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AN N A R B O R . Ml 4 8 1 0 6 18 B E D F O R D ROW . L O N D O N W C1R 4 E J . E N G L A N D 8112117 L i n g o ,W alter Bo y d A STUDENT ENROLLMENT FORECASTING MODEL FOR LANSING COMMUNITY COLLEGE (MICHIGAN) Michigan State University University Microfilms international 300N. ZeebRoad, Ana Arbor,MI 48106 PH.D. 1980 A STODEOT ENROLLMENT FCRECASTING MCDEL FOR LANSING CCMMUNTIY COLLEGE (MICHIGAN) By Walter Boyd Lingo A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Administration and Higher Education 1980 ABSTRACT A STUDENT ENROLLMENT FORECASTING MODEL .FOR LANSING COMMUNITY COLLEGE (MICHIGAN) By Walter B. Lingo This study was designed to develop a useful student enrollment forecasting model for Lansing Cbmnunity Cbllege. From the descrip­ tive data collected hypotheses regarding the forecasting of student enrollment are suggested for subsequent experimental study. Eight calculation methods: simple average, moving average, double moving average, exponential smoothing, double exponential smoothing, ratio method, simple correlation and regression analysis, and multiple correlation and regression analysis, were selected to forecast the 1979 student enrollment at Lansing Cbmnunity College. From these eight calculation methods fifty-one 1979 student enroll­ ment forecasts were generated. Each calculation method required at least one influencing factor to conpute a student enrollment forecast. The calculation methods of simple average, moving average, double moving average, exponential smoothing, and double exponential smoothing required only the influencing factor of past Lansing Cbmnunity Cbllege stu­ dent enrollment data. factors: The ratio method incorporated two influencing past student enrollment and tri-county (Clinton, Eaton, and Ingham) census data. The final two calculation methods, simple and multiple correlation and regression analysis, produced forecasts Walter Boyd Lingo through the application of twenty-two selected influencing factors/ independent variables. Each of the fifty-one forecasts resulting fran the eight listed calculation methods, and the selected influencing factors, were ranked by its accuracy in forecasting the Lansing Cbmnunity College 1979 fulltime equated student enrollment. The ranking was based on the percentage of error of each forecast. Ihe calculation method that produced the most accurate fore­ cast, based on the percentage of error, was the ratio method/18-20 year olds with a percentage of error of -0.4. The above fact re­ vealed that the tested mathematical function methods did not produce a more accurate forecast than a non-mathematical function calculation method. The range of the percentage of error produced by the eight cal­ culation methods (fifty one scores) tested was 512.6. This indicated that the selection of a calculation method in forecasting student enrollment can produce diverse scares. In addition, the influencing factors that produced the highest correlation coefficients did not produce a correspondingly high accuracy rate in forecasting student enrollment. The major finding of this study was that the model that most accurately forecasted the 1979 fulltime equated student enrollment was able to forecast the 1980 student enrollment within an equal percentage of error. DEDICATION I wish to dedicate this completed dissertat ion to my wife, Ruth Ann, whose love and industriousness has been an unending source of inspiration. i ACKNOWIEDGMENIS I-wish to express my great gratitude to the following people: Dr. Michael il. Byrne for his friendship and advice; Ms. Allyson R. Reynolds- for her assistance; Dr. William G. Schaar for His constant support; and to Dr. Diane L. Stolen for her statistics related counsel. I would like to particularly acknowledge my gratitude to the members of my doctoral ccmnittee: Dr. Vandel C. Johnson (chairman), Dr. Keith P. Anderson, Dr. Max R. Raines, and Dr. John H. Suehr. ii TABLE OF CONTENTS Page DEDICATION................................................. i ACKNOWLEDGMENTS........................................... ii TABLE OF C O N T E N T S ........................................ iii LIST OF TABLES.............................................. v Chapter I. STATEMENT OF THE PROBLEM............................... 1 N e e d ...................................... 1 Purpose .......................................... 3 Hypotheses ........................................ 3 Theory......... 4 Overview............................................ 5 II. REVIEW OF LITERATURE................................... 6 Introduction ........................ 6 Representative W orks................................. 6 Specific Studies.................................... 16 S u m m a r y ........................................... IS III. DESIGN OF THE S T U D Y .................................. 19 Introduction....................................... 19 Influencing Factors (independent variables).......... 19 Calculation M e t h o d s ................................ 35 Operational Measures................................ 41 Design............................................. 44 Testable Ifypotheses................................ 45 Analysis........................................... 46 S u m n a r y ........................................... 46 IV. ANALYSIS OF R E S U L T S .................................. 48 Introduction....................................... 48 Null Hypothesis.................................... 48 Hypothesis l a ......................................86 Hypothesis l h ............................. 86 Hypothesis 1 c ..................................... 92 iii TABLE OF CONTENTS (cont'd.) Page V. SUMMARY- AND DISCUSSION................................... 95 S u o m a r y ...............................................95 Conclusions........................................... 97 Discussion.............................................98 Calculation M e t h o d s ................................... 98 Influencing F a c t o r s ................................... 99 Implications for Further R e s e a r c h ...................... 99 Hypotheses for Experimental S t u d y ..................... 101 Approach to the F Uture................................ 101 ENDNOTES................................................... 104 BIBLIOGRAPHY- ................................................110 iv LIST OF TABLES Table Page 3.1 Consumer Price Index (all items).................... 20 3.2 Employment Data (Clinton-Eaton-Ingham-Ionia)......... 21 3.3 United States Gross National Product (1976 Dollars) 3.4 Lansing Ccmnunity Cbllege Tuition Rate D a t a ......... 23 3.5 Lansing Ccmnunity Cbllege Fall Term Enrollment Data 3.6 Michigan Selected Public Oomnunity Cbllege Fall Enrollment D a t a .................................. 25 3.7 Michigan Higher Education Fall Term Enrollment Data 3.8 Michigan State University Fall Enrollment D a t a ....... 28 . . 22 . . . . 24 27 3.9' Lansing Cbmnunity Cbllege General Student Data (State Count D a t a ) .................................29 3.10 Lansing Cbmnunity College Fall Term Student Age Data . . 31 3.11 Lansing Ccmnunity Cbllege Data of Students by High S c h o o l ................................. 32 3.12 Lansing Ccmnunity Cbllege Divisional Credit Generation Data (percent of Total Cbllege Credits) . . . . . . . . 33 3.13 Tri-Cbunty Census Data By Age (Clinton-Eaton-Ingham) . . 36 4.1 Fulltime Equated Student Enrollment Calculation Method: Simple A v e r a g e ........................... 49 4.2 Fulltime Equated Student Enrollment Calculation Method: Moving Averages........................... 51 4.3 Fulltime Equated Student Enrollment Calculation Method: Double Moving Average..................... 52 4.4 Rilltime Equated Student Enrollment Calculation Method: Exponential Smoothing ...................... 54 Fulltime Equated Student Enrollment (1972 through 1979) Calculation Method: Double Exponential Smoothing (a=.l) 55 4.5 4.6 Applying Tri-County Census Data (18-20 Year Olds) Calculation Method: Ratio M e t h o d ................ . 57 4.7 Applying Tri-Cbunty Census Data (21-25 Year Olds) Calculation Method: Ratio M e t h o d ................. 58 4.8 Applying 'R’i-County Census Data (26-30 Year Olds) Calculation Method: Ratio M e t h o d ................. 59 v LIST OF TABLES (cont'd.) Tattle 4.9 Page Applying Tri-County Census Data (18-30 Year Olds) Calculation Method: Ratio Method.................... 60 4.10 Applying Tri-County Total Census Data Calculation Method: Ratio Method .................... 61 4.11 Rilltime Equated Student Enrollment Calculation Method: Simple Correlation and Regression Analysis (formula: Y = a + h x ) ........................... 63 Rilltime Equated Student Enrollment Calculation Method: Multiple Correlation and Regression Analysis (formula: Y » a + + bgXp . . . bnxn) ......... 65 Forecasts of Innsing Cbmnuntiy College Rilltime Equated Student Enrollment....................... 68 4.14 Results of the F Statistic Test* On Selected Independent Variables In the Simple Correlation and Regression Analysis........................... 72 4.12 4.13 4.15 4.16 4.17 4.18 Results of the F Statistic Test* On Selected Runs In the Multiple Correlation and Regression Analysis . . 74 Independent Variables Ranked By Resulting Coefficient of Determination from the Simple Correlation and Regression Analysis.............................. 77 Independent Variable Ranked by Resulting Coefficient from Simple Correlation and Regression Analysis .. '. . 80 Simple Correlation and Regression Analysis Values of the Correlation Coefficient Required for 95% Level of Significance When Hb’ P = 0 Items (x) Versus Lansing Conmunity Cbllege FUlltime Equated Enrollment (y) . . . 83 4.ISf "Multiple Correlation and Regression Analysis Values of the Correlation Cbefficent Required for 95% Level of Significance When Ho: P = 0 ............... 85 4.20 A Ranking of the Lansing Ccnmuntiy Cbllege Rilltime Equated Student Enrollment Forecast By Calculation Method Based on the Percentage of Error ....... . . 4.21 A Cbmparison of the Independent Variables' Correlation Coefficient Versus Hie 1979 Lansing Cbmnunity College Rilltime Equated Student Enrollment Forecasting Accuracy (Percentage of E r r o r ) ............... 90 vi 87 LIETT OF TABLES (cont’d.) Table 4.22 4.23 Page Forecasting 1980 Fulltime Equated Enrollment Applying Tri-County Census Data (18-20 Year Olds) Calculation Method: Ratio Me t h o d ................... 93 A Stannary of the Results of the Tested Hypotheses in ................................ this Study 94 vii Chapter I Statement of the Problem Need Cbllege administrators need information to effectively plan. Student enrollment which translates to fiscal income is one of the nest fundamental elements in planning, and therefore the need for insight regarding future student enrollment is of paramount impor­ tance. The inpact of unforseen increases or decreases in student enrollment at a comnunity college can create great institution-wide problems. Normally, the problems of unexpected increases in student enrollment, which require inmediate administrative response, are generally more palatable inasmuch as additional revenue is usually generated; however, this revenue is not always conmensurate with the required encumberance of dollars created by increased student enroll­ ment. The problems which acconpany unforeseen decreases in student enrollment are far more distasteful, for this situation nearly always results in fewer dollars than projected in the budget. Com­ pounding the problem, a decrease in student enrollment often creates a very vicious spiral: decreased student enrollment is followed by a reduction in fiscal support; reduced fiscal support forces cut­ backs in personnel and programs; fewer programs often result in even fewer students and in turn yet fewer dollars, et cetera. The ability to accurately predict changes in student enrollment can permit administrative decision-making that will minimize the Impact of decreased student enrollment and maximize the advantages 2 of Increased student enrollment. Given the many ailments within the present economic climate, coupled with the resulting uncertainties, it is a risky and ccnplex undertaking to forecast student enrollment at a specific Institution. The risk and conplexity of forecasting a conmunity college's student enrollment is great but the need for the positive adaptibility the knowledge of an accurate forecast can pro­ duce is equally great. The Lansing State Journal in its September 2, 1979, edition quoted the president of Lansing Cbmnunity College: "Trying to pre­ dict Lansing Cbmnunity College's fulltime enrollment for the upcoming schoolyear is like guessing the number of waves that will hit the beach,"1 This statement emphasizes the conplexity of developing a student enrollment forecasting model at Lansing Ccmnunity Cbllege. The development of a reliable student enrollment forecasting model for Lansing Cbmnunity Cbllege will provide an instrument that can produce valuable information from which administrative level deci­ sions can be made without guessing. If the application of the product and by-products of this re­ search was restricted to the provincial needs of one institution, its value would be extremely limited. It is proposed that the commonality existing between a great many ccmnunity colleges through­ out the United States and Lansing Cbmnunity College will permit a more limitless sharing of the product and by-products of this re­ search. The primary contribution of this research will directly benefit Lansing Community Cbllege, and Lansing Cbmnunity Cbllege will thus profit from the potential adaptability produced by the informa­ tion in meeting its needs. 3 Purpose The primary purpose of this study is to develop an applicable model that produces an accurate student enrollment forecast for Lansing Cbmnunity Cbllege. As a by-product (secondary purpose) of the development of "the model" noteworthy facts relative to the influencing factors and the demographics of student enrollment at Lansing Cbmnunity Cbllege are expected to be discovered. It is fur­ ther expected that these noteworthy facts might also be applicable to comparable comnunity colleges. In addition it is anticipated that the fulfillment of the primary purpose (the model) will enable other institutions to apply that model to the forecasting of their student enrollment (s ). hypothesis Numerous methods could be applied to the forecasting of student enrollment, each having inherent strengths and weaknesses. It is expected that one and only one of the selected calculation methods will most accurately forecast student enrollment at Lansing Cbmnunity Cbllege. In addition to the calculation method, the identification of major influencing factors, such as, economics, enrollment, and demo­ graphics may potentially contribute to accurate student enrollment forecasting. Further it is expected from the analysis of the major influencing factors and the applied and restating models that: H^a : The calculation methods which employ the mathematical functions of both simple and multiple regression will produce more accurate forecasts than the other applied, in this study, calcula­ tion methods. 