30)+ . . . .01(218)+.46(164)+.32 . . . (596)+.07(195)+.20(158)+ . . . .81(229)+.48(175)+.54 . . . ( 2 6 8 ) + l . 37(188)+.51(83)+ . . . . 23(4C2)+.19(86)+9.43 . . . (C0)+.02(92)+3 .43(42)+ 299 Wayne (con1t ) (42) (43) (44) (45) (46) (47) (48) (49) (50) (51) (53) (54) (57) (58) (60) (61) (62) (63) (64) (65) (66) (67) (68) (69) (70) (71) (72) (74) (75) (76) (77) (79) (81) (82) (83) 614 212 59 274 71 55 391 320 24 245 245 191 201 39 223 192 198 30 218 164 596 195 198 229 175 258 188 83 402 86 60 92 42 15 201 .0021 .0021 .0074 .0031 .0041 .0439 .0015 .0015 ,1057 .0139 .0046 .0028 .0015 .0267 .0138 .0014 .0087 .0617 .0001 .0046 .0032 .0007 .0020 .0081 .0048 .0054 .0137 .0051 .0028 .0019 .0943 .0002 .0343 .3169 .0008 1.0000 . . . 3 i .69(15)+.08(201)= . . . 8,675.26+100=86.75 miles Wexford (5) (7) (9) (10) (16) (28) (43) (45) (51) (53) (54) (57) (58) (59) (62) 53 393 100 56 127 51 47 79 50 74 43 13 225 87 81 .0077 .0039 .0058 .0618 .0039 .0097 .0096 .0019 .0193 .0039 .0096 .0309 .0077 .0270 .0290 .77(53)+.39(3 93)+.58(1 00)+ . . . 6.18(56)+.39(127)+.97 . . . (51)+.96(4 7)+ .1 9(79)+ . . . 1.93(50)+ .39(74)+ .9 6 . . . ( 43 )+3.09(13)+.77(225)+ . . . 2.70(87)+2.90(81)+.77 . . . (32)+76.06(10)=2,392.39+ . . . 100=23.92 miles 300 Wexford (con1t ) (67) (83) 32 10 .0077 .7606 1.0000 APPENDIX E CORRELATION MATRICES 301 C o rre la tio n MATRIX--State o f Michigan Equation Modified User C h a ra c te ris tic s Model HORPOW -0.56653 -.03989 +.59540 +.30864 1.0000 RESIDS .20309 -.07853 -.16954 -.06105 -.17467 COMMAR -.35826 .12158 .35247 .14696 .38786 -.19375 1.0000 YATCLUB -.23071 .33604 .11767 .02836 .11348 -.08894 -.02544 BOAT LEN -.54068 .23061 .51077 .17346 .62535 -.23217 .40765 INCOME -.20624 .09617 .13749 .14816 .30006 -.16462 .16365 INCOMESQ -.21252 .09789 .13937 .14795 .29623 -.17906 .16322 INCOMAGE ,18420 .06573 .13048 .13212 .25489 -.21476 .15285 TYPE 2-1 TYPE 3-1 TYPE 4-1 HORPOS RESIDS COMMAR TYPE 1-1 1.0000 C o rre la tio n MATRIX— S tate o f Michigan Equation, Aggregate P a rtic ip a tio n Model LINCOME (X4 ) -.44219 -.44783 1.00000 HINCOME (X5) .48119 .48036 -.86423 POPDEN (X6) .30620 .98609 -.44927 DGLAKE (X7) .41220 -.09286 PMRACES (X8) .21042 .62207 SDISTAN (X9) .60416 .41545 PCCAMPS (X]0) .62922 -.66290 .79873 -.46861 SUWATER (XT1) .47629 HMCOURT (X13) .88512 .87285 .58638 ARSERV (Xi4) .99573 .98536 .62326 .58209 LABORER (X23) -.45129 -.51371 SERWORK (X26) WARCRAFT (X28) -.52379 TRVELD .58914 DINCOME LINCOME HINCOME POPDEN PMRACES SDISTAN PCCAMPS SUWATER Correlation MATRIX—State of Michigan Equation, Aggregate Participation Model ARSERV (X14) .90152 .42325 SALWOK (X17) .53646 CRAFTS (Xlg ) -.47061 OPERA (X20) -.54502 -.50565 304 CLERIC (X18) -.44321 FARMMAN (X?4) -.42148 -.60696 FARMLAB (X25) -.40652 -.46645 SERWORK (X26) WACRAFT (X28) .74881 -.42806 -.65053 CRAFTS OPERA .46565 -.45488 TREQUIP (X29) HMCOURT PROFESS MANADM SALWOK CLERIC FARMMAN APPENDIX F STATISTICS FROM INITIAL REGRESSION EQUATIONS 305 STATISTICS FROM INITIAL REGRESSION EQUATION, ALL VARIABLES, REGION 1— DETROIT Regression Coefficients ★ Variable (a) (Xi) (X2) (X3 ) (X4 ) (x5) (X6) (x7 ) (Xg) (Xg) (Xio) (X ll) (X l2) (X l3) (X14) (Xl6) (Xl?) (X]S) (Xl9) (X20 ) (X2 l ) (X22 ) (X23) (X24) (X25) (x27) (X29) (X30) . 34.600031 13.148446 13.805253 9.924474 11.940791 0.019479 -12.054335 3.091807 - 0.090843 - 0.597129 - 5.869255 6.082023 1.365402 2.943962 0.860122 - 1.122992 0.006781 1.459226 - 3.554467 - 4.036475 1.132263 18.521408 5.158391 1.805007 - 0.393649 6.692298 -12.975475 -12.198856 20.226824 7.779197 10.325022 8.266970 8.737971 0.023015 4.137616 4.387019 5.144378 4.212349 9.874933 7.280685 2.410380 1.090399 0.319399 0.635170 0.006530 0.596642 6.777269 12.273565 6.753476 11.806793 7.415392 6.753476 7.198675 7.408217 16.243211 22.887508 Level of 2 Significance Mean .083 .087 .178 .228 .168 .402 .004 .488 .934 .858 .560 .409 .578 .007 .007 .074 .300 .014 .607 .739 .843 .113 .494 .775 .911 .370 .430 .601 .79092 .02554 .12015 .04825 50.97729 .40019 .17502 .08420 .24125 .01041 .02554 .54305 1.59603 15.92999 48.27247 2460.54115 3.60833 .20341 .00757 .17502 .00851 .06055 .26206 .07569 .05676 .00378 .00189 306 Intercept Type 1-1 Type 2-1 Type 3-1 Type 4-1 HOR POW RESIDS 1-1 WATFRNT 2-1 COMMAR 3-1 SUMCOTS 4-1 PUBMAR 5-1 YATCLUB 6-1 BOATRANS NOBOOWN BOAT LEN AGE AGESQUR FAMSIZE OCCU 1-1 OCCU 2-1 OCCU 3-1 OCCU 4-1 OCCU 5-1 OCCU 6-1 OCCU 7-1 OCCU 9-1 OCCU 11-1 OCCU 12-1 Standard Errors of Regression Coefficients REGION 1-D E T R O IT .