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(:1: ... , '3...) 5111.? 4015,, 1"” LIBRARY MK N Michigan State University This is to certify that the dissertation entitled ASSESSING THE IMPACT OF WEATHER VARIABILI'IY ON LEISURE TRAVEL USING MICHIGAN HIGHWAY TRAFFIC presented by CHARLES JINYEN SHIH has been accepted towards fuifillment of the requirements for the Doctoral degree in Park, Recreation, and Tourism Resources 8 mm Major Professor's Signature Aqqost 2b , 2009 1.1 Date MSU is an Affirmative Action/Equal Opportunity Employer _. —.—.-n_n-I-l-l-t-O-l-l-l-I-I-t-l-l-I--I-D-I-I-l-I-O-l-l-I-l—O-n--I-o-v-O-l-I-l-O-l-‘-l-l-0-I-O-l-l-I-l- PLACE IN RETURN BOX to remove this checkout from your record. To AVOID FINES return on or before date due. MAY BE RECALLED with earlier due date if requested. DATE DUE DATE DUE DATE DUE 5/08 K:IProj/Acc&Pres/CIRCIDaIeDue.indd ASSESSING THE IMPACT OF WEATHER VARIABILITY ON LEISURE TRAVEL USING MICHIGAN HIGHWAY TRAFFIC By Charles J inyen Shih A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Park, Recreation, and Tourism Resources 2009 impa. role ir Iowarc climatc measun levels 01 II excluding EXpIanatc and precip temporal V; mOdeIs ofa‘ identified 35 across Michi (IOUUSI static; across locatio; tourism traffic dunné’ Winter. ABSTRACT ASSESSING THE IMPACT OF WEATHER VARIABILITY ON LEISURE TRAVEL USING MICHIGAN HIGHWAY TRAFFIC By Charles Jinyen Shih The primary purpose of this study was to construct statistical models to assess the impact of weather variability on travel activity. Weather condition plays an important role in making many leisure and tourism activities feasible and enjoyable, and a trend towards a warming climate has been recognized. Nevertheless, research on weather, climate and leisure travel has been relatively lacking, especially studies involving measuring of the quantitative relationships between weather variation and participation levels of leisure travel. In this study, daily Michigan highway traffic counts from eighteen stations, excluding commercial truck traffic, were used to represent leisure travel activities. Explanatory variables in the models include weather conditions (maximum temperature and precipitation), economic conditions (Consumer Confidence and gasoline prices), and temporal variables controlling for the availability of leisure time. After testing regression models of different functional forms on a single traffic station, the double-log model was identified as the best fitting model. This model was then applied to other traffic stations across Michigan. Modeling results indicated that for stations dominated by leisure traffic (tourist stations), the effects of weather variability on leisure traffic were consistent across locations. Particularly, temperature had a positive effect on fluctuations in daily tourism traffic during spring, summer, and fall, while precipitation had a negative effect during winter. In separate approaches, a threshold temperature was discovered for acadl IOIHI maul can b< [flaunt larch. changn summer with the use of the spline function. The models for studying lagged effects of weather yielded inconsistent results. The findings of this study had both theoretical and managerial implications. For academic research, results of this study can be incorporated with future climate scenarios to investigate long-term implications of climate change on the leisure travel industry. For practical purposes, information of how weather conditions impact daily business volume can be useful to tourism managers for guiding day-to-day operations. For tourism planners and developers, understanding the effects of weather variability on activity levels is beneficial in making mid- to long-term planning decisions in order to adapt to a changing climate. comp sincer Niche researl Holecc‘ student commi' Roy BI. guided many IC Wife for ACKNOWLEDGEMENTS Without the encouragement and support provided by a few individuals, the completion of this dissertation would not have been possible. I would like to express my sincere gratitude to my advisor and chairperson of the dissertation committee, Dr. Sarah Nicholls, for her continuous insights, support, and patience throughout completion of this research. I am also deeply grateful to my former academic advisor, Dr. Donald F. Holecek, for his long time support and encouragement throughout my study as a doctoral student. A special thank you is extended to the other members of my dissertation committee. Dr. Christine Vogt provided insights in Michigan tourism industries while Dr. Roy Black provided his knowledge in econometrics and methodology, both of which guided me through completion of this dissertation. I owe my greatest thanks to my parents, who supported me unconditionally for many long years to work towards finishing my degree. Finally, I would like to thank my wife for her support and sacrifice during the course of my study. iv LIS LIS Chaj Intrc Chapt Rene Chap] MEIIN TABLE OF CONTENTS LIST OF TABLES ..................................................... vii LIST OF FIGURES ..................................................... ix Chapter 1 Introduction ........................................................... 