4 ILj^: The influencing factors that produce the highest simple correlation coefficient scores (measured against Lansing Ooramnity College's fulltime equated enrollment) will provide the most descriminating student enrollment forecasting data when applied to multiple regression analysis. Hlc: The model that most accurately retrospectively "forecast" the 1979 Lansing Cbmnunity Cbllege fulltime equated student enroll­ ment will forecast the 1980 fulltime equated student enrollment with­ in an equal percentage of error. Theory There is no existing consensus on the most reliable student enrollment influencing factor(s) nor the most applicable calculation method to accurately forecast student enrollment at a given institu­ tion. The available calculation methods and the numerous potential influencing factors together provide researchers the challenge of exercising the scientific method of trial and error. It was stated by Granger in his inaugural address (1977) at the University of Nottingham that, "The current trend in forecasting is towards model 2 building." A model for the purpose of this research shall be de­ fined as a technique (calculation method/influencing factors) which when imitated can produce a fulltime equated student enrollment fore­ cast for Lansing Cbmnunity College. It is ray belief that a reliable model can be developed through a system of trial and error. This belief is based on the expectation I theorize that a model developed through trial and error, which most accurately forecasted the 1979 fulltime equated student enrollment (a known quantity) at Lansing Cbmnunity Cbllege will be an 5 effective model In forecasting 1980 and future fulltime equated student enrollments at Lansing Conmunity College. Overview Though the primary purpose of this research is the development of a useful student enrollment forecasting model, it should be noted that numerous other related purposes might be served as well. Potential purposes related to the primary purpose are demographic descriptions, manpower studies, planning data, resource needs, latent demands, and, of course, policy recomnendations. This overview of the setting within which this study exist should enhance one's appre­ ciation of the potential value of this study. In order to maximize the acceptance of the research and the sub­ sequent conclusions the design of this research is detailed in Chap­ ter III. The design is based to a large extent on the experiences and results of other researchers whose work is reviewed at length in Chapter II. Chapter II REVIEW CF LITERATURE Introduction Although many college administrators are interested in informa­ tion related to student enrollment trends, a ccmnensurate amount of contemporary literature on the subject of forecasting student enroll­ ment has not been written. literature is inferior. This is not to imply that the available It should be noted that many heretofore un­ reported studies may become public as the pressure of inflation de­ mands greater refinement in institutional planning and subsequent de­ sire for more accurate student enrollment forecast models emerge. In the absence of a voluminous bibliography of related literature my review will reflect the most representative literature available. There are four works which warrant special attention inasnuch as each specifically addresses the topic of forecasting student en­ rollment. They are: Statewide Planning in Higher Education (Chap­ ter VII - "Meeting Area Educational Program and Capacity Needs")1 ; 2 Methodology of Enrollment Projections for Colleges and Universities ; 3 Projecting College and University Enrollments ; and Higher Education 4 Etarollment Forecasting . Hollowing a review of the above cited works will be a detailed review of selected representative student enroll­ ment forecast studies. D. Kent Halstead who authored Statewide Planning in Higher Edu­ cation included a chapter (VII) entitled "Meeting Area Educational Program and Capacity Needs," in which he specifically addresses pro­ blems related to student enrollment forecasting. Halstead maintains that, ". . . the fundamental purpose of higher education planning at the state level is to provide information and reconmendations for the development of a total statewide system of postsecondary education 5 that residents expect and society requires." In fulfilling the fundamental purpose stated above Halstead suggests that studies must be conducted and those studies should in­ volve the following three objectives: . . . to provide within the State an enrollment capacity for anticipated student attendance in each area of recog­ nized program need, to encourage institutional develop­ ment and growth consistent with assigned differential functions, and to expand existing facilities and initiate new programs in such a way as to enhance geographical accessibility and effective program clustering.6 No statewide planning in higher education can be complete with­ out the application of projection methodology. Halstead notes that, "Even with the most exacting techniques, however,predicting college enrollments is a hazardous undertaking because of the number, variety, 7 and uncertainty of the variables involved." The variables Halstead is concerned about and which he devotes considerable space and data compilation to include: . . . state population growth and economic development; high school retention rates and geographic distribution of graduates; future anticipated admission policies, curriculums, . . . overall college entrance rates, pat­ terns of student residence, attendance rates at indivi­ dual institutions and the ability of institutions to accomodate everyone who would enroll. . . .8 We should be cautioned that the above listed variables are applicable to statewide planning but may not apply carte blanche to the fore­ casting of student enrollment at individual institutions. 8 Methodology of Enrollment Projections for Colleges and Universi­ ties by L.V. Lins, . . is an attempt to assist the many individu­ als throughout the country who have need for making institutional and/or statewide estimates of future college enrollments. Lins notes that in forecasting student enrollment, "All factors related to enrollment of a particular institution must be considered. Factors submitted by Lins to consider in the development of a student enrollment forecast model include: admission policy, housing, in­ structional facilities, staff, programs, high school graduates, post­ baccalaureate students, related economic structure, international situations, birth rates, veteran enrollments, educational benefits and/or loan and scholarship programs, migration, mortality rates, and Selective Service drafts and deferments. The above list suggest the complexity and riskiness inherent in the forecasting of student enrollment. Lins sums up this section, "Good forecasts will call for logically integrated, analytical techniques."^ The remaining contents of his publication are divided into four chapters: (1) "Enrollment Projection Techniques", (2) "Short-Range Estimates of Enrollment", (3) "Long-Range Projections of Enrollment", and (4) "Data Presentation". A review of the chapter on enrollment projection techniques will be omitted in favor of authors who treat the topic in a more statis­ tical form. In Lins' discussion of short-range estimates of enroll­ ment he suggest that in institutions, " . . . with large evening and/ or part-time programs, total enrollment is a quite unsatisfactory ba­ sis on which to estimate. . . . a better index. . . may be faculty­ 12 load data and number of credits. . . ." Inasmuch as Lansing Ccm- rnunity College possesses a disproportionate percentage of parttime students/evening programs this suggestion is noteworthy. Lins in this writing indicated that he represents an institution without a limited enrollment policy. out a limited enrollment policy. Lansing Ccmnunity is also with­ Lins, based on forecasting results at his institution, ". . .has found that a combined ratio, cohortsurvival method yields the best short-range estimates of enrollment." Under the heading of long range projections of enrollment Lins' maintains that, "Enrollment projections can be made as far as 17 years into the future without estimating births." 14 This of course is based on the fact that nearly all the students who will attend school within seventeen years are born and can be relatively accur­ ately counted. Projecting College and University Enrollments: Analyzing the Past and Focusing the Future by Wayne L. Mangel son, Donald M. Norris, Nick L. Poulton, and John A. Seeley, is a subjective approach to the topic of student enrollment forecasting and lacks documentation. In spite of this weakness the work merits review in that it presents a unique perspective. The text is presented in three parts: (1) Major Findings, (2) Review and Analysis of Past Projections, and (3) Means of Improving Enrollment Projections. The major findings submitted by Mangelson resulted from an analysis of several enrollment studies. 1. The major findings included: The underlying assumptions in existing enrollment studies have been inadequate for projecting college enrollments. a. The usage of only the 18-21 year old age cohort as the basis for projection is misleading. 10 2. 3. 4. 5. Broader cohort populations must be utilized in order to reflect the extension of the period of education and the participation of older learners. b. Although it is necessary to utilize birth rate assumptions in predicting the size of traditional college cohort populations beyond 1990, it must be recognized that birth rate trends are currently in a state of flux. c. Most projection studies assume implicitly that trends in underlying factors influencing atten­ dance patterns will continue along established lines. Many of such assumptions seem unlikely. d. Projection studies have assumed that the insti­ tutional composition of higher education will not change. Hie emergence of the notion of postsecon­ dary education suggests that different institution­ al forms and enrollment patterns should be consi­ dered for the future. Existing projection studies are not easily compared. a. Definitions of terms vary among the individual studies. b. The actual factors projected as well as their levels of disaggregation vary from study to study. c. Overly aggregated data may mask significant trends in certain enrollment categories. The use of extrapolation assumes that the future will reflect the past along certain important dimensions. To be confident of the results of extrapolation, the factors selected for extrapolation must be appropriate and trend relationships must be understood. a. The enrollment projections of the early sixities, which were based on enrollment trends of the fifties, underestimated consistently the actual enrollments of the early sixties. b. The enrollment projections of the early seventies, however, based on the enrollment trends of the sixties, overestimated consistently the actual enrollment figures of the past several years. c. Existing projections fall short of the mark by extrapolating enrollments, rather than by the influencing factors that actually determine enrollments. By extrapolating enrollments rather than the under­ lying factors actually influencing enrollments, existing projections fail to incorporate mechanisms for explaining why enrollments are changing. There­ fore, existing studies are unable to predict what changes in enrollment trends will occur. It is reccrrmended that new projection techniques be developed, grounded on an understanding of the relationships between enrollments and underlying social values (e.g., credentialian), social 11 6. 7. 8. conditions (e.g., demographic factors), diffusion of conmmications technology (e.g., cable television), public policy (e.g., financial aid), and educational systems factors (e.g., new institutions). a. The incorporation of underlying factors into enrollment projections will improve the quality of actual enrollment projections. b. Also, the educator can utilize both the improved projection and the predictions of key factors to develop educational and institutional policy. Although a number of the influencing factors are not measured currently, they are regularly monitorable. The future states of the underlying factors may be predicted utilizing a combination of the following three techniques: extrapolation of reasonable trends, alteration of trends based on changes in relevant moderating factors, and the recognition of floors and ceilings that may operate to restrict variations in trends to within certain limits. Considering the mechanisms for monitoring and pre­ dicting the factors influencing postsecondary educa­ tional enrollments, it is recotrmended that a framework be developed for describing the relationships among the key underlying factors and potential learners, educational aspirants, and actual enrollments, appro­ priately disaggregated.15 In examining the intended purpose of an enrollment projection study Mangel son states that the purpose, ". . . determines in most cases the definition of quantities used, many of the assumptions made, the types of output categories projected, and to some degree the methodological approach used." 16 The purpose(s) of a study according to Mangelson serve to create conceptual bases which he, ". . . groups under three headings: limits to comparison, methodo- 17 logical limitations, and the limitation of underlying assumptions." Issues discussed under the heading of limits to comparison included: definition of terms vary among individual studies, actual factors projected, as well as their levels of disaggregation, vary from study to study, and the masking of significant trends through 12 over aggregation. Methodological limitations of course vary from method to method. The following three statements regarding methodo­ logical limitations are worthy of note: (1) The use of extrapolation assumes that the future will reflect the past and often ignores the fact the linear growth along traditional lines is ques­ tional given the uncertainties of current enroll­ ment trends.18 (2) The selection of the factors to be extrapolated determines largely the utility of the projection.19 (3) Projection studies that suggest policy alternatives do not develop fully the linkage between the en­ rollment figures and those policy alternatives.20 Given that each study is built on underlying assumptions, it should be noted that those assumptions create limitations. Gener­ ally assumptions are based on extrapolations from available data. These assumptions do not permit an examination of the underlying factors actually influencing enrollments. Mangelson maintains that, ". . . until studies incorporate mechanisms for explaining why enrollments are changing we will be unable to predict that changes in enrollment trends will occur." 21 In the final chapter Mangelson outlines factors which he feels influence postsecondary educational enrollments. They are classi­ fied as social values, social conditions, diffusion of commnications technology, public policy, and educational systems factors. Under the heading of social values he suggest that values placed on knowledge, self-improvement, and formal education combined to create an attitude. Attitude along with other factors affect an individual's behavior and postsecondary enrollment. Social conditions are described as those conditions which are objectively measurable, such as demographics, economics, and leisure 13 time. Hie advantage of this kind of data is the statistical manage­ ability it possesses. Hie diffussion of technology into educational endeavors ad­ dressed the inpact of such innovations as canputer-assissted instruc­ tion, aduio-visual cassettes, and a host of similar technologies. Mangelson states that, "The effects of such technologies must be assessed with considerable prudence, the distinction being drawn clearly between window dressing and programs of substantive impor92 tance.” Public policy (the level of public financial support) and the educational system (available opportunities) are the final two con­ cerns expressed by Mangelson. He concludes, "By expanding the basis for the projection of postsecondary education's enrollments, the potential exists for expanding the uses of such projections as ,.23 well.” Hie final work is the Paul Wing publication, Higier Education Forecasting, which was released for limited distribution by the Board of Directors of the National Center for Higher Education Management Systems (NCHEMS) at the Western Interstate Oomnission for Higher Education (WICHE) in Boulder, Colorado. The author proposes in his preface that this publication ”. . . provides a comprehensive treatment of the subject (enrollment forecasting) which will be of value to enrollment forecasting practitioners at higher education institutions and national agencies, as well as 24 those at state agencies." Though a good deal of the topics with­ in this writing are technical, much of the discussion is nontechnical and thus provides a fine source for the establishment of a general 14 understanding of the problems involved in forecasting higher education student enrollment. Wing addresses the topic of student enrollment forecasting under the following headings: general consideration, alternative enrollment techniques, constructing an enrollment forecasting pro­ cedure, and a summary with conclusions. The principal concern of forecasting higher education student enrollments according to Wing is ". . . the accurate prediction of future enrollments in specific higher education programs and/or 25 institutions.” In an attempt to identify sane of the subtleties and difficulties inherent in student enrollment forecasting, he introduced some general considerations such as federal financing plans, student attitudes, and judicial decisions which influence student enrollment. The uses of student enrollment forecasts can be classified under one of two general headings according to Wing. Those two classifications are: (1) Short and medium-range forecasts which can be used as a partial basis for a variety of planning and management activities (for example - budgeting) (2) long-term forecasts which provide a means for altering or reinforcing general expectations for the future, which if properly followed-up enable policy makers to adjust their priorities and frames of reference gradually, over a period of years.26 Additional uses of student enrollment forecasts suggested by Wing included: (1) Capital planning and budgeting. Contrasting projected enrollments with the current and projected capacity of physical facilities can provide a basis for capital investment decisions. 