-C o n tin u e d . Variable OCCU 13-1 OCCU 14-1 OCCU 17-1 INCOME INCOMESQ INCOMAGE EDUCATN Regression , Coefficients * ( x3 l) (X32) (x35) Ix»l Level of , Significance 18.942935 7.631836 8.859254 2.401604 0.117574 0.032249 0.310965 6.764665 4.771915 10.018295 - 3.048400 0.152457 0.021769 0.219280 R = .3672' Standard Errors of Regression Coefficients R2 = .13484 .720 .539 .257 .202 .192 .507 ,488 4 307 3 .00284 .09839 .02176 5.72116 40.89977 271.83793 12.55251 Sv¥ = 29.6S685 JA Values which appear in this column fo r X 5 , X]4» X ig , X17, X ig , X35* X37, are fo r continuous variables, and show the estimated effects of such variables on the regression lin e . Values fo r (Xq-X4 ) , (X g -X n ), X] 2 * and ( X19-X35) assume equal slope across a ll categorical classes. These la t te r values give the estimated net change in attrib u tab le to zero-one variables in the various categorical classes. 2 Mean X 3 8 , and X3 g slope of the coefficients intercept For 1,022 degrees of freedom. M ultiple correlation co e ffic ie n t. Coefficient of m ultiple determination. 5 Standard Error o f Estimate. V a ria b le s X2 8 , X3 3 , and X34 had a value - 0 fo r a ll observations. dependent variable was 29.49480. The mean value fo r the STATISTICS FROM INITIAL REGRESSION EQUATION, ALL VARIABLES, REGION 6— Lansing Regression 1 Coefficients Variable* (a) (X-i) (X2 ) (X3 ) (xj) ( X 5) Cx5 ) (X?) (X8 ) (Xg) (Xio) (Xl2) (x 13) (X14) (X16) (X] 7 ) (Xis) (X19) (X20) ( x 21 (X 22 (X23) (X24) (x 2s) (X2 7 ) . 31.450982 18.691171 61,742538 20.869342 -11.676807 0.072400 - 8.642484 -20.930768 1.497064 8.689051 -28.432827 5.584693 12.393486 0.376937 - 0.118903 0.001969 1.980579 -40,371435 -53.194946 -30.881080 -54.918564 -35.020995 -39.454217 -36.193698 -44.374399 -55.641434 56.043273 12.983473 33.332711 23.400141 25.707193 0.076195 15.076187 18.141682 23.855702 15.273587 37.888381 5.137223 2.723809 0.888597 1.591062 0.016674 1.702961 22.287543 24.088158 22.365824 27.122778 23.296149 21.683001 23.352069 23.427739 42.035986 Level of 2 Significance Mean .151 .065 .373 .650 .343 .557 .250 .950 .570 .454 .278 <.0005 .672 .940 .906 .246 .071 .028 .169 .044 .134 .070 .123 .059 .187 .92366 .00763 .02672 .01145 29.00763 .38550 .04580 .02290 .51145 .00382 .55344 1.71374 14.15267 49.28626 2554.42366 3.22137 .14504 .03435 .14504 .01527 .06489 .32061 .06107 .05344 .00382 308 Intercept Type 1-1 Type 2-1 Type 3-1 Type 4-1 HOR POW RESIDS 1-1 WATFRNT 2-1 COMMAR 3-1 SUMCOTS 4-1 PUBMAR 5-1 BOATRANS NOBOOWN BOAT LEN AGE AGESQUR FAMSIZE OCCU 1-1 OCCU 2-1 OCCU 3-1 OCCU 4-1 OCCU 5-1 OCCU 6-1 OCCU 7-1 OCCU 9-1 OCCU 10-1 Standard Errors of Regression Coefficients REGION 6— LANSING.-Continued. Regression 1 Coefficients Variable OCCU 14-1 OCCU 17-1 INCOME INCOMESQ INCOMAGE EDUCATN (X30) ii I!?,) (X37) -47.870225 -48.738236 - 2.935518 0.450281 - 0.080475 0.835713 R = .53543 R2 = .2867 Standard Errors of Regression Coefficients 23.553202 23.646294 8.127652 0.347855 0.105276 0.705182 Level of Significance* Mean .043 .040 .718 .197 .445 .237 .09924 .04580 5.23057 33.54481 253.26649 11.92366 Syx = 34.4302' 309 ^Values which appear in th is column fo r Xc, X13, X1 4 , X-jg, X ^ , X-|o, X3 g, X3 7 ® X3g, and X3g are fo r continuous variables, and show the estimated effects of such variables on tne slope of the regression lin e . Values fo r (X^-X4 ) , (X g -X n ), X32 * ant* (X-j9-X 3 5 ) assume equal slope coefficients across a ll categorical classes. These la tte r values give the estimated net change in intercept attrib u tab le to zero-one variables in the various categorical classes. 2With 230 degrees of freedom. ^Multiple correlation co e ffic ie n t. ^Coefficient of m ultiple determination. Standard Error of Estimate. V a riab le s X-j-j, Xgg, X2g» X3 q, X3 i , X33, and X3$ had a value = 0 fo r a ll observations. mean value of the dependent variable was 36.64122. The STATISTICS FROM INITIAL REGRESSION EQUATION, ALL VARIABLES, REGION 7C— SAGINAW BAY Regression Coefficients 1 Variable Intercept Type 1-1 Type 3-1 HOR POW RESIOS 1-1 WATFRNT 2-1 COMMAR 3-1 SUMCOTS 4-1 BOATRANS NOBOOWF BOAT LLN AGE AGESQUR FAMSIZE OCCU 1-1 OCCU 2-1 OCCU 3-1 OCCU 4-1 OCCU 5-1 OCCU 6-1 OCCU 7-1 OCCU 9-1 OCCU 11-1 OCCU 13-1 OCCU 14-1 (a) (X O (xj) CX5 ) (x6 > (xS) CXg) (Xg) ( X il) tx3) (X14) ( X l6 ) Sgi (X 9) (X20) (X21) (X22) CX23 ) (X24) (X25) U 27) (X29 ) (X3 1 ) (X32 ) 91.049955 - 1.944470 -23.639548 0.097721 - 7.214900 - 5.825381 1.421553 - 3.135821 -12.439959 - 0.438066 - 1.163342 - 1.222332 0.008416 4.322712 -11.110714 - 2.299274 - 2.065611 -16.533922 -24.631585 - 3.646774 - 7.230253 22.710413 -29.627590 -25.662060 -14.862429 Standard Errors of Regression Coefficients 61,066401 15.743281 32.846380 0.208674 12.960727 13.295381 21.149680 14.288054 7.950929 2.898784 0.835874 1.976785 0.017946 2.671201 22.134956 27.673204 20.968428 34.202237 22.213317 20.705942 23.100893 25.521574 37.684580 35.103066 18.986305 Level Significance^ Mean .902 .474 .641 .579 .662 .947 .827 0.94167 0.00833 16.70833 0.33333 0.38333 0.02500 0.17500 0.42500 1.82500 14.52500 54.15000 3090.71667 2.82500 0.11667 0.01667 0.13333 0.00833 0.06667 0.13333 0.05000 0.03333 0.00833 0.00833 0.35000 .121 .880 .167 .538 .640 .109 .617 .934 .922 .630 .270 .861 .755 .376 .434 .467 .436 REGION 7C— SAGINAW B A Y.