1 Study Objectives and Hypotheses ................................. 2 Summary of Procedures ........................................ 4 Definitions of Key Terms ....................................... 6 Contribution and Significance ................................... 7 Limitations and Delimitations ................................... 8 Overview of the Dissertation .................................... 9 Chapter 2 Review of Literature ................................................... 11 Leisure Travel and Tourism Demand ............................. 11 Time-Series Approach .................................... 12 Causal Approach: Regression Methods ....................... 12 Determinants of Tourism Demand ........................... 13 Demand for Individual Destinations .......................... 14 Impact of Weather and Climate on Leisure Travel ................... 15 Weather Variability and Tourism ............................ 16 Climate Change and Tourism ............................... 21 Studies Employing The Tourism Climatic Index (TCI) ........... 25 Studies of Climate Change and the Ski Industry ................ 26 Indirect Impacts of Climate Change .......................... 27 Highway Traffic and Tourism ................................... 28 Review of Regression Approach ................................. 29 Hypothesis Testing ....................................... 30 Modeling Performance .................................... 31 Assumptions and Violations ................................ 31 Regression Functional Forms ............................... 32 Spline Function .......................................... 34 Lagged Approach ........................................ 34 Summary of Literature Review .................................. 34 Chapter 3 Methodology ...................................................... 37 The Study Area ............................................... 37 The Conceptual Model ........................................ 39 Selection of Variables .................................... 39 Model Specification ........................................... 49 Model Comparison and Evaluation ............................... 53 Comparing Regression Models against the Naive Method ......... 55 Applying Selected Model to Multiple Stations ...................... 56 Other Approaches to the Study of Weather and Tourism Traffic ........ 57 Chapter 4 Results ........................................................... 59 Regression Analysis for Five Functional Forms ..................... 59 Spring Model ............................................. 60 Summer Model ........................................... 62 Fall Model .............................................. 64 Winter Model ............................................. 66 Relative Importance of Independent Variables ................... 68 Checking Regression Assumptions ............................ 70 Identifying the Most Efficient Model .............................. 78 Applying the Selected Model to Multiple Stations ................... 79 Effect of Weather Variability on Traffic across Tourist Stations ..... 81 Further Testing of Weather’s Effect on Traffic ...................... 87 Chapter 5 Summary and Conclusions ........................................... 89 Summary of the Study ......................................... 89 Findings of Hypothesis Testing .................................. 90 Weather Variables ......................................... 90 Economic Variables ........................................ 92 Temporal Variables ........................................ 93 Evaluating and Comparing Models ............................... 93 Applying the Best Fitting Model ................................. 95 Modeling Threshold Temperature and Lagged Effects ................ 95 Comparison with Existing Studies ................................ 96 Implications and Applications .................................. 98 Theoretical Implications .................................... 98 Managerial Implications .................................... 100 Suggestion for Future Research ................................. 102 Appendix: Regression Results of Traffic Stations ....................... 105 References ...................................................... 122 vi Table l. Sur 2. Sun 3. Ave 4. Wei 5. DCSI 6. Top 7. List 8. Loca LIST OF TABLES Table Page 1. Summary of Existing Weather and Tourism Literature ........................ l8 2. Summary of Existing Climate and Tourism Literature ........................ 22 3. Average Monthly Weather Conditions Comparison (1971-2000) ................ 38 4. Weighting System for North-South Bounds Leisure Traffic .................... 40 - 5. Descriptions and Expected Signs of Independent Variables .................... 43 6. Top Ten Michigan Destinations for AAA Michigan Members .................. 51 7. List of Functions and Variables in Regression Analysis ....................... 51 8. Locations of Selected Michigan Traffic Stations ............................ 