15 (2) Operating budgets for institutions or programs. Projected enrollments can serve as a basis for short- and medium-range budgetary estimates. (3) Support for other management systems. Enrollment projections can be applied in analysis of such things as intersegnental student flows (for example, junior college transfers), unit costs of instruction, student access to higher education, inpact of in­ structional programs on labor markets, different strategies for allocating resources, and funding requirements.27 Wing concluded that forecasting techniques and procedures have been under development for several decades by analysts and research­ ers in a number of fields and that the application of the various forecasting techniques to the specific problems of higher education enrollment forecasting have lagged far behind the technical develop­ ments. Inasmuch as a presentation of selected calculation methods (extracted from more technical treatise) are included in Chapter III in detail I will review here only Wing's suggested classes of alternative enrollment forecasting calculation methods. Wing's four broad classes of enrollment forecasting calculation methods are: (1) (2) (3) (4) Curve Fitting: Techniques and models that produce forecasts based primarily on historical enrollment data# Causal Models: Tecniques and models that produce forecasts based on historical relationships between enrollments and other parameters) or variable(s) (for example, high school graudates). Intention Surveys: Techniques based on surveys of the intentions of potential students, producing forecasts or other techniques. Subjective Judgment: Those elements and aspects of forecasting procedures based on the judgment of the forecaster rather than some quantitative technique or procedure.28 In a succeeding chapter Wing concludes that, "In practice, causal models have proven to be better than curve-fitting models in most forecasting situations, particularly when enrollment 29 patterns are changing. Guidelines for constructing a forecasting procedure are sub­ mitted by Wing in five steps: (1) (2) (3) (4) (5) Partition the population of students. . . Identify the most appropriate forecasting techniques. . . perform the calculations. . . . . . conpute the total enrollment figure by suirming the estimates for each of the individual categories. . . . validation of the results.30 As a cautionary submission Wing notes that there is a tendency for administrators to take forecasting too seriously in seme situa­ tions. He suggest that a means of making more evident the risk of over reliance on a specific student enrollment forecasts ". . . is to provide explicit estimates of fmaximum likely' enrolLients along 31 with the 'preferred* estimates." The most significant contribu­ tion of this publication is its practical approach to the goal of the development of a functional student enrollment forecasting model. Review of Specific Studies Besides the review presented above, a nunrber of specific enrollment forecasting studies are important, highly relevant to this study, and merit mention. The importance and relevance of these studies rest on the introduction of selected student enroll­ ment influencing factors and the resulting accuracy of the applica­ tion of previously conpleted studies related to other institutions that have forecasted enrollment employing factors such as: past 32 33 34 35 enrollments Cbffman , Cbmnittee on Enrollment , Lins , Meier , 17 36 37 38 Nswton , and Ihtham ; high school graduates Banks , Educational 39 40 41 42 43 Research , Springer , and Thonpson ; work force Gold , Johnston , 44 45 Martinko , and StaLth ; participation of high school graduates in 46 47 48 higher education Degan and Hassell ; population pool Prestiage 49 50 51 and U.S. Bureau of Census ; cohort survival Oliver and Zimner ; 52 53 54 migration Petersen and Purves ; economic indicators Gell ; land 50 57 58 use Tatham ; square footage Duncan ; new programs New York State ; and S.A.T. scores Jewett 59 An equally Important ingredient in the development of an effi­ cient student enrollment forecast model is the selection of the '’most applicable" calculation method(s). Examples of methods and 60 the resulting degree(s) of accuracy include: New York State re­ ported a range of 0.4 to 3.5 percent error using ratio methods and 61 student surveys to predict statewide college enrollment; Evans utilized cohort survival and subjective .judgement to achieve accuracy within 1 percent in predicting freshmen enrollment in the California 62 state college system; Zimner reported an error range of -6.12% to 6.88% in predicting total enrollment in the Minnesota college system applying cohort survival, multiple correlation and regression. Markov transition model, polynomial modelt and ratio methods; and 63 finally a one year department forecast, Qrwig yielded a 1-6% error range using cohort survival, moving averages, the Markov transition model, and the single averages method. There are numerous calcula­ tion methods available and careful review of the literature must be made to determine which method is most applicable to the fulfillment of the purpose of a particular model. This review of specific 18 studies provided information that significantly contributed to the selection of both the student enrollment influencing factors and calculation methods applied in this study. Stannary As can be seen from the literature, although research in stu­ dent enrollment forecasting is sketchy, there is every indication that the calculation methods known and the potentially applicable student enrollment influencing factors might well be sufficient to produce accurate student enrollment forecasts. Quite likely, further research will generate more specific information regarding the calculation methods and influencing factors that facilitate accurate student enrollment forecasting. Chapter III Design of the Study Introduction This chapter contains a graphic presentation (tables 3.1 - 3.13) of student enrollment influencing factors (independent variables), a description of selected calculation methods, the operational measures to be applied in this study, the design of the study, its testable hypotheses, a description of the analysis to be used, and finally a summary. Influencing Factors (independent variables) Prior to detailing the design of this research the items to be considered as potential influencing factors of student enrollment at Lansing Comnunity College are presented. The factors will be intro­ duced under the following headings: 1. Economic (Tables 3.1 - 3.4) 3.1 Consumer Price Index (all items) 3.2 Enployment Data (Clinton-Eaton-Ingham-Ionia) 3.3 United States Gross National Product (1976 Dollars) 3.4 Lansing Cbmnunity College Tuition Rate Data 2. Enrollment (Tables 3.5 - 3.8) 3.5 Lansing Comnunity College Fall Term Enrollment Data 3.6 Michigan Selected Public Comnunity College Fall Enrollment Data 3.7 Michigan Higher Education Fall Term Enrollment Data 3.8 Michigan State University Fall Enrollment Data 3. Lansing Comnunity College Demographics (Tables 3.9 - 3.12) 3.9 Lansing Comnunity College General Student Data (State Count Data) 3.10 Lansing Comnunity College Ih.ll Term Student Age Data 3.11 Lansing Comnunity College Data of Students by High School 3.12 Lansing Cbmmnity College Divisional Credit Generation Data (Percent of Tbtal College Credits) 19 20 Table 3.1 Consumer Price Index Call items) Index (minus one year) Index (minus two years) Year Index 1957 84.3 81.4 80.2 1958 86.6 84.3 81.4 1959 87.3 86.6 84.3 1960 88.7 87.3 86.6 1961 89.6 88.7 87.3 1962 90.6 89.6 88.7 1963 91.7 90.6 89.6 1964 92.9 91.7 90.6 1965 94.5 92.9 91.7 1966 97.2 94.5 92.9 1967 100.0 97.2 94.5 1968 104.2 100.0 97.2 1969. 109.8 104.2 100.0 1970 116.3 109.8 104.2 1971 121.3 116.3 109.8 1972 125.3 121.3 116.3 1973 133.1 125.3 121.3 1974 147.7 133.1 125.3 1975 161.2 147.7 133.1 1976 17Q.5 161.2 147.7 1977 181.5 170.5 161.2 1978 195.3 181.5 170.5 1979 219.4 195.3 181.5 219.4 195.3 1980 Source: — Economic Report of the President, 1979 (Washington: G.P.O. 1979), Table B-42T United States Department of labor Bureau of Labor Statistics, Washington 25, D.C. 21 Table 3.2 Employment Data (Clinton-Eaton- Ingham-Ionia) Year Civilian Labor Force Unemployment Rate Number of Unemployed 1970 177,600 6.5 11,500 1971 183,500 6.4 11,800 1972 190,500 6.2 11,800 1973 194,100 5.0 9,7-00 1974 197,300 7.7 15,200 1975 200,300 11.9 23,900 1976 208,100 8.6 18,000 1977 221,500 7.7 17,000 1978 227,500 6.3 14,400 1979 235,000 6.7 15,700 Soar* Michigan Employment Security Cotnnission, Lansing, Michigan 22 Table 3.3 United States Gross National Product (1976 Dollars) Year G.N.P. Year G.N.P. 1957 442.8 1969 935.5 1958 448.9 1970 982.4 1959 486.5 1971 1,063.4 1960 506.0 1972 1,171.1 1961 523.3 1973 1,306.6 1962 563.8 1974 1,413.2 1963 594.7 1975 1,516.3 1964 635.7 1976 1,691.6 1965 688.1 1977 1,887.4 1966 753.0 1978 2,128.3 1967 796.3 1979 2,327.1 1968 Source: 868.5 Economic Report of the President Washington: G.P.O., 1979 23 Table 3.4 Iansing Cbnraunity Cbllege Tuition Bate Data Year Resident Non-Resident Out-of-State 1957 3.11 4.33 4.33 1958 3.11 4.33 4.33 1959. 3.11 4.33 4.33 I960 3.11 4.33 4.33 1961 3.11 4.33 4.33 1962 3.50 5.00 5.00 1963 3.50 5.00 5.00 1964 4.12 5.63 5.63 1965 4.12 5.63 5.63 1966 5.00 7.00 7.00 1967 6.00 8.50 8.50 1968 6.20 8.80 8.80 1969 6.80 9.60 9.60 1970 7.00 11.00 31.00 1971 7.00 13.00 31.00 1972 7.00 13.00 31.00 1973 7.00 13.00 31.00 1974 7.00 13.00 22.50 1975 8.50 14.50 24.00 1976 8.50 14.50 24.00 1977 8.50 14.50 24.00 1978 11.00 11.00 17.00 27.00 17.00 27.00 1979. Sour Lansing Cbnntinity Cbllege Office of the Registrar 24 Table 3.5 Lansing Coranunity College Fb.ll Term Enrollment Data Year Rilltime Equated Headcount Rilltime Parttime 1957 166 425 62 363 1958 310 678 205 473 1959 401 857 265 592 1960 561 1297 334 963 1961 774 1604 549 1055 1962 1037 2124 720 1404 1963 1136 2320 719 1601 1964 1457 3021 1029 1992 1965 2114 3842 1526 2316 1966 2748 4166 1975 2191 1967 2880 4946 2038 2908 1968 3481 6047 2438 3609 1969 4019 7130 2754 4376 1970 4244 7230 2970 4260 1971 4435 7951 2983 4968 1972 4654 8773 2988 5785 1973 5334 10640 3208 7432 1974 6699 13280 3998 9282 1975 8357 15901 5476 10425 1976 8399 17102 5181 11921 1977 8750 19042 4815 14227 1978 8048 18313 4420 13893 1979. 9019 21000 4718 16282 Lansing Cbmnunity College Office of the Registrar Thble 3.6 Michigan Selected Public Oonminity Cbllege Pali Enrollment Data* Henry Ford Macanb Mott 3543 2880 4406 3877 2469 1772 2272 3836 5069 5929 4264 2754 2273 1967 2872 3889 5138 6324 4793 4080 2645 1968 3506 4132 5229 7414 4986 6801 3077 1969 3987 4040 5991 8930 4370 8870 3395 1970 4438 4331 5854 10007 4757 9807 3649 1971 4606 4283 5269 10196 5041 9514 3705 1972 4638 4011 5614 9518 5199 8717 3725 1973 4678 4161 6159 10103 5182 8913 3873 1974 5509 4881 7064 11561 6489 9871 4681 1975 6123 5751 7530 13714 7774 11383 5085 1976 5929 5367 7548 12594 5724 10572 4729 1977 5842 5469 8048 12288 4577 10495 4671 1978 6074 5694 7906 12434 5513 10555 4929 1979 5516 7203 11153 12167 5090 10661 3794 Year Delta 1965 2122 1966 G.R.J.C. Oakland Table 3.6 (cont'd.) Delta - Delta Cbllege, University Center, Michigan G.R.J.C. - Grand Rapids Junior College, Grand Rapids, Michigan Henry Pbrd - Hairy Pbrd Cfcnmmity College, Dearborn, Michigan Macomb - MacariB Cbanty Caunanity Cbllege, Warren, Michigan Mott - Mott Ccraninity Cbllege, Flint, Michigan Chkland - Oakland Oannanity College, Union lake, Michigan Schoolcraft - Schoolcraft Cennnnity College, Livonia, Michigan Source: Senate Fiscal Agency Office Lansing, Michigan 'Historical Enrollment Sunmary" (unpublished) ♦The enrollment data is fulltime equated student enrollment Table 3.7 Michigan Higher Education Fall Term Enrollment Data* Year Public Four Year Cblieges Public Community Colleges Independent Colleges Total Higher Education Enrollment 1966 174,010 45,380 38,065 257,455 1967 185,197 51,972 42,609 279,778 1968 198,478 61,852 41,923 302,253 1969 208,224 70,422 42,727 321,373 1970 217,547 77,343 42,845 337,744 1971 220,341 79,507 42,599 342,447 1972 219,235 79,849 43,198 342,282 1973 222,398 82,848 44,008 349,245 1974 230,885 98,853 48,364 378,102 1975 242,061 115,861 52,543 410.465 1976 236,942 109,750 50,773 397.465 1977 236,618 108,365 51,014 395,997 1978 236,035 106,649 50,647 393,331 1979 196,751 111,564 53,177 361,492 ^qurce: Senate Fiscal Agency Office, Lansing, Michigan "Historical Enrollment Sunmary" (unpublished) ♦The enrollment data is fulltime equated student enrollment. 28 Table 3.8 Michigan State University Flail Enrollment Data Year Headcount 1964 34,487 1965 38,802 1966 41,474 1967 42,053 1968 44,421 1969 44,173 1970 43,569 1971 44,887 1972 44,909 1973 45,195 1974 47,367 1975 48,670 1976 46,921 1977 47,034 1978 46,567 1979 47,355 SOUT' Senate Fiscal Agency Office Lansing, Michigan "Historical Enrollment Sunmary" (unpublished) Table 3.9 Lansing Ocramnity Cbllege General Student Data (State Cbunt Data) Year Total Students Eresitimen (-40 credits) Sophanores (4CH- credits) 1969 7181 5873 1308 4893 1970 7396 5645 1751 1971 7951 6023 1972 8773 1973 Married Men rried fcmen 2288 2002 747 4868 2528 1891 837 1928 4988 2963 1978 1038 6679 2094 5207 3566 2280 1374 10,640 8208 2432 5971 4669 2765 1836 1974 13,280 10,380 2S00 7319 5961 3380 2307 1975 15,901 12,120 3781 8385 7084 3687 2774 1976 17,102 12,773 4329 8709 8393 3725 3356 1977 19,042 14,154 4888 9267 9775 3868 3977 1978 18,313 13,582 4731 8558 9755 3658 4384 1979 18,826 13,857 4969 8600 10,226 2835 3836 Sour< lapsing Cqenjnnity College Office Qf tKe Dean of Student Personnel Services Men Women T&ble 3.9 (cont'd.) lansing Gbommity College General Student Data (State Count Data) New Students ReActaissions Returning Transfers Resident Out of District Out of State reig 2943 674 3564 374 5230 1871 50 30 2811 1049 3536 464 5603 1738 43 12 3145 1169 3637 459 6253 1676 18 4 3568 1528 3677 581 6981 1764 28 0 4393 4433 1814 542 8471 2128 38 3 5221 5720 2339 375 10,508 2699 30 43 6866 4392 4643 632 12,466 3305 46 84 5653 8654 2795 883 13,073 3820 36 173 6317 3302 9423 860 14,486 4206 95 255 6278 3638 8924 597 13,496 4505 57 255 5417 4272 9173 772 14,354 4169 53 Lansing Oonjnunity College Office of the Dean of Student Personnel Services Table 3.10 lansing Cbnmnnity Cbllege Eall Term Student Age Data Percent of Total Enrollment Age 1971 1972 1973 1974 1975 1976 1977 1973 1979 -21 39.0 35.9 31.5 30.4 29.3 28.1 26.2 25.8 26.4 21-25 29.8 29.1 28.1 27.5 27.7 27.8 26.4 25.5 27.1 26-30 13.0 14.0 15.5 16.1 18.6 20.2 19.4 18.6 17.8 31-35 5.8 7.1 8.5 9.0 9.4 9.1 10.3 10.6 10.7 36-40 4.3 4.3 4.9 5.0 5.2 5.0 5.6 6.5 6.2 41-45 3.4 3.7 3.8 4.1 3.7 3.8 4.0 4.3 4.0 46-50 2.0 2.6 3.1 3.3 2.6 2.4 2.9 2.9 2.7 51-55 1.2 1.4 2.0 1.8 1.6 1.6 2.0 2.0 2.0 56-60 .4 .7 .9 1.0 .7 .7 .9 1.1 .9 61+ .3 .3 .3 .5 .5 .4 1.0 1.2 1.2 Mean Age 25.0 25.5 26.2 26.8 26,0 26.5 20.3 27.6 27.5 Median Age 21.0 23.0 22.5 23.0 24.0 24.0 25.0 25.0 25.0 Mode Age 19.0 19.0 19.0 19.0 18.0 19.0 19.0 19.0 19.0 Source; lansing Cqorannity College, Office of tfie Dean of Student Personnel Services 32 , Table 3.11 lansing Oonmunity Cbllege Data of Students by High School Year High School Graduates lansing Cbnmunity Cbllege Lansing Cbmnunity Cbllege Area District 1972 7877 4491 1973 8247 4721 1974 7839 4445 1975 8211 4510 1976 8107 4493 1977 8460 4707 1978 7947 4382 1979 8208 4405 Source: lansing Cbmnunity Cbllege Office of Admissions Table 3.12 Fall Term lansing Ccxununity College Divisional Credit Generation Data (Percent of Total College Credits) DIVISIONS Year A & S' Business L.R. S.P.S. Tech./H.C. 1970 39737 (60.4J 12840 (19.4) 72 (0.1) 691 (1.0) 12436 (18.9) 1971 39249 (57.1) 13357 (19.4) 156 (0.2) 316 (1.1) 15168 (22.0) 1972 38145 (52.8) 14939 (20.7) 207 (0.2) 932 (1.2) 17918 (24.8) 1973 38954 (46.9) 20034 (24.2) 475 (0.5) 983 (1.1) 22234 (26.8) 1974 45832 (44.1) 26588 (25.6) 1413 (1.3) 1481 (1.4) 28528 (27.4) 1975 56383 (43.5) 32694 (25.2) 2547 (1.9) 2227 (1.7) 35685 (27.5) 1976 54811 (42.1) 32910 (25.2) 2624 (2.0) 3308 (2.5) 36534 (28.0) 1977 52845 (38.9) 36963 (27,2) 2898 (2.1) 3998 (2.9) 38923 (28.7) 1978 47370 (42.1) 34375 (25.2) 2642 (2.0) 4245 (2.5) 36112 (28.0) 1979 51148 (38.9) 38987 (27.2) 3089 (2.1) 4407 (2.9) 42160 (28.7) Table 3.12 (cont'd.) A & S - Division of Liberal Arts and Science Bosiness - Division of Business L.R. - Division of Learning Resources S.P.S. - Division of Student Personnel Services Tech./H.C. - Division of Technology and Health Careers Source: lansing Cbmnunity College Office of the Registrar 35 4. Population Pool (Table 3,13) 3.13 These factors Tri-Cbunty Census Data By Age (Clinton-Eaton-Ingham) will be evaluated for application in the forecasting model whose function is the accurate forecast of Lansing Cbmnunity College's fulltime equated student enrollment. Calculation Methods All student enrollment forecasts must be calculated via a predetermined method. "As with all forecasting," states Centra, "the assumption behind most of the projections presented is that there will not be any drastic changes in the nation."'1' This assunp­ tion permits researchers the liberty to select from a body of cal­ culation methods the method which is most applicable to the fore­ casting at an individual institution or other population segment. The following calculation methods will be applied in this study to the forecasting of the 1979 lansing Oomnunity College fulltime equated enrollment: 1. 