-C ontinued. Regression . Coefficients Variable* OCCU 17-1 INCOME INCOMESQ INCOMAGE EDUCATN (X3 5 ) (X36) (X3 7 J CX3 8 ) (X3g) -14.607802 - 6.880577 0.255613 0.102000 0.119981 Level of 2 Significance 23.078728 10.129767 0.467086 0.139233 0.747639 .528 .499 .586 .466 .873 X 11 2 4 R = .2590 1/?* R = . 50893 Standard Errors of Regression Coefficients Mean 0.05000 3.34900 16.28732 170.49383 11.10000 28.19175 Values in this column for X5 , X-|3 , X-|4 , X*|g> x17> x18» x36» x37> *38’ anc* *39 are ^or continu" ous variables, and give the estimated effects of such variables on the slope of the regression lin e . Values for X], X3 , (Xg-Xg)» X12 , and (X19-X 35 } assume equal slope coefficients across a ll categorical classes. These la tte r values give the estimated net change in intercept attrib u tab le to specific zero-one variables in the various categorical classes. 2 3 For 90 degrees of freedom. M ultiple correlation c o e ffic ie n t. ^Coefficient of m ultiple determination. 5 Standard Error of Estimate. * Variables X g , X4 , X-j q , Xu , X2 6 , %28’ X3Q» x3 3 » The mean value for the dependent variable was 24.52500. an(^ *34 had a value = 0 fo r a ll observations. STATISTICS FROM INITIAL REGRESSION EQUATION, ALL VARIABLES, REGION 10-TRAVERSE BAY Regression . Coefficients Variable Intercept Type 1-1 Type 2-1 Type 3-1 Type 4-1 HOR POW RESIDS 1-1 WATFRNT 2-1 COMMAR 3-1 SUMCOTS 4-1 PUBMAR 5-1 YATCLUB 6-1 BOATRANS NOBOOWN BOAT LEN AGE AGESQUR FAMSIZE OCCU 1-1 OCCU 2-1 OCCU 3-1 OCCU 4-1 OCCU 5-1 OCCU 6-1 OCCU 7-1 OCCU 9-1 (a ol il; (*5 ( x7 (X8 (Xg j[lO xn x12 X l3 X14 J16 Xl7 X l8 Xig ho h\ X22 X23 x 24 Ixl) -13.231337 - 2.018604 - 1.055200 20.872660 3.470293 0.054395 - 2.761351 13.270491 11.326654 7.023254 -17.607739 -58.528051 0.152259 4.701949 0.713395 2.070163 - 0.027384 0.975122 4.026746 10.724516 3.115157 -11.575063 5.854061 4.095677 4.873149 - 5.313315 Standard Errors of Regression Coefficients 42.750716 14.678752 19.157907 18.829205 17.413640 0.066881 9.269979 8.865665 11.841585 8.933350 17.189359 34.380010 5.472258 1.881604 0.757170 1.238067 0.011629 1.573260 11.841813 19.636332 11.366731 17.391050 13.428997 11.770728 13.284149 16.363782 Level of 2 Significance Mean .757 .891 .956 .269 .842 .417 .766 .136 .340 .433 .307 .090 .978 .013 .347 .096 .019 .536 .734 .586 .784 .506 .663 .728 .714 .746 0.85938 0.02344 0.04297 0.05469 32.28906 0.32422 0.27734 0.08594 0.21875 0.02344 0.00391 0.47656 1.85156 15.11328 53.74219 3052.99219 3.04297 0.14453 0.01563 0.21875 0.01953 0.05469 0.16797 0.06641 0.02344 REGION 10-TRAVERSE BAY.— Continued. Variable OCCU 11-1 OCOI 13-1 o r a i 4- i o r a 17-1 INCOME INCQMESQ INCDMAGE EDDlATN Regression , Coefficients * (X29) (X 3 l) (X32) (X35) (X35) (X3 7 ) (X38) CX39) Standard Errors of Regression Coefficients - 3.961916 -15.391058 2.569912 - 4.263038 -15.397757 0.550976 0.120588 0.930128 R = .49033 R2 - . 24044 Level Significance 32.989879 32.393021 11.158626 16.456272 4.901290 0.242168 0.061136 0.569042 2 .905 .635 .818 .796 .002 .024 .050 .104 Mean 0.00391 0.00391 0.21484 0.02344 4.44961 28.40261 231.85996 12.12891 Suv = 30.14595 y* ^Values in this column fo r X5 , X-jq, X u , Xig, X ^ , X-jg, X3 5 , X3 7 , X™, and X30 are fo r continuous variables, and give the estimated effects of such variables on tne slope of the regression lin e . Values fo r (X-j-X4 ) » (X g -X n ), X]g» and {X-]9 -X3 5 ) assume equal slope coefficients across a ll categorical classes. These la tte r values give the estimated net change in intercept attrib u tab le to sp ecific zero-one variables in the various categorical classes. For 222 degrees of freedom. 3 M ultiple correlation c o e ffic ie n t. ^Coefficient of m ultiple determination. 