56 9. Regression Analysis Results for Spring Traffic Models ...................... 61 10. Regression Analysis Results for Summer Traffic Models ..................... 63 11. Regression Analysis Results for Fall Traffic Models ........................ 65 12. Regression Analysis Results for Winter Traffic Models ...................... 67 13. Partial and Standardized Coefficient Estimates of Quadratic Regression Models . . .69 14. Multicollinearity and Serial Correlation Diagnostics for Linear Models .......... 71 15. Multicollinearity and Serial Correlation Diagnostics for Double-log Models ...... 72 16. Comparison of forecasting Accuracy of Regression Models ................... 79 17. Comparing Forecasting Accuracy (MAPE) between. Regression and Naive Models .......................................... 79 18. Model Performance of Tourist Stations ................................... 8O 19. Locations of Non-tourist Traffic Stations ................................. 81 vii 20. Multiple l 21. Comparis 22. Studies Ir Weather 2 Id 3. Variation ‘chlcssim ‘ RCQTCSSIUr \r (4.) {/1 PU (3 (I) w (I f“ .4 _. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. Multiple Regression Models with Lagged Weather Variables ................. 88 Comparison of Expected and Actual Signs of Coefficient Estimates ............ 91 Studies Involving Quantitative Relationships between Weather and Leisure Travel ............................................ 97 Variations in July Tourism Traffic Based on Temperature Scenarios ........... 101 Regression Results for Station # 1089 ...................................... 105 Regression Results for Station # 1109 ...................................... 106 Regression Results for Station # 1189 ...................................... 107 Regression Results for Station # 2049 ...................................... 108 Regression Results for Station # 3069 ...................................... 109 Regression Results for Station # 3129 ...................................... 1 10 Regression Results for Station # 4149 ...................................... 1 1 1 Regression Results for Station # 5229 ...................................... 1 12 Regression Results for Station # 5249 ...................................... 1 13 Regression Results for Station # 6049 ...................................... 1 14 Regression Results for Station # 6129 ...................................... 1 15 Regression Results for Station # 6469 ...................................... 1 l6 Regression Results for Station # 7309 ...................................... 1 l7 Regression Results for Station # 8209 ...................................... 1 18 Regression Results for Station # 8249 ...................................... 1 l9 Regression Results for Station # 9829 ...................................... 120 Regression Results for Station # 9849 ...................................... 121 viii Figure 1.FlowChe L.) . Major Tr: ~’ 1‘. Map of \l 4. Average 1 5. C (imparts Station =~ 6. Average j 7. Residual 8. Residual 9. Percent C 10‘ Percent l in TCmp ”- Pflcent l 111 Temp 1“ Precip LIST OF FIGURES Figure Page 1. Flow Chart Illustrating the Organization of the Study ........................ 5 2. Major Travel Routes and Locations of Traffic Stations in Michigan ............ 41 3. Map of Weather Stations .............................................. 44 4. Average Non-Holiday Traffic Counts by Day of Week for Station #4129 ........ 46 5. Comparison of Traffic Counts Between Holidays and Non-Holidays for Station #4129 ..................................................... 47 6. Average Non-Holiday Daily Traffic Counts by Season for Station #4129 ....... 50 7. Residual Plots for Linear Models ........................................ 74 8. Residual Plots for the Double-log Models ................................. 76 9. Percent Change in Daily Traffic Associated with l-degree Increase in Temperature during Spring for Tourist Traffic Stations .................... 83 10. Percent Change in Daily Traffic Associated with l-degree Increase in Temperature during Summer for Tourist Traffic Stations .................. 84 11. Percent Change in Daily Traffic Associated with l-degree Increase in Temperature during Fall for Tourist Traffic Stations ...................... 85 12. Percent Change in Daily Traffic Associated with l-degree Increase in Precipitation during Winter for Tourist Traffic Stations ................... 