2. 3. 4. 5. 6. 7. 8. Sinple Average Moving Average Double Moving Average Exponential Smoothing Double Exponential Smoothing Ratio Method Sinple Regression and Correlation (Y - a + bx) Multiple Regression and Correlation (Y = a + bjX^ + . . . t>nxn) The method of sinple average is nothing more than the calcula­ tion of the mean (x). x = xl + x2R--------+ 0 * * The mean is defined as: Glass adds. "The value of the mean is es- pecially affected by what might be called outliers, i.e., scores shich lie far from the center of the group of scores. Whether Table 3.13 Tri-Cbunty Census Data By Age (Clinton-Eaton-Ingham) AGE TOTAL 21-25 TOTAL 26-30 FEMALE 18-30 MALE 18-30 TOTAL 18-30 Year TOTAL TOTAL 18-20 1970 378,000 34,625 40,994 27,711 51,924 51,133 103,057 1971 382,000 36,239 43,612 27,847 53,949 53,504 107,453 1972 386,000 37,853 46,230 27,984 55,975 53,256 114,231 1973 390,000 39,467 48,848 28,120 58,000 60,618 118,618 1974 394,000 41,082 51,467 28,257 60,026 62,990 123,016 1975 398,000 42,696 54,085 28,394 62,052 65,361 127,413 1976 401,800 44,310 56,703 28,530 64,253 67,733 131,986 1977 405,600 45,925 59,322 28,667 66,279 70,104 136,383 1978 409,400 47,539 61,940 28,803 68,304 72,475 130,779 1979- 413,200 49,153 64,558 28,940 70,330 74,346 145,176 Source? "Papulation Projections for Michigan to the Year 2000" Information Systems Division, Office of the Budget Department of Management and Budget lansing, Michigan 37 this is an advantage depends upon the particular questions you are 2 asking of the data.” The moving average calculation method offers the advantage of placing greater weight on more current data than on more dated data. Mathematically a moving average is conputed: „ 1978A + IVTfi + 1 9 7 ^ + . . . 1979 = fj where: A = actual F = forecast K = number of actual years applied It can be seen in the above formula that a reduction in N places greater weight on more recent data and an increase in N places less weight on recent data. As stated by Brown, ’’The process of conputing the moving average is quite sinple and straight forward. It is accurate: the average minimizes the sum of squares of the differences between the most recent N observations and the estimate 3 of the coefficient in the model." This advantage should be consi­ dered in the light of the fact, " . . . that when there are changes in the basic pattern of the variable being forecast moving averages may not adapt rapidly to the changes." Wheelright goes on, "This limitation of sinple moving averages to adapt to trend, seasonal and cyclical patterns can be overcome at least in part by using higher 4 order smoothing techniques." Exponential smoothing is a higher order smoothing technique. As defined by Brown, "Exponential smoothing is quite a common sort of averaging. In the field of systems engineering, this is the sinplest case of proportional control. The estimate is corrected with each new observation in proportion to the difference between 5 the previous estimate and the new observation." The formula for the calculation of exponential smoothing is: 1979** = 1978A + a(1978F - 1978A) where: A = actual V = forecast a = constant The value of alpha (a) must be between 0 and 1. Thus the ef­ fect of a large and small alpha is completely analogous to the ef­ fect of including a small number of observations in computing a moving average versus including a large number of observations in a moving average. Two obvious limitations in the moving average calculation, that is, the need to store the last N observations and the fact of equal weight to all N observations, are removed in the exponential smooth­ ing method. According to Wheelwri^it, "What we should like is a weighting seems that would apply the most weight to the most recent 6 observed values and decreasing weights to the older values." Expo­ nential smoothing does just that plus it eliminates the need for storing all past observations. The limitations of exponential smoothing are much the same as moving averages: (1) not effective in handling trends, (2) they are nonstatistical methods and thus difficult to evaluate in any exact terms. It is interesting to note that the sinple average and the moving average have the inherent weakness that a forecast will always fall below or above the actual data if a trend exist. The double 39 moving average is an attempt to eliminate the phenomenon. This is done by ", , . taking the difference between the single moving average and the double moving average and adding it back to the 7 single moving average." Unfortunately the same two limitations, that is, storage of data and equal weight for all observations, exist in the method of double moving averages as in moving averages. Double exponential smoothing as with single exponential smoothing is able to eliminate the two limitations cited above. applying double exponential In smoothing the same concluding steps as described in the double moving averages are executed, that is, we add to the single exponential smoothed value the difference between itself and the double smoothing and then adjust. The ratio method produces student enrollment forecasts based on trends in ratios of enrollment to selected variables. Once the ratio is established, here a decision must be made whether to use the median, mean, or most recent ratio and which calculation method to apply, it is then possible to make a forecast by multi­ plying the calculated ratio by the projected variable. This method has been used widely and is based on the assunption that "the habit" reflected in the calculated ratio will continue. It should be noted that all of the above calcualtion methods discussed heretofore are "non-statistical". model is defined by Wheelwright as, A non-statistical . . models that do not follow the general rules of statistical analysis and probability theory . . . , based much more on intuition . . . than on 40 g fundamental statistics," The intent of including the above models is that required statistical wizardry is minimal and thus; if one of the above models "proves efficient," the appeal to apply that model woul— be greater. A measure of efficiency for each of the applied models will be detailed later in this chapter. Sinple correlation and regression analysis is a statistical method which attempts to determine the relationship between enroll­ ment (dependent variable) and an "influencing factor" (independent variable). In forecasting work simple correlation and regression analysis is considered to have the following strengths and weaknesses: Strengths: 1. A greater range of forecasting situations can be handled with regression analysis than with smoothing techniques (non-statistical models). 2. It is a statistical model and thus its accuracy can be closely evaluated in terms of statistical measures. Weaknesses: 1. It is suitable only for linear relationships. 2. It requires a considerable amount of data to produce statistically significant results. 3. It treats all observations of the data as being equal. Multiple Cbrrelation and Regression Analysis applies the same principle as the sinple correlation and regression analysis. The difference in practice is that there are situations in which more than one independent variable (influencing factor) can be used and then simple correlation and analysis is not adequate and should be replaced by multiple correlation and regression analysis. In 41 addition to the above mentioned advantage we can compute the individual coefficient of correlation for each of the pairs of independent variables. As a statistical model there are tests of significance which can evaluate the model. The application of the above tests will produce a better understanding of each equation and the reliability which might be placed on each equation. Of course the chief interest in the value of multiple correlation and regression analysis is its applicability to the forecasting of student enroll­ ment. Before this interest can be realized, the influencing factors (independent variables) must be statistically examined. Operational Measures Past Lansing Cbnraunity College fulltime equated enrollment data will be the only influencing factor applied to the following student enrollment forecasting methods: 1. 2. 3. 4. 5. Sinple Average Moving Average Double Moving Average Exponential Smoothing Double Exponential Smooth The ratio method of forecasting Lansing Ooamunity College’s fulltime equated enrollment will enploy only census data. Hie census data will include the population pool of Clinton, Eaton, and Ingham counties and will incorporate the following age ranges: 1. 2. 3. 4. 5. 1 8 - 2 0 Year Olds 2 1 - 2 5 Year Olds 2 6 - 3 0 Year Olds 1 8 - 3 0 Year Olds Tbtal Population 42 The sinple correlation and regression analysis calculation method will be applied to all included influencing factors and will serve two purposes. The first is to produce data which will allow the application of the Y = a + bx formula to the forecasting of the 1979 Lansing Cbnmunity College fulltime equated student enrollment. The second purpose is to evaluate each of the influencing factors via statistical methods (which will be detailed later in this chap­ ter). That evaluation will be followed by the application of the multiple correlation and regression analysis calculation method to the statistically evaluated and selected influencing factors. The sinple correlation and regression analysis will be applied to the following dependent variables (lansing Cbnmunity Cbllege enroll­ ments) and influencing factors (independent variables): I. Fulltime Equated Enrollment (dependent variable) A. Independent Variables 1. LansingOoamunity College Headcount Enrollment 2. lansingObnrainity Cbllege Fulltime Enrollment 3. lansingCbnmunity Cbllege Parttime Enrollment 4. LansingCbnmunity Cbllege Area/High School Graduates 5. lansingCbnmunity Cbllege District/High School Graduates 6. United States Gross National Product 7. Michigan Public Cbnmunity Cblleges Enrollment 8. Michigan Independent Colleges Enrollment 9. Michigan Tbtal Higher Education Enrollment 10. Michigan Public Four Year Cblleges Enrollment (Headcount) 11. Michigan Public Pbur Year Cblleges Enrollment (FIE) 12. Michigan State University(Headcount) 13. Michigan State University (FYES) 14. lansing Cbnmunity CbllegeTuition (out of state) 15. lansing Cbnmunity CbllegeTuition (resident) 16. lansing Cbnmunity Cbllege Tuition (non-resident) 17. Consumers Price Index (all items) 18. Consumers Price Index (all items) minus one year 19. Consumers Price Index (all items) minus two years 20. Delta College 21. Grand Rapids Junior Cbllege 43 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. II. Fulltime Enrollment (dependent variable) A, III. Independent Variables 1. Michigan State University Enrollment (headcount) 2. Consumers Price Index (all items) 3. Cbnsuners Price Index (all items) minus one year 4. Consumers Price Index (all items) minus two years 5. United States Gross National Product Parttime Enrollment (dependent variable) A. IV. Schoolcraft Cbllege Macomb County Cbnmunity Cbllege Henry Ford Ooamunity Cbllege C.S. Mott Cbnmunity Cbllege Oakland Cbunty Comnunity Cbllege lansing Cbnmunity Cbllege - Division of Arts & Sciences lansing Cbnmunity College - Division of Student Personnel Services Lansing Cbnmunity Cbllege - Division of Technical Health Careers Tanst-tng Cbnmunity College - Division of Business lansing Cbnmunity Cbllege - Division of Learning Resources Tri-County Census Data (18-30/male) Tri-County Census Data (18-30/female) Tri-Cbunty Census Data (18-20) Tri-Cbunty Census Data (21-25) Tri-Cbunty Census Data (26-30) Tri-Cbunty Census Data (18-30) Civilian Work. Force Nurrber of Unemployed Unenployed Rate Independent Variables 1. Michigan State University Enrollment (headcount) 2. Consumers Price Index (all items) 3. Consumers Price Index (all items) minus 1 year 4. Consumers Price Index (all itmes) minus 2 years 5. United States Gross National Product Headcount Enrollment (dependent variable) A. Independent Variables 1. Michigan State University Enrollment (headcount) 2. Consumers Price Index (all items) 3. Consumers Price Index (all items) minus 1 year 4. Consigners Price Index (all items) minus 2 years 5. United States Gross National Product 44 The resulting data from the sinple correlation and regression analysis will be evaluated to determine which independent variables will be employed in the multiple correlation and regression analysis. The methods of evaluation for the data from each of the forty independent variables tested will include: 1. 2. 3. 4. 5. Ranking by correlation coefficient. Ranking by coefficient of determination. Eliminate independent variables (R) which do not permit rejection of Ho: P ■ 0 at 95% confidence level. Accept only regression equations which are significant at the 95% confidence level (F - statistic). Subjective judgment. The application of multiple regression and correlation analysis will encompass six runs of separate combinations of selected inde­ pendent variables tested. These combinations will be determined by the collective influence of the above stated methods of evaluation. The data produced by these six runs will be tested by the following measurement devices: 1. 2. 3. 4. Examine correlation coefficient. Examine coefficient of determination. Reject models which do not produce a large enough R to permit rejection of Ho: P = 0 at the 95% confidence level. Accept only regression equations which are significant at the 95% confidence level (F - statistic). The framework around which this study is built is quite straight forward. The design of the study or plan is predictive. It is the goal of this study, through the application of several selected mo­ dels, to discover a model which accurately "predicts" the 1979 full­ time equated student enrollment at lansing Oomnunity Cbllege. The basic design then requires the thoughtful selection of the factors most influential to student enrollment and the subsequent application 45 of those factors to calculation methods which mathematically/ statistically possess the power to effectuate reliable results. This design will allow a conclusion regarding the relative accuracy of the nodels tested to the prediction of the 1979 fulltime equated student enrollment at Lansing Cbnmunity Cbllege. Testable Hypotheses Null hypotheses: No difference will be found in the 1979 fore­ casting accuracy (lansing Cbnmunity Cbllege fulltime equated student enrollment) of the selected calculation methods as measured by the percentage of error. Synbolically: Ho: Legend: M, = the difference from 9019 generated by the sinple average calculation method’s forecast of the Lansing Cbnmunity Cbllege fulltime equated stu­ dent enrollment. M = the forecasted student enrollments + 9019 gener­ ated by each of the selected calculation methods. Alternate hypothesis R^: The calculation methods which enploy the mathematical functions of sinple and multiple regression produce more accurate forecasts than the other applied calculation methods in this study. Alternate hypothesis B^: The influencing factors (independent variables) which possess the highest correlation coefficient (measured against the dependent variable) will produce the most accurate student enrollment forecast. Alternate hypothesis H^: The model which most accurately forecast the 1979 fulltime equated student enrollment at Lansing Cbranunity Cbllege will forecast the 1980 enrollment within an equal percentage of error. 46 Analysis The null hypothesis and the alternate hypothesis a and b will be tested by comparing the accuracy of their respective forecast. This will be done by cooputing the percentage of error. putation is specifically only This com­ a matter of subtracting the forecasted enrollment (s) from the actual enrollment (9019) and dividing the difference by the actual enrollment (9019) thus producing the percentage of error. Alternate hypothesis lc must be tested by determining which of the applied models produces the most accurate 1979 fulltime equated student enrollment. This will be done by comparing the percentage of error of each model. Upon determining which model has the lowest percentage of error that model will be used to forecast the 1980 lansing Cbnmunity Cbllege fulltime equated enrollment. The resulting percentage of error can then be compared to the percentage of error of the selected model in predicting the 1979*s enrollment and the test for hypothesis lc will be complete. The design of this study is such that from collected data use­ ful information will be generated relative to the accurate fore­ casting of student enrollment at Tarising Cbnmunity College. The testing of the above described hypotheses are expected to respective­ ly reveal: A. The relative accuracy of selected calculation methods to forecast the 1979 fulltime equated student enrollment of Lansing Cbnmunity Cbllege. 