5 Standard error of estimate. it Variables X2 5 , Xgg, X3 Q, X3 3 , and X34 had a value = 0 fo r a ll observations. value of the dependent variable was 31.84766. The mean STATISTICS FROM INITIAL REGRESSION EQUATION, ALL VARIABLES, REGION 12A— MARQUETTE-IRON MOUNTAIN Regression , Coefficients Variable* Intercept Type 1-1 Type 2-1 Type 3-1 Type 4-1 HOR POW RESIDS 1-1 WATFRNT 2-1 COMMAR 3-1 SUMCOTS 4-1 PUBMAR 5-1 BOATRANS NOBOQWN BOAT LEN AGE AGESQUR FAMSIZE OCCU 1-1 OCCU 3-1 OCCU 4-1 OCCU 5-1 OCCU 6-1 OCCU 7-1 OCCU 9-1 OCCU 11-1 OCCU 13-1 OCCU 14-1 U) (Xi) (X2 ) (X3 ) (X4 ) (X5 ) (X6 ) (x 7 ) cx8 ) (Xg) (X10) ( X i2) (x 3 ) (X14) Cxi6 ) (Xi7) (x la ) (X19) (X21) (X22) (X23) (x 24) (X25) (XZ7) (X2g) (X31) CX32) 80.679723 22.014925 -17.257420 42.176964 32.077843 - 0.171941 - 2.328867 2.895586 -36.606852 - 4.313560 24.445517 4.033884 12.285726 0.969531 - 3.277394 0.018262 1.503884 -14.737218 - 5.114983 - 9.514436 -15.872773 - 3.487154 2.265620 3.073139 7.593360 -31.313564 7.328208 Standard Errors of Regression Coefficients 74.138372 14.172334 38.33375 41.987903 39.659647 0.199191 14.055417 16.562457 35.404194 14,086739 32.521654 8.474249 3.397059 2.273120 2.356621 0.022307 2.090614 23.953665 22.383276 32.914421 25.252662 23.057552 24.243073 24.432529 41.826172 41.243350 22.085005 Level Of 0 Significance Mean .279 .124 .654 .318 .421 .390 .869 .862 .304 .760 .454 .635 <.0005 .671 .168 .415 .474 .540 .820 .773 .531 .880 .926 .900 .856 .450 .741 0.89916 0.00840 0.01681 0.01681 18.76471 0.37185 0.11465 0.01681 0.39496 0.01681 0.57983 1.67227 13.84874 50.84034 2732.06723 3.42857 0.14286 0.20168 0.01681 0.05882 0.23529 0.08403 0.07563 0.00840 0.00840 0.13445 REGION 12A— MARQUETTE-IRON MOUNTAIN.-Continued. Regression ■. Coefficients * Variable OCCU 17-1 INCOME INCOMESQ INCOMAGE EDUCATN Standard Errors of Regression Coefficients CX3 5 ) (X3 7 ) (*38> « m ) 79.386824 -11.718156 - 0.237022 0.271759 0.774585 R = ■53833 R2 = Level of g Significance Mean .056 .282 .600 .129 .520 0.00840 4.00647 22.45717 200.12050 12.07563 40.988167 10.832339 0.449756 0.177241 1.199490 • 289?4 Syx ‘ 33.42805 Values in this column fo r X5 , Xi 3 , X ^ , Xi 6 , X17 , Xiq, X3 6 , X3 7 , X3 8 , and X3 g are fo r continuous variables, and show the estimated effects of such variables on the slope of the regression lin e . Values fo r (X-j-X4 ) * CX5 -X 7q )> X-j2 * ant* (x19~x35? assume et)ua^ slope coefficients across a ll categorical classes. These la tte r values give trie estimated net change in intercept attrib u tab le to specific zero-one variables in the various categorical classes. For 87 degrees of freedom. 3 M ultiple correlation co efficien t. ^Coefficient of m ultiple determination. 5 Standard Error of Estimate. 1c Variables X-j-], X2o» X25, X28* X3 Q1 X « , X3 4 , had a value = 0 for a ll observations. mean value of the dependent variable was 28.9327. The STATISTICS FROM THE IN ITIA L REGRESSION EQUATION, ALL VARIABLES, THE STATE OF MICHIGAN Variable* Intercept Type 1-1 Type 2-1 Type 3-1 Type 4-1 HOR POW RESIDS 1-1 WATFRNT 2-1 COMMAR 3-1 SUMCOTS 4-1 PUBMAR 5-1 YAT CLUB 6-1 BOATRANS NOBOOWN BOATLEN AGE AGESQUR FAMSIZE OCCU 1-1 OCCU 2-1 OCCU 3-1 OCCU 4-1 OCCU 5-1 OCCU 6-1 OCCU 7-1 OCCU 9-1 OCCU 10-1 OCCU 11-1 OCCU 12-1 (a) (Xi) (X2) (X3 ) CX4) (X5) (*6 ) CX7 ) Cx8 ) (Xg) !xio ) x 1) (x 2) (x13) X 4) (X ) (X 7 ) (Xig) (X 9 ) (X20 ) (X2 l ) (x22) (X2 3 ) (X24) c x ||) (X2 7 ) (x2a) (Xgg) (X30) Regression , Coefficients Standard Errors of Regression Coefficients 9.680392 6.669133 10.841906 9.014766 10.794299 0.045626 - 8.973539 3.342072 0.609173 2.888814 - 0.096124 3.723876 3.744756 3.979111 0.500767 - 0.033049 - 0.002633 0.949018 1.270673 - 4.100618 0.096012 - 0.650402 2.242742 0.747356 - 0.112150 3.695966 - 2.139105 - 1.079919 - 6.305095 9.372951 3.015796 5.061623 3.841148 4.017613 0.012913 2.089817 2.189922 2.905245 2.087495 5.065265 4.896971 1.126519 0.485508 0.150776 0.287596 0.002821 0.308601 3.532572 4.755454 3.456149 4.952981 3.757836 3.404931 3.684416 3.887242 21.309344 6.433061 12.765285 Level of g Significance .026 .030 .018 .007 .001 <.0005 .123 .816 .163 .933 .453 .001 <.0005 .001 .875 .353 .002 .718 .393 .927 .865 .558 .810 .926 .344 .883 .842 .627 Mean 0.87124 0.01494 0.05838 0.03236 34.29418 0.40371 0.17900 0.05250 0.28694 0.00928 0.01154 0.54899 1.69314 14.99004 50.04594 2651.97307 3.36999 0.15479 0.01675 0.17923 0.01448 0.06200 0.25979 0.07355 0.04639 0.00045 0.00656 0.00136 STATE OF MICHIGAN.