86 ix tourisn weathe accum' 1973LI playing change attracti Climate (IHIErg been 31 Chapter 1 Introduction Weather conditions often play important roles in travelers’ participation in tourism and recreation activities. Many recreation activities require specific sets of weather conditions to make them possible or enjoyable. For example, adequate snow accumulation and low air temperatures are needed for skiing (Crowe, McKay and Baker, 1973; Scott, McBoyle and Mills, 2003). Likewise, rainfall can deter vacationers from playing water sports on the beach or simply make road conditions less desirable to travel. From a supply perspective, long-term climate trends and the possibility of climate change are critical to tourism businesses because such change can affect the attractiveness of an area as a travel destination. There is increasing evidence regarding climate change that suggests global trends towards rising temperatures and sea levels (Intergovernmental Panel on Climate Change (IPCC), 2007). Consequently, there have been an increasing number of studies on the impact of climate change on recreation and tourism in recent years, with an emphasis on describing the long-term implications of climate change for the tourism industry. However, to empirically investigate the long- term impact of climate change on the tourism industry, quantifiable relationships between historical weather variability and participation levels first need to be established. It is this kind of fine scale research, targeting relationships between levels of tourism activity and short-term variations in weather conditions, that is particularly lacking. Problem T1 weather v relationshi tourism int Purpose of The conditions 0 future resear adaptation st ability {0 m0 business Ope This 5 weather Variz forms Were C l'fihicle COUm conditions. a. this Study fOC multiple IOCat “'eaiher Van’ a] Problem Statement The problem addressed in this study is that the quantitative relationships between weather variability and tourism activities are not understood. Knowledge of these relationships is crucial for studying future, long-term impacts of climate change on the tourism industry. Purpose of Study The main purpose of this study is to estimate the effects of variation in weather conditions on tourism activities. The results of this study can serve as a foundation for future research concerning the long-term implications of climate change as well as adaptation strategies for the tourism industry. In addition, the findings demonstrate the ability to model daily variation in participation levels, with implications for tourism business operators who may utilize this information for planning and staffing purposes. Study Objectives and Hypotheses This study employed two major steps in an attempt to assess the effects of weather variability on leisure travel. First, regression models with different functional forms were constructed for a single highway traffic station. Specifically, daily highway vehicle counts were regressed against independent variables including weather conditions, economic conditions, and the availability of leisure time. The second part of this study focused on identifying the best fitting model, which was then applied to multiple locations. The ensuing discussion was focused on understanding the impacts of weather variability on leisure traffic volume across the study area. Object travel Q1165 "aria Obie Iraye ”Tana The following objectives and hypotheses were identified to frame the study: Objective 1: To construct adequate regression models to explain variation in daily leisure travel activity for a single, sample traffic station Hypothesis 1.1: Variations in maximum temperature has a positive effect on daily leisure traffic volume. Hypothesis 1.2: Variations in precipitation has a negative effect on daily leisure traffic volume. Hypothesis 1.3: Variations in economic conditions have positive effects on daily leisure traffic volume. Hypothesis 1.4: Variations in gas prices have negative effects on daily leisure traffic volume. Hypothesis 1.5: Variations in the availability of leisure time have positive effects on daily leisure traffic volume. Hypothesis 1.6: The volume of leisure traffic increases overtime Question 2.1: What form of regression model is the best fitting model for explaining variation in daily traffic volume? Hypothesis 2.1: Regression models with nonlinear forms are better fitting models than those with linear forms for explaining variation in daily leisure traffic. Objective 3: To examine the quantitative relationships between weather variability and travel activity across different geographical areas, with an emphasis on day-to-day management and longer term planning and development implications weather represei collecte are not : Ordinar collects nanons Other it Indextt categol. fimeav Year, an “'88 als‘ of mod:— Jul): AL Februar- l filhcriOU Hypothesis 3.1: Effects of variations in weather conditions on travel activity differ across multiple locations Summary of Procedures Figure 1 illustrates the procedures employed in this study to assess the impacts of weather variability on tourism activities. Daily highway traffic volume was used to represent travel activity in the state. Twelve years of daily records of vehicle counts were collected from eighteen traffic stations. Commercial truck counts were excluded, as they are not relevant to leisure travel. Multiple regression models were constructed using the Ordinary Least Squares (OLS) approach. Twelve years of weather data were also collected, consisting of daily maximum temperatures and precipitation from the recording stations closest to the traffic stations so as to best represent local weather conditions. Other independent variables including gasoline prices and the Consumer Confidence