6. The relative inpact of the selected influencing factors upon the accurate forecasting of the fulltime equated student enrollment at lansing Oomounity Cbllege. The relative accuracy of the applied calculation methods to forecast the 1979 fulltime equated student enrollment of lansing Cbnmunity Cbllege. A recomnended model to forecast the 1980 fulltime equated student enrollment at lansing Cbnmunity Cbllege. Chapter IV Analysis of Results Introduction The accumulated data of this study will be analyzed, discussed, and interpreted in this chapter. The above task will be achieved by directly presenting the results of the four stated hypotheses. Null Hypothesis The null hypothesis: No difference will be found in the 1979 forecasting accuracy (lansing Oonmunity Cbllege fulltime equated student enrollment) of the selected calculation methods as measured by the percentage of error. Symbolically: Legend: Ho: = Mx M, = the difference from 9019 generated by the sinple average calculation method's forecast of the lansing Cbnmunity Cbllege fulltime equated stu­ dent enrollment. Mx = the forecasted student enrollments - 9019 gener­ ated by each of the selected calculation methods. The selected calculation methods which were used to forecast the 1979 fulltime equated student enrollment of Lansing Cbnmunity Cbllege included: 1. Sinple Average (Tfcble 4.1) 2. Moving Average (Table 4.2) 3. Double Moving Average (Table 4.3) 4. Exponential Smoothing (Table 4.4) 5. Double Exponential Smoothing (Table 4.5) 6. Ratio Method (Tables 4.6 - 4.10) 48 Thble 4.1 Forecasts of the Succeeding Year's lansing Cbnmunity Cbllege Fulltime Equated Student Enrollment Calculation Method: Simple Average Year Running Tbtal Divisor Sinple Average Forecasted Enrollment Actual Enrollment (Year) 1957 166 1 166.0 166 310 (1958) 1958 476 2 238.0 238 401 (1959) 1959 877 3 292.3 292 561 (1960) 1960 1438 4 359.5 359 774 (1961) 1961 2212 5 442.4 442 1037 (1962) 1962 3249 6 541.5 541 1136 (1963) 1963 4385 7 626.4 626 1457 (1964) 1964 5842 8 730.2 730 2114 (1965) 1965 7956 9 884.0 884 2748 (1966) 1966 10704 10 1070.4 1070 2880 (1967) 1967 13584 11 1234.9 1234 3481 (1968) Table 4.1 (cont'd.) Year Running Tbtal Divisor Sinple lbrecasted Average Enrollment Actual Enrollment (Year) Percentage of Error 1968 17065 12 1422.0 1422 4019 (1969) -64.6 1969 21084 13 1621.8 1621 4244 (1970) -61.8 1970 25328 14 1809.1 1809 4435 (1971) -59.2 1971 29763 15 1984.2 1984 4654 (1972) -57.3 1972 34417 16 2151.0 2151 5334 (1973) -59.6 1973 39751 17 2338.2 2338 6699 (1974) -65.0 1974 46450 18 2580.5 2580 8357 (1975) -69.1 1975 54807 19 2884.5 2884 8399 (1976) -65.6 1976 63206 20 3160.3 3160 8750 (1977) -63.8 1977 71956 21 3426.4 3426 8048 (1978) -57.4 1978 80004 22 3636.5 3636 9019 (1979) -59.6 Table 4.2 Forecasts of the 1979 Tanslng Oonmmity Obllege Fulltime Equated Student Enrollment Calculation Method: Moving Averages Years Total Enrollment (Schoolyears) F 1979 (Moving Average) 1979A Percentage of Error 1969-78 62939 (10) 6293.9 9019 -30.2 1970-78 58920 (9) 6546.6 9019 -27.4 1971-78 54676 (8) 6834.5 9019 -24.2 1972-78 50241 (7) 7177.2 9019 -20.4 1973-78 45587 (6) 7597.8 9019 -15.7 1974-78 40253 (5) 8050.6 9019 -10.7 1975-78 33554 (4) 8388.5 9019 - 6.9 1976-78 25197 (3) 8399.0 9019 - 6.8 1977-78 16798 (2) 8399.0 9019 - 6.8 8048 (1) 8048.0 9019 -10.7 1978 F = Forecasted Enrollment A = Actual Enrollment Ihble 4.3 Forecasts of the 1964 through 1979 lansing Cbnmmity College Fulltime Equated Student Enrollment Calculation Mehtod: Double Moving Average Bbur Year Running Four Year Moving Average of Obi. 3 Value of A* Value of B** Forecast (A + B) Year Actual Enrollment 1957 166 1958 310 1959 401 1960 561 1961 774 360 1962 1037 512 1963 1136 693 1964 1457 877 607 1147 179.8 1327 1965 2114 1101 796 1406 203.1 1609 1966 2748 1436 1027 1845 272.4 2117 1967 2880 1864 1320 2408 362.3 2770 1968 3481 2300 1675 2925 416.3 3341 1969 4019 2806 2102 3510 468.9 3979 Average Table 4.3 (cont'd.) Year Actual Enrollment Ibur Year Running Average Bbur Year Moving Average of Ool. 3 Value of A* Value of B** Pbrecast (A + B) Percentage of Error 3970 4244 3282 2563 4001 478.9 4480 5.6 2971 4435 3656 3011 4301 429.6 4731 6.7 1972 4654 4045 3447 4643 398.3 5041 8.3 1973 5334 4338 3830 4846 338.3 5184 - 2.8 1974 6699 4667 4177 5157 326.3 5483 -18.2 1975 8357 5281 4583 5979 464.9 6444 -22.9 1976 8399 6261 5137 7385 748.6 8134 - 3.2 1977 8750 7197 5852 8542 895.8 9438 7.9 1978- 8048 8051 6698 9404 901.1 10305 28.0 1979 9019 8389 7475 9303 608.7 9912 9.9 8554 8048 9060 337.0 9397 1980 *A is the result of the difference between colums 3 and 4 added back to colum 3. **B is colum 3 minus colum 4 multiplied by .666 Table 4.4 Forecasts of the Succeeding Year's lansing Cbmnunity Cbllege Fulltime Equated Student Enrollment Calculation Mefatod: Exponential Smoothing Exponentially Smoothed Values and Percentage of Error* Actual Enrollment 3970 4244 1971 4435 1972 vH Year Percentage of Error P.E. 4244 - 4.3 4244 - 4.3 4244 - 4.3 4654 4263 - 8.4 4340 - 6.7 4416 - 5.1 3973 5334 4302 -19.3 4497 -15.7 4630 -13.2 3974 6699 4542 -32.2 5598 -16.4 6492 - 3.1 3975 8357 4758 -43.1 6149 -26.4 6678 -20.1 1976 8399 5118 -39.1 7253 -13.6 8189 - 2.5 1977 8750 5446 -37.8 7846 -10.3 8378 - 4.3 1978 8048 5776 -28.2 8298 + 3.1 8713 + 8.3 1979 9019 0003 -33.4 8173 - 9.3 8115 -10.0 « os - .5 II P.E. a - .9 K . Table 4.5 Forecasts of the Succeeding Year's lansing Cbmnunity Cbllege Fulltime Equated Student Enrollment (1972 through 1979) Calculation Method: Double Exponential Smoothing (a = .1) Single Exponential Smoothing Double Exponential Smoothing Value of A Value of B Forecast of A+BM Percents of Error Year Actual Enrollment 1970 4244 — -- — — ------ — 1971 4435 4244 4244 — — --- — 1972 4654 4263 4244 4282 2.10 4284.1 -7.9 1973 5334 4302 4250 4354 5.77 4359.8 -18.2 1974 6699 4542 4278 4806 29.30 4835.3 -27.8 1975 8357 4758 4326 5190 47.95 5238.0 -37.3 1976 8399 5118 4405 5831 79.14 5910.1 -29.6 1977 87.50 5446 4509 6383 104.00 6487.0 -25.9 1978 8048 5776 4636 6916 126.54 7042.5 -12.5 1979 9019 6003 4778 7228 135.97 7363.9 -18.3 Table 4.5 (cont'd.) A = 1.2 (x'+l) - (x"+l) B = a (x'+l - x"+l) 1 - a M = 1 (or the mnber of yeans ahead we want to forecast) F Single Exponential Staoootb - x'+l = x+a (x - x), where x equals previous year's known enrollment and F equals forecasts for previous year. Double Exponential Smoothing = x"+l = a (x'+l) + (1-a) (x"+l) 57 T&ble 4.6 Fbrecasting 1979 Fulltime Equated Student Enrollment Applying Tri-Cbunty Census Data (18 - 20 Year Olds) Calculation Method: Ratio Method Year Census Data 1 8 - 2 0 Year Olds Enrollment 1970 34,625 4244 .122 1971 36,239 4435 .122 1972 37,853 4654 .122 1973 39,467 5334 .135 1974 41,082 6699 .163 1975 42,696 8357 .195 1976 44,310 8399 .189 1977 45,925 8750 .190 1978 47,539 8048 .169 1979 49,153 1979 Ibrecast=8975.33* Percentage of Population .1826** ♦Pbrecast based on the ratio trend percentage multiplied by the projected population. **Ttie percentage figure was calculated with the moving average method (1976-1977-1978/N=3). 58 Table 4.7 Forecasting 1979 Fulltime Equated Student Enrollment Applying Tri-Oounty Census Data (21 - 25 Year Olds) Calculation Method: Ratio Method Year Census Data 2 1 - 2 5 Year Olds Enrollment 1970 40,994 4244 .103 1971 43,612 4435 .101 1972 46,230 4654 .100 1973 48,848 5334 .109 1974 51,467 6699 .130 1975 54,085 8357 .154 1976 56,703 8399 .148 1977 59,332 8750 .147 1978 61,940 8048 .129 1979 64,558 1979 FOrecast=9122.04* Percentage of Population .1413** ♦Forecast based on the ratio trend percentage multiplied by the projected population. ♦♦The percentage figure was calculated with the moving average method (1976-1977-1978/N = 3). 59 Table 4.8 Forecasting 1979 Fulltime Equated Student Enrollment Applying Tri-Cbunty Census Data (26 - 30 Year Olds) Calculation Method: Ratio Method Year Census Data 26 - 30 Year Olds Enrollment 1970 27,438 4244 .154 1971 27,603 4435 .160 1972 27,768 4654 .167 1973 27,933 5334 .190 1974 28,098 6699 .238 1975 28,263 8357 .295 1976 28,604 8399 .293 1977 28,769 8750 .304 1978 28,934 8048 .278 1979 29,099 1979 Porecast=8485.3# Percentage of Population .2916** ♦Forecast based on the ratio trend percentage multiplied by the projected population. ♦♦The percentage figure was calculated with the moving average method (1976-1977-1978/N =3). 60 Thble 4.9 forecasting 1979 Fulltime Equated Student Enrollment ^plying Tri-Cbunty Census Data ( 1 8 - 3 0 Year Olds) Calculation Method: Ratio Method Year Census Data 1 8 - 3 0 Year Olds Enrollment Percentage of Population 1970 103,057 4244 .041 1971 107,453 4435 .041 1972 114,231 4654 .040 1973 118,618 5334 .044 1974 123,016 6699 .054 1975 127,413 8357 .065 1976 131,986 8399 .063 1977 136,383 8750 .064 1978 140,799 8048 .057 1979 145,176 1979 fbrecast=8899.28* .613** ♦Forecast based on the ratio trend percentage multiplied by the projected population. ♦♦The percentage figure was calculated with the moving average method (1976-1977-1978/N = 3). 61 Table 4.10 forecasting The 1979 Rilltime Equated Student Enrollment Applying Tri-Cbunty Tbtal Census Data Calculation Method: Ratio Method Year Tbtal Census Data Enrollment Percentage of Population 1970 378,000 4244 .011 1971 382,000 4435 .012 1972 386,000 4654 .012 1973 390,000 5334 .014 1974 394,000 6699 .017 1975 398,000 8357 .021 1976 401,800 8399 .021 1977 405,600 8750 .022 1978 409,400 8048 .020 1979 413,200 1979 Ibrecast=8677.20+ .021#+ ♦forecast based on the ratio trend percentage multiplied by the projected population. ♦♦The percentage figure was calculated with the moving average method (1976-1977-1978/N = 3). 62 7. Simple Cbrrelation and Regression Analysis (Table 4.11) 8. Multiple Cbrrelation and Regression Analysis (Table 4.12) All of the above listed calculation methods produced at least a single forecast of the 1979 Lansing Cbnmunity College fulltime equa­ ted student enrollment. In addition the moving average calculation method produced ten forecasts; the ratio calculation method produced five forecasts; the sinple correlation and analysis calculation me­ thod produced twenty two forecasts; and finally the multiple corre­ lation and regression analysis calculation method produced six fore­ casts . A concise system to compare the results of the selected calcu­ lation methods was used. That system is the percentage of error. Sinply stated the percentage of error is the actual fulltime equated student enrollment (9,019 in 1979) of Lansing Cbnmunity Cbllege minus the forecasted lansing Cbnmunity Cbllege fulltime equated student enrollment divided by the actual 1979 fulltime equated stu­ dent enrollment at Lansing Cbnmunity Cbllege. Table 4.13 presents the results of all the 1979 lansing Cbnmunity Cbllege fulltime equa­ ted student enrollment forecasts that were calculated in this study including the enrollment forecast and the percentage of error. The sumnary presented in Table 4.13 reflects, with no need for statistical justification, the conspicuous evidence that requires the rejection of the null hypothesis. The percentage of error range is so great (-62.0 to 512.2) that there is just no doubt the 1979 results of fulltime equated student enrollment forecasting at Lansing Oomnunity Cbllege is affected by the selection of a calculation me­ thod. Table 4.11 Calculation Method: forecasts of the 1979 Lansing Cbmnmity Cbllege Fulltime Equated Student Enrollment Simple Cbrrelation and Regression Analysis (formula: Independent Variable (x) 1. Michigan Independent Cblleges Enrollment (53,177) 2. a b Y = a+bx) forecast (Y) Percentage of Error -14,946.1 .449 8,930.4 - .98 lansing Cbmnmity Cbllege Headcount (21,000) 337.6 .457 9,934.6 10.15 3. Michigan Pdhlic Cbmnmity Cbllege Enrollment (111,564) -1,862.6 .089 8,066.6 -10.56 4. lansing Cbnmunity Cbllege Fulltime Enrollment (4,718) -266.1 1.718 7,839.4 -13.08 5. lansing Cbmnmity College Area/High School Graduates (8,208) -22,581.9 3.697 7,763.1 -13.92 6. Lansing Cbmnmity Cbllege District/High School Graduates (4,405} 20,883.7 -2.982 7,748.0 -14.09 7. lansing Cbmnmity Cbllege Farttime Enrollment OB, 2821 8. Michigan foblic 4 Year Colleges (Headcount) Enrollment (240,600) 690.4 .598 10,427.0 15.61 10,313.3 .074 7,491.1 -16.94 Table 4.11 (cont’d.) Independent Variable (x) a b Forecast (Y) Percentage of Error 9. Cbnsuners Price Index - Minus 1 Tear (195.3) -6,004.5 85.677 10,728.2 18.95 10. Consumers Price Indes - Minus 2 Years (818.5) -6,765.9 96.470 10,743.4 19.11 11. Maconb C.C.C. (12,167) -2,230.3 .778 7,235.6 -19.77 12. Delta College (5,516) -1,863.4 1.602 6,973.2 -22.68 13. Oakland C.C. (10,661) 47.4 .640 6,870.4 -23.82 14. Michigan Total Higher Education Enrollment (361,492) -7,812.6 .040 6,647.1 -26.30 15. Michigan State University Enrollment. (47,355) 5,656.7 -0.009 6,072.2 -32.68 16. Cbnsuners Price Index ( 219.4) -6,015.8 82.637 12,114.8 34.32 17. Schoolcraft C.C. (3,794) -2,676.3 2.138 5,435.3 -39.74 IS. Michigan Public 4 Year Colleges (F.T.E.) (196,751) -9,206.5 .073 5,156.3 -42.82 19. Mott C.C. (5,090) -2,663.9 1.536 5,154.3 -42.85 20. Henry Bbrd C.C. (11,153) -4,108.4 1.529 12,944.5 43.52 21. United State/Gross National Product (2,327.4) -2,694.5 6.734 12,978.2 43.90 22. Grand Rapids J.C. (7,203) -8,195.6 2.980 13,269.3 47.13 Table 4.12 Ebrecasts of the 1979 Iansing Oamunity College Fulltime Equated Student Enrollment Calculation Method: Multiple Correlation and Regression Analysis (formula: Y = a+b^x^+b^Xg • • *^nxn) 1979 Forecast Run I XI X2 23 X4 X5 X6 X7 28 3,424.894 -62.02 13,283.752 47.28 United States/GrossNational Product (2327.4) (b=1.499) Michigan Public Oamunity Cbllege Enrollment (111,564) (b=.067) Cbnstroers Price Index (219.4) (b=24,743) Grand Rapids Junior Cbllege Enrollment (7,203) (b=-.345) Iansing Oamunity Cbllege Tbition (resident) (11.00) (b=-260.367) Tri-Ooanty Census Bata (18-30) (49,153) (b=.16) Michigan Total Higher Education Enrollment (361,492) (b^.000) Civilian Labor Ebrce (253,000) (J6=-.036) Run IT XI X2 23 X4 X5 XB 27 a « -1396.353 Percentage of Error a = 1321.161 United States Gross/National Product (2,327.4) (b=4.515) Michigan Public Oamunity College Enrollment (111,564) (b=.248) Consumers Price Index (219.4) (b=-37.518) Grand Rapids Junior College (7,203) (b=-0.738) Michigan Independent Cbllege Enrollment (53,177) (b^-0.013) Iansing Oamunity Cbllege Ttaition (resident) (11.00) (b=114.105) Tri-Cbunty Census Bata (18-30) (49,153) (b=-0.009) Table 4.12 (cont'd.) X8 X9 X10 Xll a = 2101.647 512.23 24,063.653 166.81 United States/(fross National Product (2,327.4) (b=4.046) Michigan Public Cbmnunity Cbllege Enrollment (111,564) (b=.210) Cbnsuners Price Index (219.4) (b=-29.956) Grand Rapids Junior Cbllege (7,203) (b=-.912) Michigan Independent Cbllege Enrollment (53,177) (b=.135) Iansing Cbmnunity Cbllege Tuition (resident) (11.00) (b=250.994) Tri-Cbunty Census Data (18-30) (49,153) (b=-.015) Delta College (5,516) (b=-.689) Schoolcraft Cbllege (3,794) (b=-1.066) Michigan Tbtal Higier Education Enrollment (361,492) (b=-0.023) Run IV XI X2 X3 M X5 X6 X7 X8 X9 55,217.189 Delta College (5,516) (b=-3.158) Schoolcraft Cbllege (3,794) (b=0„790) Michigan Tbtal Higher Education Enrollment (361,492) (b=-.004) Maconb Cbnnunity Cbllege (12,167) (b=-0.097) Run H I XI X2 X3 X4 X5 X6 X7 X8 X9 X10 1979 forecast Percentage of Error a = 1082.792 United States/Gross National Product (2,327.4) (b=4.594) Michigan Public Oonmunity Cbllege Enrollment (111,564) (b=.235) Cbnsuners Price Index (219.4) (b=-33.989) Cfrand Rapids Junior Cbllege (7,203) (b=-.683) Michigan Independent Cbllege Enrollment (53,177) (b=-.035) Iansing Cbnnunity Cbllege TUition (resident) ( 11.00) (b=77.269) Tri-Cbunty Census Data (18-30) (49,153) (b=-.011) Delta Cbllege (5,516) (b=-3.342) Schoolcraft Cbllege (3,794) (b=.922) TSble 4.12 (cont'd.) Run V XI X2 X3 X4 X5 S3 X7 XB Percentage of Error 3,535.296 -60.80 a = 1744.461 United States/Gross National Product (2,327.4) (b=5.177) Michigan Public Cbnnunity Cbllege Enrollment (111,564) (b=.229) Consumers Price Index (219.4) (b=-41.160) Grand Rapids Junior Cbllege (7,203) (=-.735) Michigan Independent Cbllege Enrollment (53,177) (b=-.276) Iansing Cbnnunity Cbllege Tbition (resident) (11.00) (b=-20.983) Tri-Cbunty Census Data (18-30) (49,153) (b=-.019) Delta Cbllege (5,516) (b=-.2.388) Run VI XI X2 X3 X4 X5 X6 X7 1979 Forecast a = -2100.6848 United States/Gross National Product (2,327.4) (b=1.184) Michigan Public Cbmnunity College Enrollment (111,564) (b=.074) Consumers Price Index (219.4) (b=37.124) Grand Rapids Junior Cbllege (7,203) (b=-.412) Michigan Independent College Enrollment (53,177) (b=-.002) Iansing Cbmnunity Cbllege Tuition (resident) (11.00) (b=-329.961) Tri-Cbunty Census Data (18-30) (49,153) (b=“.026) 9,074.160 .61 Table 4.13 A Summry of the Results of the Application of the Selected Calculation Methods Forecasts of Lansing Cbmnunity Cbllege Fulltime Equated Student Enrollment Calculation Method I. Sinple Average (Table 4.1) 1. Simple Average (N = 22) II. Moving Average (Table 4.2) 1. 