-Continued. Regression Coefficients Variable OCCU 13-1 OCCU 14-1 OCCU 15-1 OCCU 16-1 OCCU 17-1 INCOME INCOMESQ INCOMAGE EDUCATN Standard Errors of Regression Coefficients - 5.271192 4.461224 20.088138 -17.973505 1.654696 - 1.107231 0.079811 0,005809 0.176822 0<31 (*32 (*33 (X 3 4 CX35 CX35 (X37 1*38 ( X 39 R= !953 8.393942 3.572615 21.33314 17.501339 4.417927 1.174667 0.057770 0.015692 0.143250 R2 = .10864 Level of 2 Significance .538 .209 .349 .305 .708 .349 .163 .711 .215 Mean 0.00339 0.13781 0.00045 0.00068 0.02263 4.92385 32.15150 239.84793 12.03055 Svv = 29.73S55 Values which appear in this column fo r (X-|-X4 ) , (X g -X ]]), X-|2 * and (X19 -X3 5 ) assume equal slope coefficients. Regression coefficients fo r these variables give the estimated net e ffe c t on the intercept term. Values fo r variables X5 , X1 3 , X]4 » Xig, X1 7 , Xig, X3g» X3 7 , X3 8 , and X3 g give estimated net effe c t on the slope of the regression lin e . 2 For 4381 degrees of freedom. 3 M ultiple correlation c o e ffic ie n t. ^Coefficient of m ultiple determination. Standard Error of Estimate. *The mean value of the dependent variable was 28.7148. STATISTICS FROM THE INITIAL REGRESSION EQUATION, ALL VARIABLES, THE STATE OF MICHIGAN Variable Intercept TRAVELD DINCOME LINCOME HINCOME POPOEN DGLAXE PMRACES SOISTAN PCCAMPS SUWATER PBLSITE HMCOURT ARSERV PROFESS MANADM SALWOR CLERIC CRAFTS OPERA LABORER FARMMAN FARMLAB (a (x 2 (*3 X4 IX 5 tXg X? l X8 (Xq X10 X11 x19 x20 x23 X24 X25 Regression Coefficients Standard Errors of Regression Coefficients 9,727.174811 7.869137 - 0.001048 - 0.239358 66.889963 0.531051 - 7.938825 -63.902708 -27.566422 0.013628 0.046662 -12.939940 - 1.325806 5.825296 -212.663072 - 3.108161 -337.320577 -29.489353 -143.470991 -79.590738 -175.279040 8.046832 -275.577827 14,829.481203 6.217067 0.001448 59.247762 41.285897 1.365628 5.050546 34.438723 31.653554 0.491320 0.019720 19.772066 8.274936 9.614895 149.221282 115.843666 189.607668 146.968146 150.137061 138.959613 159.919964 154.219828 201.528181 Level of ! Significance Mean .515 .211 .472 .997 .111 .699 .122 .069 .388 .978 .021 .515 .873 .547 .160 .979 .081 .842 .343 .569 .278 .959 .177 43.53012 331,933.15662 21.53012 23.48193 165.19277 29.09639 2.96663 12.03012 388.46988 9,594.77952 9.18072 42.85542 50,69880 12.13711 7.47301 6.07036 13.39566 15.84217 17.27205 5.07807 2.86096 1.19783 STATE OF MICHIGAN.-Continued. Regression Coefficients Variable* SERWORK HOUWORK WACRAFT TREQUIP Standard Errors of Regression Coefficients ^26^ (Xgy) 0<28> (X2 9 ) -13.614884 -595.967989 25.192953 -95.743757 R = .92002 Level of 1 Significance 153.288944 262.167381 3.445244 205.732342 2 3 R = .8468 .930 .027 <.0005 .643 S = 836.9941 yx ^For 56 degrees of freedom. 2 M ultiple correlation co efficien t. 3 Coefficient of m ultiple determination. 4 Standard Error of Estimate. * The mean value o f the dependent v a ria b le was 2,403.03614. 4 Mean 13.04229 1.15084 94.26867 4.30566 STATISTICS FROM THE IN ITIAL REGRESSION EQUATION, TOP 30 COUNTIES OF ORIGIN * Variable (a) (X2) (X3) (X4) (Xc) (X6) (X7) (Xo) (X9) (X10) (X n ) (X i2) (X*j 3 ) (X14) (X15) (X16) (X17) (Xio) (Xiq) (X2 n) (X23) (X24) Level of j Significance Mean 15,720.334944 16.037461 0.003018 251.310693 -113.203100 1.746125 11.866864 0.635951 -0.719106 2.788693 0.216298 -113.739196 -25.079377 -13.049183 -137.718705 -653.431672 203.398244 -121.467663 13.382087 -276.546670 728.932509 312.706836 110,662.500823 15.428900 0.008141 359.179482 103.486826 3.288200 23.580670 96.215601 66.105103 2.316890 0.084935 122.286546 48.429563 30.015474 1,016.419004 954.071248 1,168.982064 1,226.933700 1,071.752958 1,055.579722 1,399.789575 866.294664 .375 .735 .535 .354 .632 .649 .995 .992 .315 .084 .421 .640 .693 .901 .543 .873 .927 .991 .810 .684 .742 55.26667 819,700.33333 16.73333 29.96667 394.16667 31.70000 5.48000 16.20000 380.76667 8,319.92000 9.03333 63.63333 118.43333 13.02933 7.24700 6.46067 15.02200 15.78767 18.21433 4.29767 1.78800 320 Intercept TRAVELD DINCOME LINCOME HINCOME POPDEN DGLAKE PMRACES SDISTAN PCCAMPS SUWATER PBLSITE HMCOURT ARSERV PROFESS MANADM SALWOR CLERIC CRAFTS OPERA LABORER FARMMAN Regression Coefficients Standard Errors of Regression Coefficients TOP 30 COUNTIES OF O R IG IN .-C ontinued. Variable FARMLAB SERWORK HOUWORK WACRAFT TREQUIP Standard Errors of Regression Coefficients Regression Coefficients ic (X25) (Xoc) (X2 7 ) (X28) (X2g) 2,202.005600 1,261.491940 3,787.463882 18.944907 1,062.138701 424.917899 20.480208 -6,266.944177 20.536416 -1,224.533777 R = .9809 R = .9622' ^With 3 degrees of freedom. 2 M ultiple correlation co efficien t. 3 Coefficient of m ultiple determination. 