1978 (N = 1) 2. 1977-78 (N = 2) 3. 1976-78 (N = 3) 4. 1975-78 (N = 4) 5. 1974-78 (N = 5) 6. 1973-78 (N = 6) 7. 1972-78 (N « 7) 8. 1971-78 (N = 8) 9. 1970-78 (N = 9) 10. 1969-78 (N = 10) III. Double Moving Average (Thble 4.3) 1. Double Moving Average IV. Exponential Staoothing (Table 4.4) 1. a = .1 2. a = .5 3. a = .9 1979 Forecast Percentage of Error 3,836 -50.6 8,048 8.399 8.399 8,388 8,050 7,597 7,177 6,834 6,546 6,293 -10.7 9,911 9.9 6,003 8,173 8,115 -33.4 - 9.3 6.8 6.8 - - 6.9 -10.7 -15.7 -20.4 -24.2 -27.4 -30.2 10.0 - Table 4.13 (cont'd.) Calculation Method V. VI. VII. 1979 Forecast Percentage of Error Double Exponential Smoothing (Table 4.5) 1. a = .1 2. a = .5 3. a = .9 7,363 8,631 7,555 -18.3 - 4.3 -16.2 Ratio 1. 2. 3. 4. 5. 8,975 9,122 8,485 8,899 8,677 0.4 1.1 5.9 1.3 3.8 12,114 10,728 10,743 6,973 13,269 12,944 7,763 7,748 7,839 9,934 10,427 7,235 8,930 8,066 5,156 7,491 34.32 18.95 19.11 -22.68 47.13 43.52 -13.92 -14.09 -13.08 10.15 15.61 -19.77 - 0.98 -10.56 -42.82 -16.94 Method/Tri-County Census Data 1 8 - 2 0 Year Olds (Table 4.6) 21 - 25Year Olds (Table 4.7) 26 - 30Year Olds (Table 4.8) 1 8 - 3 0 Year Olds (Table 4.9) Total Population (Table 4.10) Simple Correlation and Regression Analysis (Table 4.11) 1. Consumers Price Index 2. Consumers Price Index - Minus 1 Year 3. Cbnsuners Price Index - Minus 2 Years 4. Delta Cbllege 5. Grand Rapids Junior Cbllege 6. Henry Ford Cbaminity Cbllege 7. Iansing Cbnnunity College Area/High School Graduates 8. Tarising Oomnunity Cbllege District/High School Graduates 9. Tansing Cbmmnity Cbllege Fulltime Enrollment 10. Iansing Cbnnunity Cbllege Headcount 11. Tansing Cbnnunity Cbllege Parttime Enrollment 12. Maconb County Cbnnunity Cbllege 13. Michigan Independent Colleges Enrollment 14. Michigan Public Cbnnunity Cbllege Enrollment 15. Michigan Public 4 Year Colleges (F.T.E.) 16. Michigan Public 4 Year Colleges (Headcount) Enrollment g Table 4.13 (cont'd.) Calculation Method 17. 18. 19. 20. 21. 22. VIII. Michigan State University Enrollment Michigan Total Higher EducationEnrollment Mott Cbnnunity College Oakland Cbnnunity Cbllege Schoolcraft Cbnnunity College United States/Gross National Product Multiple Correlation and Regression Analysis (Thble 4.12) 1. Run I 2. Run II 3. Run III 4. Run IV 5. Run V 6. Run VI 1979 Forecast Percentage of Error 6,072 6,647 5,154 6,870 5,435 12,978 -32.68 -26.30 -42.85 -23.82 -39.74 43.90 3,424 13,283 55,217 24,063 3,535 9,074 -62,0 47.2 512.2 166.8 -60.8 0.6 g 71 It should be noted that the simple and multiple correlation and regression analysis calculation methods were the only two statis­ tical models, and thus it is possible to make statistical statements about the accuracy and significance of these regressions. The inde­ pendent variables that were included in the forecasting of the 1979 fulltime equated student enrollment at Tarising Community Cbllege survived the following statistical evaluations: 1. F Statistic Test A. Simple Correlation and Regression Analysis (Thble 4.14) B. Multiple Correlation and Regression Analysis (Table 4„15) 2. Coefficient of Determination (Tfcble 4.16) 3. Correlation Coefficient (Table 4.17) 4. Correlation of Coefficient/Ho: p = 0 A. Simple Correlation and Regression Analysis (Table 4.18) B. Multiple Correlation and Regression Analysis (Table 4.19) In order to execute the two formulae, Y = a + bx and Y = a + b, x, + . . . fc>nxn it was necessary to extract both the a and b from each of the simple and program runs. multiple correlation and regression analysis "Mini-Regression: A Snail Computer Program for Per­ forming Multiple Regression-Analysis" from Mini-Tab was the program that produced the bulk of this study's statistical data and it was this program from which a and b were extracted. Inasmuch as the possibility of a miscalculation existed a cross check was conducted to verify the value of each a and b. The cross check of each linear regression (only the sinple correlation and regression) was conducted. Using Texas Instruments 59 Program: Table 4.14 Results of the F Statistic Test* Ob Selected Independent Variables In the Simple Cbrrelation and Regression Analysis Independent Variable F Statistic Iansing Cbmnunity Cbllege Area/High School Graduates 1.75 Iansing Cbnnunity Cbllege District/High School Graduates 0.34 Iansing Cbnnunity Cbllege Enrollment (Headcount) 1,004.13 Iansing Cbnnunity Cbllege Enrollment (Parttime) 334.22 Iansing Cbmnunity Cbllege Enrollment (Fulltime) 885.46 Tri-Cbunty Census Ebia (18 - 30 Year Olds) Male 56.16 Tri-Cbunty Census Data (18 - 30 Year Olds) Female 58.36 Tri-Cbunty Census Data (18 - 20 Year Olds) 58.73 Tri-County Census Data (21 - 25 Year Olds) 59.73 Tri-Cbunty Census Data (26 - 30 Year Olds) 58.87 Tri-Cbunty Census Data (18 - 30 Year Olds) 73.76 Civilian Labor Force (Clinton-Eaton-Ingham-Ionia) 25.98 Number of Unemployed (Clinton-Eaton-Ingham-Ionia) 10.39 Unemployment Rate (Clinton-Eaton-Ingham-Ionia) 2.92 Iansing Cbmnunity Cbllege lUition (resident) 211.11 Lansing Cbnnunity Cbllege Tuition (non-resident) 285.31 Tansing Cbnnunity College-Division of Arts & Sciences 51.04 Iansing Cbmnunity Cbllege-Division of Student Personnel Services (Total Credits) 38.54 Lansing Cbmnunity Cbllege-Division of Technical Health Careers (Tbtal Credits) 582.55 Degrees of Freedom 95% Confidence Level Accept/Reject 6 6 21 21 21 8 8 8 8 8 8 8 8 8 21 21 8 Reject Reject Accept Accept Accept Accept Accept Accept Accept Accept Accept Accept Accept Reject Accept Accept Accept 8 Accept 8 Accept Table 4.14 (cont'd.) Independent Variable Iansing Cbnnunity Cbllege-Division of Business Iansing Cbmnunity College-Division of Learning Resources Iansing Oamunity College Thition (out of state) Michigan State University (FYES) Michigan State University (Headcount) Consumers Price Index (all items) Cbnsuners Price Index (all items) minus 1 year Cbnsuners Price Index (all itans) minus 2 years Delta Cbllege Enrollment Grand Rapids Junior College Enrollment Hairy Ford Cbnnunity Cbllege Enrollment (fulltime equated) Schoolcraft Cbmnunity Cbllege Enrollment Oakland Cbmnunity Cbllege Enrollment Mott Cbmnunity College Enrollment Macotrfo Cbmnunity College Enrollment United States Gross National Product (1976 dollars) Michigan Public Four Year Colleges Enrollment (headcount) Michigan Total Higher Education Enrollment (FYES/FIE) Michigan Public Cbmnunity Colleges Enrollment (ffYES/FEE) Michigan Independent Colleges Enrollment (IYES/TTE) Michigan Public Four Year Colleges Enrollment (FIE) F Statistic 580.98 896.88 39.05 14.38 0.02 259.07 202.50 165.59 105.09 153.41 84.07 104.88 25.51 9.08 89.75 932.83 57.74 66.85 197.11 198.52 25.91 Degrees of Freedom 8 8 21 9 14 20 21 21 12 12 12 12 12 12 12 18 14 8 12 9 9 95% Confidence level Accept/Reject Accept Accept Accept Accept Reject Accept Accept Accept Accept Accept Accept Accept Accept Accept Accept Accept Accept Accept Accept Accept Accept ♦This test indicates the significance (or lack of significance) of the total regression equation at the 95% confidence level. Table 4.15 Results of the F Statistic Test* On Selected Runs In the Multiple Correlation and Regression Analysis Run Run I 95% Confidence Level Accept/Re.ject F Statistic Degrees of Freedom 221.47 14 Accept 253.64 11 Accept United States Gross National Product Michigan Public Cbnnunity College Enrollment Consumers Price Index Grand Rapids Junior Cbllege Iansing Cbnnunity College Tuition (resident) Tri-Cbunty Census Data (18 - 30) Michigan Total Higher Education Enrollment Civilian labor Force Run II United States Gross National Product Michigan Public Cbnnunity Cbllege Enrollment Consumers Price Index Grand Rapids Junior Cbllege Michigan Independent College Enrollment Iansing Cbnnunity College Tuition (resident) Tri-County Census Data (18 - 30) Delta College Table 4.15 (cont'd.) Run F Statistic Degrees of Freedom 95% Confidence Level Accept/Re.ject Schoolcraft College Michigan Tbtal Higher Education Enrollment Macarb Cbnnunity Cbllege Run III 174.45 12 Accept 366.94 13 Accept United States Gross National Product Michigan Public Cbnnunity Cbllege Enrollment Consumers Price Index Grand Rapids Junior College Michigan Independent Cbllege Enrollment Iansing Cbnnunity College Tuition (resident) Tri-Cbunty Census Data (18 - 30) Delta College Schoolcraft Cbllege Michigan Tbtal Higher Education Enrollment Run IV United States Gross National Product Michigan Ebblic Cbnnunity College Enrollment Consumers Price Index Grand. Rapids Junior Cbllege Michigan Independent Cbllege Enrollment Lansing Cbnnunity Cbllege Tuition (resident) Tri-Cbunty Census Data (18 - 30) Delta College Schoolcraft Cbllege Tkble 4.15 (cont'd.) Run Run V 95% Confidence Level Accept/Reject F Statistic Degrees of Freedom 354.24 14 Accept 255.91 15 Accept United States Gross National Product Michigan Riblic Cbmnunity Cbllege Enrollment Cbmsuners Price Index Grand Rapids Junior Cbllege Michigan Independent Cbllege Enrollment Iansing Cbmnunity Cbllege Tuition (resident) Tri-Cbunty Census Data (18 - 30) Delta Cbllege Run VI United States Gross National Product Michigan Public Cbmnunity Cbllege Enrollment Cbnsuners Price Index Grand Rapids Junior Cbllege Michigan Independent Cbllege Enrollment Tanfiing Cbmnunity Cbllege TUition (resident) Tri-Cbunty Census Data (18 - 30) Table 4.16 Independent Variables Banked By Resulting Coefficient of Determination from the Sinple Correlation and Regression Analysis Independent Variable vs Iansing Cbmnunity Cbllege (FIE) Coefficient of Determination Iansing Oommnity College -Division of Learning Resources .991 Tansing Cbnnunity Cbllege -Division of Technical Health Careers .986 Iansing Cboramity Cbllege -Division of Business .986 United States Gross National Product .981 Iansing Cbnnunity College Headcount Enrollment .980 Lansing Cbnnunity Cbllege Fulltime Enrollment .977 Michigan Public Cbnnunity Colleges Enrollment .943 Lansing Cbnnunity College Parttime Enrollment .941 Iansing Cbnnunity College Tuition (non-resident) .931 Cbnsuners Price Index (all items) .928 Grand Rapids Junior Cbllege .927 Michigan Independent Colleges Enrollment .923 Table 4.16 (cont'd.) Independent Variable vs Iansing Cbmnunity Cbllege (FIE) Iansing Cbnnunity Cbllege (resident) Cbnsuners Price Index (all items) minus Coefficient of Determination .910 1 year .906 Tri-Cbunty Census Data (18 - 30) .902 Delta Cbllege .898 Schoolcraft College .897 Michigan Tbtal Higher Education Enrollment .893 Consumers Price Index (all items) minus 2 years .887 Macomb County Cbnnunity Cbllege .882 Tri-Cbunty Census Data(18 - 20) .880 Tri-Cbunty Census Data (21 - 25) .880 Tri-Cbunty Census Data(25 - 30) .880 Tri-Cbunty Census Data (18 - 30) .879 Henry fbrd Community Cbllege .875 Tri County Census Data (18 - 30) male .875 Iansing Cbmnunity Cbllege - Division of Arts& Sciences .865 Table 4.16 (cont'd.) Independent Variable vs Lansing Cbmnunity College (FTE) Coefficient of Determination Iansing Gonminity Cbllege - Division of Student Personnel Services .828 Michigan Public Pour Year Colleges Enrollment .805 Civilian Work Force .765 Michigan Public Ibur YearColleges Enrollment (FIE) .742 Oakland County Conmmity Cbllege .680 Iansing Cbnnunity Cbllege Tiition (out of state) .650 Michigan State University (FSES) .615 Number of Unonployed .565 Mott Cbmnunity Cbllege .431 Unemployment Rate .270 Tansing Cbmnunity Cbllege Area/High School Graduates .226 Iansing Cbnnunity Cbllege District/High School Graduates .054 Michigan State University Enrollment (Headcount) .001 Table 4.17 Independent Variable Banked By Correlation Coefficient from Sinple Correlation and Regression Analysis Independent Variable vs Iansing Oamunity Cbllege (FIE) Correlation Coefficient Iansing Oamunity Cbllege - Division of Learning Resources .996 United States Gross National Product .993 Tansing Gomnunity College Headcount Enrollment .993 Iansing Oamunity College - Division of Business .990 Iansing Oamunity College - Division of Technical Health Careers .990 Iansing Oamunity Cbllege Fulltime Enrollment .998 Michigan Riblic Oamunity Colleges Enrollment .971 Iansing Cbnnunity College Tbition (non-resident) .970 Consumers Price Index (all items) .965 Grand Bapids Junior College .964 Michigan Independent Colleges Enrollment .963 Iansing Oamunity Colleges Parttime Enrollment .961 Table 4.17 (contfd.) Independent Variable vs Iansing Cbmnunity Cbllege (FIE) Correlation Coefficient Iansing Cbmnunity College Tbition (resident) .954 Cbnsuners Price Index (all iteens) minus 1 year .952 Tri-County Census .950 Data (18 - 30) Delta College .948 Schoolcraft Cbllege .947 Michigan Tbtal Higher Education Enrollment .945 Tri-Cbunty Census Data(18 - 30) female .942 Tri-Cbunty Census Data(18 - 20) .939 Tri-Cbunty Census Data (21 - 25) .938 Tri-County Census Data(26 - 30) .938 Macomb County Community College .938 Consumers Price Index (all items) minus 2 years .938 Hairy Ford Cbmnunity College .936 Tri-County Census .935 Data(18 - 30) male Iansing Cbmnunity College - Division of Arts & Sciences .930 Table 4.17 (cont'd.) Independent Variable vs Iansing Oommnlty Cbllege (FTE) Correlation Coefficient Iansing Comnunity College - Division of Student Personnel Services .910 Michigan Public Pour Year Colleges Enrollment .897 Civilian Work Ibrce .874 Michigan Public Pour YearColleges Enrollment (PTE) .862 Oakland County Cbnnunity Cbllege .825 Iansing Connunity College Tuition (out of state) .806 Michigan State University (FYES) .784 Nuirber of Unemployed .752 Mott Cbnnunity College .656 Unemployment Bate .520 Iansing Cbnnunity College Area/High School Graduates .475 Iansing Cbmnunity Cbllege District/High School Graduates -.231 Michigan State University Enrollment (Headcount) -.035 Ihble 4.18 Simple Correlation and Regression Analysis Values of the Correlation Coefficient Required for 96% Level of Significance When Ho: P = 0 Items (?) Versus Tansing Cbnnunity Cbllege Fulltime Equated Enrollment (y) Item (x) .95% Confidence Interval Degrees of Ereedcm Coefficient Correlation ! 1. Iansing Cbmnunity Cbllege Headcount .413 21 .990 2. United State/Gross National Product .444 18 3. Iansing Gomnunity Cbllege FUlltime Enrollment .413 21 .988 4. Michigan Public Cbnnunity Cbllege Enrollment .532 12 .971 5. Iansing Cbmnunity Cbllege Parttime Enrollment .413 21 .970 6. Consumers Price Index .423 20 .964 7. Grand Rapids J. C. .532 12 .963 8. Michigan Independent Colleges Enrollment .602 . 9 .961 9. Consuners Price Index-Minus 1 Year .413 21 .952 10. Delta Cbllege .532 12 .948 11. Schoolcraft C. C. .532 12 .947 ' .990 Table 4.18 (cont'd.) 12. Michigan Tbtal Higher Education Enrollment .632 8 .945 13. Cbnsuners Price Index-Minus 2 Years .413 21 .942 14. Maocmb C. C. C. .532 12 .939 15. Henry Ford C. C. .532 12 .935 16. Michigan Public 4 Year Colleges .497 14 .897 17. Michigan Public 4 Year Colleges Enrollment .602 9 .862 18. CUkland C. C. .532 12 .825 19. Mott C. C. .532 12 .656 20. Iansing Cbnnunity Cbllege Area/High School Graduates .707 6 .475* 21. Lansing Cbmnunity Cbllege District/High School Graduates .707 22. Michigan State University Enrollment .497 ♦Rills outside the 95% confidence interval -.231* 14 -.035* £ Table 4.19 Multiple Correlation and Regression Analysis Values of Correlation Coefficient Required for 93% Level of Significance When Ho: p = o Runs* 99% Confidence Interval Degrees of Freedom Coefficient of Correlation Score Run I .497 14 .996 Run II .553 11 .998 Run III .532 12 .997 Run IV .514 13 .996 Run V .497 14 .998 Run VI .482 15 .996 ♦See Thble 4.15 for more detailed information relative to a specific multiple correlation and regression analysis run. 86 {(2nd) (P^n) 01, (SBR) (CIB), (RST) and enter data) the a and b of the applied formulae, Y = a + bx and Y = a + b, x, + hnxn , were deemed to be acceptable. Alternate hypothesis H ^ : The calculation methods that employ the mathematical functions of simple and multiple regression produce more accurate forecasts than the other applied calculation methods in this study. Table 4.20 presents a ranking of the applied calculation methods of this study based solely on the percentage of error in forecasting the 1979 fulltime equated student enrollment at Iansing Cbmnunity College. Based on the information reflected in Ihble 4.20 alternate hypothesis must be rejected. The most accurate forecast was not the result of a mathematical function calculation method. The least accurate forecast was the product of a calculation method of the mathematical function derivation. The range in the percentage of error resulting from the mathematical function based calculation methods was 547.2. The above three facts alone dictate the rejec­ tion of the alternate hypothesis H1n. Alternate hypothesis The influencing factors (independent variables) that possess the highest correlation coefficient measured against the dependent variable) will produce the most accurate stu­ dent enrollment forecast. The test of this hypothesis is presented in Table 4.21. 4.21 exhibits a ranking of the independent variables. Table This ranking is based on the correlation coefficient resulting from the sinple correlation and regression analysis of the independent variable versus the Tansing Camnunity Cbllege fulltime equated student Table 4.20 A Ranking of the Lansing Oocnunity Cbllege Fulltime Equated Student Enrollment Forecast By Calculation Method Based on the Percentage of Error . Calculation Method 1. Ratio Method/Tri-Cbunty Census Data > 1 8 - 2 0 Tear Olds 2. Multiple Correlation and Regression Analysis - Run VI 3. Sinple Correlation and Regression Analysis - Michigan Independent Colleges Enrollment 4. Ratio Method/Tri-Cbunty Census Data - 2 1 - 2 5 Year Olds 5. Ratio Method/Tri-Cbunty Census Data - 1 8 - 3 0 Year Olds 6. Ratio Method/Tri-Cbunty Census Data - Tbtal Population 7. Double Exponential Smothing - a = .5 8. Ratio Method/Tri-County Census Data - 26 - 30 Year Olds 9. Moving Average - 1977-78 (N = 2) Moving Average - 1976-78 (N = 3) 11. Moving Average - 1975-78 (N = 4) 12. Exponential Smoothing - a = .5 13. Double Moving Average - Double Moving Average 14. Exponential Sknoothing - a = .9 15. Sinple Correlation and Regression Analysis - Iansing Cbmnunity Cbllege Headcount 16. Sinple Correlation and Regression Analysis - Michigan Public Oomnunity College Enrollment 17. Moving Average - 1978 (N = 1) Moving Average - 1974-78 (N = 5) 19. Sinple Correlation and Regression Analysis - Tanking Cbmnunity Cbllege Fulltime Enrollment 20. Sinple Correlation and Regression Analysis - Iansing Cbmnunity Cbllege Area/High School Graduates Percentage of Error -0.4 0.6 -0.9 1.1 -1.3 -3.8 -4.3 -5.9 —6.8 -6.8 -6.9 -9.3 9.9 -10.0 10.1 10.5 -10.7 -10.7 -13.0 -13.9 Table 4.20 (cont'd.) Calculation Method 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. Sinple Correlation and Regression Analysis - LansingGoranunityCbllegeDistrict/High School Graduates Sinple Correlation and Regression Analysis - IansingCtrarjunityCbllege ParttimeEnrollment Moving Average - 1973-78 (N = 6) Double Exponential Sknoothing - a = .9 Simple Correlation and Regression Analysis - Michigan Public 4 TearColleges(Headcount) Enrollment Double Exponential Sknoothing - a = .1 Sinple Correlation and Regression Analysis - Consumers Price Index - Minus 1 Year Sinple Correlation and Regression Analysis - Consumers Price Index - Minus 2 Tears Sinple Correlation and Regression Analysis - Maccnb County Cbnnunity Cbllege Moving Average - 1972-78 (N = 7) Sinple Correlation and Regression Analysis - Delta College Sinple Correlation and Regression Analysis - Oakland Cbmnunity Cbllege MovingAverage - 1971-78 (N = 8) Sinple Correlation and Regression Analysis - Michigan Tbtal Higher Education Enrollment Moving Average - 1970-78 (N = 9) Moving Average - 1969-78 (N = 10) Sinple Correlation and Regression Analysis - Michigan State Exponential Smoothing - a = .1 Sinple Correlation and Regression Analysis - Consumers Price Index Sinple Correlation and Regression Analysis - Schoolcraft Community College Sinple Correlation and Regression Analysis - Michigan Public 4 Year Colleges (F.T.E.) Simple Correlation and Regression Analysis - Mott Commnity Cbllege SinpleCorrelation and Regression Analysis - Henry Ford Cbmnunity Cbllege SinpleCorrelation and Regression Analysis - United States Gross NationalProduct SinpleCorrelation and Regression Analysis - Grand Rapids Junior College Multiple Correlation and Regression Analysis - Run II Percentage of Error -14.0 15.6 15.7 16.2 16.9 -18.3 18.9 19.1 -19.7 -20.4 -22.6 -23.8 -24.2 -26.3 -27,4 -30.2 -32.6 -33.4 34.3 -39.7 -42.82 -42.85 43.5 43.9 47.1 47.2 Tbble 4.20 (cont'd.) Percentage of Error Calculation Method 47. 48. 49. 50. 51. Sinple Average - Sinple Average MultipleCorrelation and Regression MultipleCorrelation and Regression MultipleCorrelation and Regression MultipleCorrelation and Regression Analysis Analysis Analysis Analysis - Run V Run I Run IV Run III -59.6 -60.8 -62.0 166.8 512.2 oo to "Table 4.21 A Comparison of the Independent Variables' Correlation Coefficient Versus The 1979 lansing Cbmnunity College Fulltime Equated Student Enrollment Forecasting Accuracy (Percentage of Error) Independent Variable Correlation Coefficient Percentage of Error lansing Cbnraunity College Fulltime Enrollment .998 -13.08 Lansing Cbmnunity College Headcount .993 10.15 United States/Gross National Product .993 43.90 Michigan Public Cbmnunity College Enrollment .971 -10.56 Consumers Price Index .965 34.32 Grand Rapids Junior College .964 47.13 Michigan Independent Colleges Enrollment .963 - 0.98 lansing Cbmnunity College Parttime Enrollment .961 15.61 Consumers Price Index - Minus 1 Year .952 18.95 Delta College .948 -22.68 Table 4.21 (cont'd.) Independent Variable Correlation Coefficient Percentage of Error Schoolcraft Cbmnunity College .947 -39.74 Michigan Total Higher Education Enrollment .945 -26.30 Consumers Price Index - Minus 2 Years .938 19.11 Maconfc Cbunty Cbmnunity College .938 -19.77 Henry fbrd Cbmnunity College .936 43.52 Michigan 4 Year Colleges (Headcount) Enrollment .897 - 7.32 Michigan Public 4 Year Colleges (F.T.E.) .862 -42.82 Oakland Cbnmmity College .825 -23.82 Mott Oommnity College .656 -42.85 lansing Cbmnunity Cbllege Area/High School Graduates .475 -13.92 lansing Cbnmmity Cbllege District/High School Graduates -.231 -14.09 Michigan State University Enrollment -.035 -32.68 92 enrollment. The acceptance of alternate hypothesis then is dependent upon the percentage of error column in Table 4.21 reflec­ ting a descending percentage of error trend. As a consequence of the fact that there is not even a hint of descending values in the percentage of error column, alternate hypothesis Alternate hypothesis H^.: The model that is rejected. most accurately forecast the 1979 fulltime equated student enrollment at lansing Cbmnunity Cbllege will forecast the 1980 enrollment within an equal percentage of error. Table 4.13 reveals that the model that produced the most accurate forecast of the 1979 Lansing Cbmnunity Cbllege fulltime equated student enrollment was the Ratio Method/Tri-Cbunty Census Data ( 1 8 - 2 0 Year Olds). The percentage of error was -000.48785. The acceptance of alternate hypothesis H^c requires that a forecast of the 1980 Tnnwing Cbmnunity College fulltime equated student * enrollment, applying the Ratio Method/Tri-Cbunty Census Data (18 - 20 Year Olds) produce a percentage of error figure within ± 000.48785. The forecast of the Lansing Cbmnunity College 1980 fulltime equated student enrollment presented in Thble 4.22 produced a percentage of error equal to 0.37. This figure dictates that the alternate hypothesis H^c be accepted. Table 4.23 presents a sunrnary of the results of the four hypotheses tested in this study. 93 Table 4.22 Forecasting 1960 Fulltime Equated Enrollment Applying Tri-County Census Data (18 - 20 Year Olds) Calculation Method: Ratio Method Year Census Data 18 - 20 Year Olds Enrollment Percentage of Population 1970 34,625 4,244 .122 1971 36,239 4,435 .122 1972 37,853 4,654 .122 1973 39,467 5,334 .135 1974 41,082 6,699 .163 1975 42,696 8,357 .195 1976 4,310 8,399 .189 1977 45,925 8,750 .190 1978 47,539 8,048 .169 1979 49,153 9,019 .183 1980 50,767 1980 Forecast=9,168.52* .1806** The 1980 Lansing Ccmnunity College fulltime equated enrollment was 9134 . The forecasted enrollment of 9,168.52 produces a percen­ tage of error equal to .3779. ♦Forecast based on the ratio trend percentage multiplied by the projected population. ♦♦This percentage of population figure was calculated with the moving average method (1977-1978-1979/3). Table 4.23 A Summary of the Result? of the Tested Ifypotheses in this Study Hypothesis Null: Result No difference will be found in the 1979 forecasting accuracy (lansing Coranunity College fulltime equated student enrollment) of the selected calculation methods as measured by the percentage of error. H^a: Reject The calculation methods which employ the mathematical functions of simple and multiple regression produce more accurate forecasts than the other applied calculation methods in this study. Hjb: Reject The influencing factors (independent variables) that possess the highest correlation coefficient (measured against the dependent variable) will produce the most accurate student enrollment forecast. HjC: Reject The model which most accurately forecast the 1979 fulltime equated student enrollment at lansing Conrainity Cbllege will forecast the 1980 enrollment within an equal percentage of error. Accept CHAPTER V SUMMARY AND DISCUSSION Sutmaary This study was designed to develop a useful student enrollment forecasting model for Lansing Cbnmmity Cbllege. From the descrip­ tive data collected hypotheses regarding the forecasting of student enrollment can be generated and subsequently tested by the Division of Student Personnel Services/Lansing Cbmnunity Cbllege. Eight calculation methods: simple average, moving average, double moving average, exponential smoothing, double exponential smoothing, ratio method, simple correlation and regression analysis, and multiple correlation and regression analysis, were selected to forecast the 1979 student enrollment at lansing Cbmnunity Cbllege. From these eight calculation methods fifty-one 1979 student enroll­ ment forecasts were generated. Each calculation method required at least one influencing factor to compute a student enrollment forecast. The calculation methods of simple average, moving average, double moving average, exponential smoothing, and double exponential smoothing required only the influencing factor of past lansing Cbmnunity Cbllege stu­ dent enrollment data. factors: The ratio method incorporated two influencing past student enrollment and tri-county (Clinton, Eaton, and Ingham) census data. The final two calculation methods, sinple and multiple correlation and regression analysis, produced fore­ casts through the application of twenty-two selected influencing factors/independent variables. 95 96 The restating data from the sinple correlation and regression analysis were statistically evaluated to screen the independent variables for application in the multiple correlation and regres­ sion analysis. The evaluation of the data from each of the forty independent variables tested included: ranking by correlation coefficient of determination, testing of H d : P=0 at 95% confidence level, F-Test, and subjective judgment. The application of the multiple correlation and regression analysis in this study included six runs of separate corrbinations of test-determined independent variables. The six test-determined combinations were the result of the collective influence of the methods of evaluation listed in the above paragraph. The subse­ quent data produced by the six runs were then tested by the statis­ tical evaluations of correlation coefficient, coefficient of deter­ mination, testing of Kb: P=0 at the 95% confidence level, and the F-Test. Each of the fifty-one forecasts restating from the eigjht listed calculation methods, and the selected influencing factors, was ranked by its accuracy in forecasting the Lansing Cbnmmity Cbllege 1979 fulltime equated student enrollment. The ranking was based on the percentage of error of each forecast. The percentage of error was calculated by subtracting the forecasted fulltime equated stu­ dent enrollment from the actual 1979 fulltime equated student en­ rollment and then dividing the difference by the actual 1979 full­ time equated student enrollment. The calculation method that produced the most accurate fore­ cast, based on the percentage of error, was the ratio method/18-20 97 year olds with a percentage of error of -0.4. This forecast was only slightly more accurate (by 0.2) than the 0.6 produced by Run Six of the multiple correlation and regression calculation method. The above fact reveals that the tested mathematical function methods did not produce a more accurate forecast than a nan-mathematical function calculation method. The range of the percentage of error produced by the eight calculation methods (fifty one scores) tested was 574.2. This indi­ cates that the selection of a calculation method in forecasting stu­ dent enrollment can produce diverse scores. It is inportant to realize that the selection of the most appropriate calculation method is extremely inportant in the development of a student enroll­ ment forecasting model. In addition, the influencing factors that produced the highest correlation coefficients did not produce a correspondingly high accuracy rate in forecasting student enrollment. The major finding of the study was that the model that most accurately forecasted the 1979 fulltime equated student enrollment was able to forecast the 1980 student enrollment within an equal percentage of error. The most accurate model produced a -0.4 per­ centage of error in forecasting the 1979 fulltime equated student enrollment at Lansing Gonmmity College. forecast the 1980 enrollment. The same model was used to The resulting percentage of error was 0.37792. Conclusions 1. Mathematical function calculation methods do not produce fore­ casts with lower percentages of error than the non-mathematical 98 function calculation methods. 2. Accuracy in forecasting student enrollment is significantly dependent upon the selected calculation method. 3. The percentages of error produced by the forecasts of the simple correlation and regression analysis calculation method were not proportionately reflected in the correlation coeffi­ cient they generated. 4. The percentage of error resulting from the most accurate calcu­ lation method applied to the 1979 student enrollment forecast produced a forecast with greater accuracy in 1980. Discussion Certainly the challenges of developing an accurate student enrollment forecasting model for lansing Cbnmmity Cbllege are worthy of exploration. It should be apparent to even the most uninvolved administrator, faculty meatier, or staff person that it is extremely advantageous for both the students affected and the college to know as nearly as possible the student enrollment to be expected in succeeding years. Calculation Methods There are ntmerous calculation methods that could be applied to student enrollment forecasting. The eight calculation methods selected for application in this study were determined to be most appropriate as a result of a review of the literature available on the subject of student enrollment forecasting. The appropriateness was determined by their forecasting postulates, projection tech­ niques, and the type of data they required. In the literature a good deal is written explaining and evaluating various calculation 99 methods, but few studies have applied more than one calculation method to the same set of data as was done in this study. As an Increased volume of research becomes available in the topic area of student forecasting studies which apply numerous calculation methods to the same data will emerge. This emerging data will then provide necessary information as to the calculation methods that are most efficiently applicable to specific student enrollment settings. Influencing Factors Inasmuch as the actual influencing factors in the problem of accurately forecasting student enrollment are critical, it is of paramount importance that those factors be identified. The forty influencing factors evaluated in this study were not quantifiably labelled regarding their actual influence on the fulltime equated student enrollment at lansing Cbmnunity College. The evaluation did reveal significantly high correlation coefficients that suggest the value of pursuing an actual influence coefficient, that is, cause and effect. The inability to more accurately forecast stu­ dent enrollment from extremely high correlation coefficient scores suggest the possibility that there are more discriminating influen­ cing factors than were included in this study. Implications for Further Research This study concludes that there is a difference in the fore­ casting accuracy of student enrollment as a result of the selected calculation method. Given this fact it is inportant that extensive research be conducted to refine the understanding of the strengths and weaknesses of tested calculation methods. The knowledge of a 100 calculation method’s strengths and weaknesses would enable a fore­ caster to apply the calculation method whose characteristics are best matched to the character of the enrollment setting to be forecast. Another conclusion reached in this study was that the calcula­ tion methods that enployed the mathematical functions of simple and multiple regression do not produce the most accurate forecasts. The importance of this conclusion can be seen in the extreme com­ plexity, greater clerical demands, and inplied superiority of the simple and multiple regression calculation method as conpared to the greater ease in the application of alternate calculation meth­ ods. Additional research could be applied to test this conclusion on a longitudinal basis or at a large number of institutions during the same forecast period. This kind of a study could produce a more definitive response to the question of the superiority of the mathematical function versus non-mathematical function calcula­ tion methods. The importance of selecting the most discriminating influen­ cing factor(s) for the right calculation method in the forecasting of student enrollment cannot be overstated. It is important to evaluate as many factors that potentially influence student enroll­ ment as can be evaluated. Only those factors that influence student enrollment should be applied to a calculation method. Based on the results of this study it is apparent that a high correlation coeffi­ cient score is not sufficient to establish the discriminating power of a specific factor in the influentialness of student enrollment. 