4 Standard Error of Estimate. * The mean value o f the dependent v a ria b le is 2,111.3333. Level of , Significance .859 .988 .197 .358 .332 Suv = 671.2163* yx Mean 0.80167 12.42267 0.97500 74.90000 4.04267 STATISTICS FROM INITIAL REGRESSION EQUATION, BOTTOM 30 COUNTIES OF ORIGIN Regression Coefficients * Variable (a ) (X2 ) (X3 ) ( X j) (X5) (X6) (X7) (X8 ) (Xg) (Xl 0 ) (X ) (X12) (X13) (X l4 ) (X15) (x (x1jf)6) (X18) (X19) (X20> (X23) (% ) 80,477.521991 -0.497307 0.001301 122.408581 177.703301 -20.297367 -50.984321 -268.386815 40.058029 -1.920264 0.160476 23.667932 -32.616131 29.760782 -1,251.781742 -408.325643 -1,097.403521 -528.489160 -974.939796 -799.896664 -911.772947 -445.914634 Significance Mean 34,362.168358 11.460945 0.021765 110.569478 46.174009 48.006006 12.314543 54.417991 74.976628 1.162263 0.043420 48.728652 32.942718 37.096193 331.869799 208.904269 394.453530 256.514313 405.348269 275.022745 349.405674 336.283537 .968 .956 .349 .031 .701 .026 .016 .630 .197 .034 .660 .395 .481 .033 .146 .069 .131 .095 .062 .080 .277 36.53333 47,572.20000 25.46667 18.86667 29.63333 28.80000 1.80800 9.63333 353.20000 8,527.08000 9.53333 22.33333 10.83333 71.42800 7.03333 5.61633 11.60367 15.96567 17.10800 6.04533 3.90567 Level of , 322 Intercept TRAVELO DINCOME LINCOME HINCOME POPDEN DGLAKE PMRACES SDISTAN PCCAMPS SUWATER PBLSITE HMCOURT ARSERV PROFESS MANADM SALWOR CLERIC CRAFTS OPERA LABORER FARMMAN Standard Errors of Regression Coefficients BOTTOM 30 COUNTIES OF O R IG IN .-C ontinued. Regression Coefficients Variable* FARMLAB SERWORK HOUWORK WACRAFT TREQUIP Standard Errors of Regression Coefficients (X2 5 } (X26) (X27 ) (X2a> (X2 g) -1,205.449575 -613.260571 -2,396.969281 15.539556 -1,272.921713 2 431.316082 383.133049 473.167289 6.514173 471.538913 2 R = .99253 .068 .208 .015 .097 .074 Syx = 38S.35924 ^With 3 degrees of freedom. 2 M ultiple correlation c o e ffic ie n t. 3 C oefficient of m ultiple determination. ^Standard Error o f Estimate. ★ The mean value o f the dependent v a ria b le was 2 ,0 21 .133 33. Mean 1.61557 13.67333 1.17433 97.40000 4.47767 323 R = .9962 Level of 1 Significance BIBLIOGRAPHY BIBLIOGRAPHY Public Documents Barlowe, Raleigh, and S te in m u e lle r, !M.ilton H. “Trends in Outdoor Recreation." A Place to L ive; 1963 Yearbook o f A g ric u ltu re . Washington: U.S. Dept, o f A g ric u ltu re , 1963. M u elle r, Eva, and Gurin, G erald. P a rtic ip a tio n in Outdoor R ecreation: Factors A ffe c tin g Demand Among American A d u lts. ORRRC Study Report 20. Washington: U.S. Government P rin tin g O ffic e , 1962. Outdoor Recreation Resources Review Commission. Federal Agencies and Outdoor R ecreation. ORRRC Study Report 13. Washington: U.S. Government P rin tin g O ffic e , 1962. __________ . Outdoor Recreation f o r America. Government P rin tin g O ffic e , 1962. Washington: U.S. __________ . Public Outdoor Recreation Areas— Acreage, Use, P o te n tia l. ORRRC Study Report 1. Washington: U.S. Government P rin tin g O ffic e , 1962. U.S. Congress. Food and A g ric u ltu re Act o f 1962. Public Law 87-103, 87th Congress, H.R. 12391, September 27, 1962. __________ . P o lic ie s , Standards and Procedures in the Formulation, Evaluation and Review o f Plans f o r Use and Development o f Water and Related Land Resources. Senate Document 97, 87th Congress, 2nd Session, Supplement No. 1, June 4 , 1964. __________ . Pro.iections to the Years 1967 and 2000: Economic Growth, Population, Labor Force and Leisure, and T ran sp o rtatio n . ORRRC Study Report 23. Washington: U .S. Government P rin tin g O ffic e , 1962. U.S. Department o f Commerce, Bureau o f th e Census. 1967 Census o f Business; Volume V, Selected Services— Area S t a t is t ic s . P art I I , Michigan, Washington: U.S. Government P rin tin g O ffic e , 1967. __________ . 1970 Census o f Population; General Population Character­ istics"! PC(1)-B24, Michigan. Washington: Government P rin tin g O ffic e , 1970. __________ . 1970 Census o f Population; General Social and Economic C h a ra c te ris tic s . PC( 1 ) - C24, Michigan. Washington: Government P rin tin g O ffic e , 1970. 325 326 U.S. Department o f Commerce, Bureau o f the Census. 1970 Census o f Population; Volume 1, C h a ra c te ris tic s o f the Population. Part A, Number o f In h a b ita n ts . Washington: U.S. Government P rin tin g O ffic e , 1970. National Recreation Survey. ORRRC Study Report 19. Washington: U.S. Government P rin tin g O ffic e , 1962. . U.S. Census o f Population: 1960; V ol. I , Character­ is tic s o f the Population. Part 24, Michigan. Washington: Government P rin tin g O ffic e , 1960. _ _ . Books Brockman, C. Frank. Recreational Use o f Wild Lands. McGraw-Hill Book Co., In c ., 1959. New York: Clawson, Marion, and Held, B u rn ell. The Federal Lands, T h e ir Use and Management. Baltim ore: The Johns Hopkins Press, 1957. Clawson, Marion; Held, B u rn ell; and Stoddard, Charles H. Land fo r the Future. Baltim ore: The Johns Hopkins Press, 1960. Clawson, Marion, and Knetsch, Jack L. Economics o f Outdoor R ecteation. Baltim ore: The Johns Hopkins Press, 1966. Clawson, Marion. Land and Water fo r R ecreation. and Company, 1963. Chicago: Rand-McNally Cochrane, W illard W., and B e ll, Carolyn S. The Economics o f Con­ sumption. New York: McGraw-Hill Book Company, 1956. Ferguson, C. E. Microeconomic Theory. Richard D. Irw in , In c ., 1972. 3rd E d itio n . F isk, George. Leisure Spending Behavior. o f Pennsylvania Press, 1963. Homewood, 111.: P h ilad elp h ia: U n ive rsity Hibbard, Benjamin A. A History, o f the Public Land P o lic ie s . The Macmillan Company, 1924. Hicks, John R. Value and C a p ita l. Clarendon Press, 1946. 2nd E d itio n . Oxford: Is e , John. Our National Park P o licy; A C r itic a l H is to ry . The Johns Hopkins Press, 1961. Johnston, J. Econometric Methods. Company In c ., 1963. New York: New York: The Baltim ore: McGraw-Hill Book 327 K lein , Lawrence R. An Introduction to Econometrics, New Jersey: P re n tic e -H a ll, In c ., 1962. Englewood C l i f f s , Leftw ich, Richard H. The Price System and Resource A llo c a tio n . E d itio n . New York: H o lt, Rinehart and Winston, 1966. Linder, S teffa n B. The Harried Leisure Class. U n iv e rs ity Press, 1970. M arsh all, A lfre d . P rin c ip le s o f Economics. MacMillan and Co., Lim ited, 1947. New York: 8 th E d itio n . 3rd Columbia London: McConnel, C. R. Elementary Economics; P rin c ip le s , Problems, and P o lic ie s . New York: McGraw-Hill Book Company, 1960. M i l l , John S tu a rt. P rin c ip le s o f P o litic a l Economy. Edited by S ir W. J. Ashley. New York: Augustus M. K e lly , 1961. Musgrave, Richard A. The Theory o f Public Finance. H ill Book Company, In c ., 1959. New York: McGraw- P e ffe r, E. Louise. The Closing o f the Public Domain. Stanford, C a lifo rn ia : The Stanford U n iv e rs ity Press, 1951. Pigou, A. C. The Economics o f W elfare. S t. M a rtin 's Press, 1962. 4th E d itio n . New York: P ra is, S. J . , and Houtakker, H, S. The Analysis o f Family Budgets. London: Cambridge U n iv e rs ity Press, 1955. Smith, Frank E. The P o litic s of Conservation. Books, 1966. Spurr, New York: Pantheon W. A .; Kellogg, L. S .; and Smith, J. H. Business and Economic S t a t is t ic s . Rev. Ed. Homewood, I l l i n o i s : Richard Irw in In c ., 1961. Wyand, Charles S. The Economics o f Consumption. MacMillan Company, 1938. New York: The P eriod icals Bator, Francis M. "The Anatomy o f Market F a ilu re ." The Q uarterly Journal o f Economics. Vol. L X X II, No, 3 (August 1958). Clawson, Marion. "E ffec ts o f Nonprice Variables Upon P a rtic ip a tio n in W ater-Oriented Outdoor Recreation: Comment." American Journal o f A g ric u ltu ra l Economics. Vol. 50, No. 4 (November 1968). 328 Havinghurst, R ., and Feigenbaum, K. "Leisure and L ife S ty le s ." Journal o f Sociology. Vol. 64 (January 1959). American Hendee, John C. "Rural-Urban D ifferences Reflected in Outdoor Recre­ atio n P a rtic ip a tio n ." Journal o f Leisure Research. Vol. 1, No. 4 (F a ll 1969). K a lte r, Robert J . , and Gosse, Lois E. "Recreation Demand Functions and the Id e n tific a tio n Problem." Journal o f Leisure Research. Vol. 2, No. 1 (W inter 1970). Knetsch, Jack L. "Assessing the Demand fo r Outdoor Recreation." Journal o f Leisure Research. Vol. 1, No. 1 (W inter 1969). K r u t illa , John V. " Is Public In terven tio n in Water Resources Develop­ ment Conducive to Economic E ffic ie n c y ." Natural Resources Journal. Vol. 6 , No. 1 (January 1966). G ille s p ie , Glenn A ., and Brewer, Durward. "E ffects o f Nonprice Variables Upon P a rtic ip a tio n in W ater-Oriented Outdoor Recreation." American Journal o f A g ric u ltu ra l Economics. Vol. 50, No. 1 (February 1968). Loeb, Benjamin S. "The Use o f Engel's Laws as a Basis fo r Predicting Consumer Expenditures." Journal o f M arketing. Vol. 20, No, 1 (July 1955). "Sales Management." 1969). Survey o f Buying Power. Vol. 102, No. 12 (June 10, Stevens, S. S. "On the Theory of Scales o f Measurement." Vol. 103, No. 2684 (June 1946). Science. Stoevener, Herbert H ., and Brown, W illiam G. "A nalytical Issues in Demand Analysis fo r Outdoor R ecreation." Journal o f Farm Economics. Vol. 49, No. 5 (December 1967). U.S. News and World Report. "$80 B illio n fo r Leisure." No. 13 (September 15, 1969). Vol. 70, Working, E. J. "What do 'S t a tis t ic a l Demand' Curves Shov?" Journal o f Economics. Vol. 41 (February 1927), Q uarterly Reports Bureau o f Business and Economic Research. Michigan S ta tis tic a l A b strac t. East Lansing, Michigan: Graduate School o f Business Adminis­ tr a tio n , Michigan State U n iv e rs ity , 1966. 