101 Further research should be designed to specifically identify those factors that influence student enrollment. Specific recommendations for further research include: 1. Pursue at all cost the identification of at least one influencing factor with a defined cause and effect ratio. 2. Investigate in great detail the effect of unemployment upon student enrollment. 3. Apply the ratio method (enrollment/18-20 year olds) to a number of comparable institutions to test its applicability value at other institutions. hypotheses for Experimental Study 1. A null hypothesis: No difference will be found in the 1980 through 1990 forecast accuracy (lansing Cbmnunity Cbllege fulltime equated student enrollment) of ten selected calculation methods as measured by the percentage of error. 2. A null hypothesis: No difference will be found in the 1980 forecasting accuracy (lansing Cbmnunity College and nineteen comparable community colleges) of ten selected calculation methods as measured by the percentage of error. 3. The independent variables that produce the most accurate student enrollment forecast using simple correlation and regression analysis data collectively will produce the most accurate student enrollment forecast using multiple correlation and regression analysis data. 4. The most influential factors in the forecasting of student enrollment will produce the most accurate forecast using simple correlation and regression analysis. 102 Approach to the Future Increasing fiscal pressure from local, state, and federal levels is placing great demands on higher education. tions cannot survive these demands. Indeed, many institu­ Threats upon higher education in the form of such legislation as Michigan's 1980 Proposal D and local millage defeats must be met with responses emanating from as great a base of objective data as possible. Of course only one element of a necessary data base for effective higher education administration is represented by student enrollment forecasting data. A data base must include numerous conpilations similar to the data presented in this study. This data base can be interpola­ ted into information that will enable the fulfillment of the goals and objectives of an institution. E N D N O T E S ENDNOTES Chapter I: Statement of the Problem 1Keith Gave, "L.C.C. Tab: The Lansing State Journal, September 2 , 1979, p. 26. o Clive W. Granger, Investigating the Future: Statistical Forecasting Problems, Nottingham, England: The University Press, 1967, p. 46. Chapter II : Review of Literature ^D. Kent Halstead, Statewide Planning In Higher Education, Washington, D.C., U.S. Printing Office, 1974. 2 L. J. Lins, Methodology of Enrollment, Projections for Colleges and Universities, Washington, Education, 1960. ^ayne L. Mangleson, et al,. Projecting Cbllege and University Enrollments: Analyzing the Past and Focusing the Future, Ann Arbor, Michigan, Center for the Study of Higher Education, 1973. 4 Paul Wing, Higher Education Enrollment Forecasting, Boulder, Colorado: National Center for Higher Education Management Systems, 1974. 5 Halstead, p. 299. 6Ihid., p. 300. 7Ibid., p. 302. 8Ibid., p. 302. ®Lins, p. 1. 10Ibid., p. 2 . 1:LIbid., p. 6 . ^ I b i d . , p. 21. 13IBid., p. 25. 14 Ibid., p. 31. ^Mangleson , p. 3. 104 105 16Ibid.. p. 9. 17Ibid., p. 10. 18Ibid.. p. 17. 19Ibld, . p. 23. 20 Ibid.. p. 32. ^I bid.. p. 23. 22Ibld., p. 32. 23Ibid.. p. 41. ^Wing, p. V. OK Ibid., p. 1. 26lbid., p. 5. 27Ibid., p. 6. 28lbid.. p. 14. 29Ibid., p. 63. 30 Ibid.. pp. 62-64. 31Ibid.. p. 66. 32 Charlie Q. Cbffman, "State of Mississippi Enrollment Trends in Higher Education." Board of Trustees of Institutions of Higher Learning, Jackson, Mississippi, 1972. 33 Ccranittee on Enrollment Planning Maximums. Report of the Oaqnittee on Enrollment Planning Maximum Report, (Unpublished report/) Springfield, 111.: Illinois Board of Higher Education, 1972. 34 L. J. Lins, Methodology of Enrollment Projections for Colleges and Universities, Washington, D.C.: AACkAiO c/o The American Council on Edncation, 1960. 35 Terre Meier and Sherie Story, Washington Cbnmunity Colleges Piaotbook: Olympia, Washington State Board for Ocmnunity Cbllege Education, 1979. 106 36Robert D. Newton, Projections of Student Flow In the Pennsyl­ vania State University System, University Park, Pennsylvania: Office of Vice-President for Planning, Pennsylvania State University, 1969. 37 Elaine L. Tathara and Harold L. Finch, "Enrollment Forecasting Techniques," Overland Park, Kansas: Johnson County Comninity Col­ lege, 1975. 38 Jerry Banks and C. L. Hoehenstein, "Conceptual Models and Procedures far Predicting Higher Education Enrollment," Presented at 38th National QRSA Meeting, Detroit, Michigan, October 28-30, 1970. 39 Educational Research and Services Corporation, Migration of Students To and From New Hampshire, Bedford, New Hampshire, (n.d.) 40 Colby H. Springer and Michael J. Strumwasser, Nebraska Enroll­ ment Projection System, An Overview, Los Angeles, California: Systems Research, Inc., 1972. 41 Ronald B. Thompson, Projected Enrollments, Colleges and Universities, Commonwealth of Kentucky, 1972-1&85, Frankfort, Kentucky: Cbmnission on Higher Education, 1972. 42 Benjamin K. Gold, "Acadenic Performance of Los Angeles City College Transfers Entering the University of California: A Twelve Year Stannary, 1966-78," Los Angeles: Los Angeles City College, 1979 43 Stephen A. Johnston and Hazel R. Jolley, "North Carolina Cbmnunity College System Operating Program, 1975-1980," Durham, N. C.: Research Triangle Institute, 1975. 44 Agnes MartinK©, "Success of Transfer Students in Pennsylvania" Harrisburg: Pennsylvania State Department of Education, 1978. 45 Jeanne Smith, "Enrollment Data and Future Projections: Oglala Sioux Ocmmnit;y College," Pine Ridge, N. D.: Oglala Sioux Oomnunity Cbllege, 1978. 46Francis J. Degnan, An Estimate of the Total Ful1-Time Under­ graduate Cbllege Population of Connecticut Residents and a Projec­ tion of Enrollments for Higher Education in Connecticut Based upon This-Estimate, Hartford, Connecticut: Connecticut Coamission for Higher Education, 1970. 47 Raul H. Hasell, Jr., et at, "A conceptual Formulation of a System of Student Flow Models far Head Count Enrollment and CreditHour Production Estimates," (Unpublished Paper.) University, Ala-., bama: Department of Computer Science and Operations Research, University of Alabama, 1972. 107 48 James J. Prestage, "Preliminary Pburteen-Year Enrollment Estimations for Twenty-foor Public and Private Institutions of Higher Education, State of Louisiana," Baton Rouge, Louisiana: Louisiana Coordinating Council for Higher Education, 1972. 49 "U.S. Bureau of Census Higher Education Forecast," Washington D. C. : American Cbuncil on Education, 1972. 50R.M. Oliver, "Models for Predicting Gross Enrollments at the University of California," Report No. 68-3, Berkeley, California: Fbrd Foundation Research Program in University Administration, University of California, 1968. 51 John F. Zinmer, "Projecting Enrollments in a State Cbllege System," Proceedings of the Eleventh Annual Forum on Institutional Research, (1 Mayl7-20, 1971, Denver. Colorado), Seattle, Washington, w t :— 52 Richard J. Petersen and Carolyn R. Staith, Migration of College Students, Washington, D.C.: National Center for Education Statis­ tics, 1976. 53 Ralph A. Purves, "California Demographic Trends and Enroll­ ments in Higher Education," (Unpublished paper.) Berkeley, Cali­ fornia: University of California, 1971. ^Robert L. Gell and Others, "Tentative Ten-Year Enrollment Projections: Fiscal Years 1977-1986.: Rockville, Maryland: Montgomery Cbllege, 1975. ^Mathernatica, Enrollment and Financial Aid Models for Higher Education, Bethesda, Maryland, 1971’ 56Elaine L. Tatham and Harold L. Finch, "A Computer Model for Demographic Projections- in Educational Planning," Overland Park, Kansas: Johnson County Conxmnity Cbllege, 1974. 57 Otis Dudley Duncan, "Path Analysis: Sociological Examples," American Journal of Sociology, Vol 72, (1966). 58 New York State Education Department, Enrollment Projections 1968-80, NYS Higher Education, Albany, New York: Office of Planning in Higher Education, 1968. 59 J. E. Jewett, Cbllege Aflnissions piannir.tr- Use of a Segmen­ tation Model. Berkeley, California: Ford Foundation Program for Research in University Administration, Office of Vice-President Planning, University of California, 1972. 60New York State Education Department, EnmllmRnt..Projections 1968-80, NYS Higher Education, Albany, New York: Office of Plan­ ning in Higher Education, 1970. 108 C-J Jerome Evans, "Methods and Procedures far Projecting Enroll­ ment in Higher Education in California," Sacramento, California: Coordinating council for Higher Education, 1980. 62 Jbhn F. Zininer, "An Evaluation of Four Methods of Enrollment Projection as Applied to a State Cbllege System," (Unpublished Ph.D. dissertation.) University of Minnesota, 1969. Qrwig, Paul K. Jones, and Oscar T. Lenning, "Projecting Freshman Enrollment in Specific Academic Departments," Proceedings of the Eleventh Annual Forum on Institutional Research (May 17-20, 1971, Denver, Colorado), Seattle, Washington, 1971. Chapter Til: Design of the Study ^Jbhn A. Centra, Cbllege Enrollment in the 1980's: Projection and Possibilities, Princeton, New Jersey: Cbllege Entrance Examlnation Board, 1978, p. 51. 2Dave V. Glass and Julian C. Stanley, Statistical Methods in Education and Psychology, Englewood Cliffs, New Jersey: PrenticeHall, Inc., 1970, p. 61. ^Robert Brown, Smoothing, Forecasting and Predication of Discrete Time Series, New York: Prentice-Ha.il, 1963, p. 99. 4 Steven C. Wheelwright and Spyros Makridakis, Forecasting Methods Far Management, New York: John Wiley and Sons, 1973, p. 36. ^Brown, p. 104. ^Wheelwright, p. 36. 7 Ibid., p. 41. 8rhid., p. 24. B I B L I O G R A P H Y BIBLIOGRAPHY Jerry Banks and C. L. Hoehenstein, "Conceptual Models- and Procedures for Predicting Higher Education Enrollment, " Presented at 38th National QFSA Meeting, Detroit, Michigan, October 28-30, 1970. Robert Brown, Staoothing, Forecasting and Prediction of Discrete Time Series. New York: Prentice-Hall, 1963. John A. Centra, College Enrollment in the 1980*s: Projection and Possibilities, Princeton, New Jersey: College Entrance Examination Board, 1978. Charlie Q. Cbffman, "State of Mississippi Enrollment Trends in Higher Education." Board of Trustees of Institutions of Higher Learning, Jackson, Mississippi, 1972. Ccmnittee on Enrollment Planning Maximums. Report of the Cbnmittee on Enrollment Planning Maximum Report, (unpublished report.) Springfield, 111.: Illinois Board of Higher Education, 1972. Francis J. Degnan, An Estimate of the Total Full-Time UnderGractuate College Population of Connecticut Residents and a Pco.lec^ ~ tion in Connecticut Based upon Connecticut Cbmnission for Higher Education, 1970. Otis Dudley Duncan, "Path Analysis: Sociological Examples," American Journal of Sociology, Vol_72, 1966. Educational Research and Services Corporation, Migration of Students To and From New Hampshire, Bedford, New Hampshire, (n.d. ) Jerome Evans, "Methods and Procedures for Projecting Enrollment in Higher Education in California," Sacramento, California: Coor­ dinating council for Higher Education, 1970. Keith Gave, "L.C.C. Tab: September, 2, 1979. $," The lansing State Journal, Robert L. Gell and Others, "Tentative Ten-Year Enrollment Projections: Fiscal Years 1977-1986.: Rockville, Maryland: Montgomery Cbllege, 1975. Dave V. Glass and Julian C. Stanley, Statistical Methods in Education and Psychology, Englewood Cliffs, New Jersey: PrenticeHall, Inc., 1970. 110 Ill Benjamin K. Gold, "Academic Performance of Los Angeles City College Transfers Entering the University of California: A Twelve Year Stannary, 1966-78," Los Angeles: Los Angeles, City College, 1979. Clive ff. Granger, Investigating the Future: Statistical Forecasting Problems, Nottingham, England: The University Press, 1567! D. Kent Halstead, Statewide Planning In Higher Education, Washington, D.C., U.S. Printing Office, 1974. Paul H. Hasell, Jr., et al, "A Conceptual Pormulatior of a System of Student Flow Models for Head Count Enrollment and CreditHour Production Estimates," (unpublished paper.) University, Alabama: Department of Computer Science and Operations Research, University of Alabama, 1972. J. E. Jewett, College Admissions Planning: Use of a Segmen­ tation Model, Berkeley, California: Ford Foundation Program for Research in University Administration, Office of Vice-President Planning, University of California, 1972. Stephen A. Johnston and Hazel R. Jolley, "North Carolina Community Cbllege System Operating Program, 1975-1980," Durham, N. C.: Research Triangle Institute, 1975. L. J. Lins, Methodology of Enrollment Projections for Colleges and Universities, Washington, D.C.: AACRAO c/o The American Council on Education, 1979. Wayne L. Mangleson, et al., Projecting College and University Enrollments: Analyzing the Past and Focusing the Future, Ann Arbor, Michigan, Center for the Study of Higher Education, 1973. Agnes Martinko, "Success of Transfer Students in Pennsylvania." Harrisburg: Pennsylvania State Department of Education, 1978. Mathematics., Enrollment and Financial Aid Models for Higher Education, Bethesda, Maryland, 1971. Terre Meier and Sherie Story , Washington Comnunity Colleges Factbook: Olympia, Washington state Board for Cannunity Cbllege Education, 1979. New York State Education Department, Enrollment Projections 1968-80. NYS Higher Education. Albany, New York: Office of Planning in Higher Education, 1968. 112 Robert D. Newton, Projections of Student Flow in the Pennsylvania State University System, University Park, Pennsylvania: Office of Vice-President for Planning, Pennsylvania State University, 1969, R. M. Oliver, ''Models for Predicting Gross Enrollments at the University of California,11 Report No. 68-3, Berkeley, California: Ford Foundation Research Program in University Administration, University of California, 1968. M. D. Qrwig, Paul K. Jones, and Oscar T. Lenning, "Projecting Freshman Enrollment in Specific Academic Departments," Proceedings of the Eleventh Annual Foran on Institutional Research (May 17-20, l9?l, Denver, Colorado), Seattle, Washington, 1971. Richard J. Petersen and Carolyn R. Staith, Migration of College Students, Washington, D.C.: National Center for Education Statistics, 1976. James J. Prestage, "Preliminary Fourteen-Year Enrollment Estimations for Ttoenty-four Public and Private Institutions of Higher Education, State of Louisiana," Baton Rouge, Louisiana: Lousiana Coordinating Cbuncil for Higher Education, 1972. Ralph A. Purves, "California Demographic Trends and Enrollments in Higher Education," (unpublished paper.) Berkeley, California: University of California, 1971. Jeanne Staith, "Enrollment Data and future Projections: Oglala Sioux Cbmnunity Cbllege," Pine Ridge, N.D.: Oglala Sioux Cannunity College, 1978. Colby H. Springer and Michael J. Strumwasser, Nebraska Enroll­ ment Projection System, An Overview, Los Angeles, California: Systems Research, Inc., 1972. Elaine L. Tatham and Harold L. Finch, "A Computer Model for Demographic Projections in Educational Planning," Overland Park, Kansas: Johnson County Cannunity College, 1974. Elaine L. Tatham and Harold L. Pinch, "Enrollment Forecasting Techniques," Overland Park, Kansas: Johnson County Cbmnunity College 1975. Ronald B. Thompson, Projected Enrollments, Colleges and Universities, Gonmonwealth of Kentucky, 1972-1985, Frankfort, Kentucky: Commission on Higher Education, 1972. U. S. Bureau of Census Higher Education Forecast," Washington D. C.: American Council on Education, 1972. Steven C. Wheelwright and Spyros Makridakis, Forecasting Methods Far Management, New Ybrk: John Wiley and Sons, 1973. 113 Paul Wing, Higher Education Enrollment Forecasting, Boulder, Colorado: National Center for Higher Education Management Systems, 1974. John F. Zinroer, "An Evaluation of Fbur Methods of Enrollment Projection as Applied to a State College System," (unpublished Ph.D. dissertation.) University of Minnesota, 1969. John F. Zimner, "Projecting Enrollments in a State College System," Proceedings of the Eleventh Annual fbrum on Institutional Research. (May 17-20, 1971, Denver. Colorado), Seattle. Washington. 1971.