329 Brown, W illiam G .; Singh, Ajmer; and C a s tle , Emery N. An Economic Evaluation o f the Oregon Salmon and Steelhead Sport F is h e ry . Technical B u lle tin 78. C o rv a llis , Oregon: A g ric u ltu ra l Experiment S ta tio n , Oregon S tate U n iv e rs ity , 1964. Bureau o f Business and Economic Research. Michigan S ta t is tic a l A b s tra c t. Ninth E d itio n . East Lansing, Michigan: Graduate School o f Business A d m in is tra tio n , Michigan S tate U n iv e rs ity , 1972. Chubb, M ichael. Outdoor Recreation Planning in Michigan by a Systems Analysis Approach; P art I I I , The P ra c tic a l A p p licatio n o f Program RECSYS and SYMAP. Technical Report No. 12. Lansing, Michigan: Michigan Dept, o f Conservation, 1967. C ic c h e tti, Charles J . ; Seneca, Joseph J . ; and Davidson, Paul. The Demand and Supply o f Outdoor R ecreation. New Brunswick, New Jersey: Bureau o f Economic Research, Rutgers U n iv e rs ity , 1969. Clawson, Marion. Methods o f Measuring the Demand fo r and Value of Outdoor R ecreatio n . R eprint No. 10. Washington: Resources fo r the Future, In c ., 1959. E l l i s , J. B. Outdoor Recreation Planning in Michigan by a Systems Analysis Approach; P art I I . Technical Report No. 7, Lansing, Michigan: Michigan Department o f Conservation, 1966. Humphrys, C liffo r d R ., and Green, R. F. Michigan Lake Inventory B u lle tin s 1 -8 3 . East Lansing, Michigan: Michigan S tate U n iv e rs ity , Department o f Resource Development, 1962. L e is t r it z , F. L arry. The Use o f Dummy V ariab les in Regression A n a ly s is . Ag. Econ. Misc. Report No. 13. Fargo, North Dakota: A g ri­ c u ltu ra l Experiment S ta tio n , 1973. Manderscheid, Lester V. An Intro d u ctio n to S t a t is tic a l Hypothesis T e s tin g . Ag. Econ. Mimeo 867— Revised. East Lansing, Michigan: Department o f A g ric u ltu ra l Economics, Michigan S tate Uni­ v e r s ity , 1964. Michigan Department o f Conservation, Waterways D iv is io n . Transportation P re d ic tiv e Procedures: Recreational Boating and Commercial Shipping. Lansing, Michigan: Michigan Department o f Commerce, 1967. Michigan S tate Waterways Commission: B iennial R ep o rt--1968-1970. Lansing, Michigan: Michigan Department o f Natural Resources, Waterways Commission, 1970. M ils te in , D. M ., and Reid, L. M. Michigan Outdoor Recreation Demand Study; V ol. I I , A c t iv itie s Reports. Technical Report No. 6 . Lansing, Michigan: Michigan Department o f Commerce, 1966. 330 Needy, John L. "B oating." Michigan Outdoor Recreation Demand Study; V ol. I I , A c tiv itie s Reports. Technical Report No. 6 . Lansing, Michigan: Michigan Department o f Conservation, 1966. R a fte r, Mary E . , and Ruble, W illiam L. Stepwise D eletion o f V ariab les from a Least Squares Equation. STAT Series D escription No. 8 . East Lansing, Michigan: A g ric u ltu ra l Experiment S ta tio n , Michigan S tate U n iv e rs ity , 1969. Rand McNally Road A tla s ; Supplement to the 104th E d itio n o f the Rand McNally Commercial A tlas and Marketing Guide. Chicago: Rand-McNally and Company, 1968. Woodhall's T r a ile r in g Parks and Campgrounds. Woodhall Publishing Company, 1968. Highland Park, I l l i n o i s : Unpublished M a te ria ls Bond, R. S .; Bevins, M. I . ; Fiske, P. R. "Public Campground P o licy in the N o rth east." Unpublished Report, Regional P ro je c t NEM-42, Economic Analysis o f the Campground Market in the N ortheast, 1973. Bryant, W. K. "An Analysis o f Inter-Community Income D iff e r e n t ia ls in A g ric u ltu re in the United S ta te s ." Unpublished Ph.D. d is s e rta tio n , Michigan S tate U n iv e rs ity , 1963. Cole, Gerald L. "Toward the Measurement o f Demand fo r Outdoor Recre­ a tio n in the P h ila d e lp h ia — Baltimore-Washington M etropolitan Region, w ith Im p licatio n s fo r A g ric u ltu ra l Resource Use." Unpublished Ph.D. d is s e rta tio n , Michigan S tate U n iv e rs ity , 1967. D ivisio n o f Vehicle and W atercraft Records. "Size and Type o f Registered Boats in Michigan C ounties." Unpublished Report, Michigan Secretary o f S ta te 's O ffic e , 1968. Esch, Richard. "Highway Skim D istance." Unpublished D ata, Highway Planning D iv is io n , Michigan Department o f S tate Highways, Lansing, Michigan, 1973, Igo, A llis o n Jean. "An Analysis o f the V a lid it y o f Mail Surveys fo r Use in Recreation Research." Unpublished Masters Thesis, Michigan S tate U n iv e rs ity , 1971.