Index (CCI) were entered as relevant economic factors in the models. In addition, categorical variables such as weekends and holidays are created to account for leisure time availability across days of the week and holiday periods. Another dummy variable, year, an annual time trend variable that takes the value of the year of a given data point, was also included in the model. To account for the effect of seasonality, the construction of models was segmented by four seasons: spring (March, April, May), summer (June, July, August), fall (September, October, November), and winter (December, January, February). Five different functional forms, including linear, exponential, and quadratic functions, were first tested on a single traffic station. Performance of the models was Figure Figure 1 Flow Chart Illustrating the Organization of the Study evaluate (MAPE values v volume. stations. estimate emphasi explorec conditio lr reader. Climate Ci alerage a months to refers IO Ii. phenOm €112 Occuf Ol'er Climate CI. ACCC evaluated and their efficiencies were compared using the Mean Absolute Percent Error (MAPE) method, a measure of forecasting accuracy. Functional forms with lower MAPE values were considered more efficient statistical models in determining leisure travel volume. The model with the lowest MAPE was then applied to the other seventeen traffic stations. The modeling results, including explanatory power (R-square) and coefficient estimates, were examined and compared across different regions of the state, with an emphasis on identifying regional patterns. Additional modeling approaches were also explored, including lagged weather variables to test the delayed effect of weather conditions and a spline function to test the existence of a threshold temperature. Definitions of Key Terms In this section, key terms employed throughout the study are defined for the reader. Climate Climate is the description of the long-term pattern of weather, defined as the average weather for a particular region over a specified period of time ranging from months to millions of years, with the classical definition being thirty years. Climate often refers to the averages of precipitation, temperature, humidity, sunshine, wind velocity, phenomena such as fog, frost, and hail storms, and other measures of the weather that occur over a long period in a particular place (IPCC, 2007). Climate Change According to the IPCC (2007, p. 30), climate change refers to “a change in the state of the climate that can be identified (e. g. using statistical tests) by changes in the or!" natu “HIT ax'er". globe Clim sets 0 explic Clima given . Climalt “'eath (minUl: temper; Ice Bat. and Ciim mean and/or the variability of its properties, and that persists for an extended period, typically decades or longer. It refers to any change in climate over time, whether due to natural variability or as a result of human activity.” The same report also pointed out that warming of the climate system is unequivocal, backed by evidence of increasing global average air and ocean temperatures, widespread melting of snow and ice, and rising global sea levels. Climate Change Scenarios Climate change scenarios refer to representation of future climate that is based on sets of climatological relationships (IPCC, 2007). They are typically constructed for explicit use as input to climate change impact models. Climate Variability The term "climate variability" refers to deviations of climate statistics over a given period of time (such as a specific month, season or year) from the long-term climate statistics relating to the corresponding calendar period (IPCC, 2007). Weather Weather refers to the day-to-day state of the atmosphere, and its short-term (minutes to weeks) variation. Weather is commonly thought of as the combination of temperature, humidity, precipitation, cloudiness, visibility, and wind (National Snow and Ice Data Center, 2009.) Contribution and Significance The findings of this study enable further understanding of the effect of weather and climate variability on levels of participation in leisure travel. Specifically, the cor stan leisu the p. leisure planne day 0pc applied as camp. 0n partic decisions j Limitatio Th reETCSSIOn and IelSUre EXCeed the IISES abO’t'e that time “'1 the depende] commercial 1 da Ia and “en contribution of this study can be divided into two categories. From an academic standpoint, this study revealed quantitative relationships between weather variability and leisure travel on fine temporal and spatial scales, both of which had rarely been studied in the past. Such information is crucial in projecting long-term impacts of climate change on leisure travel. From the practical perspective, findings of this study can help tourism planners and business managers understand how weather variation affects their day-to- day operation. Also, the statistical models identified in this study can be duplicated and applied to other locations, destinations, or individual sectors of the tourism industry such as camping or skiing. Results of those models represent the effects of weather variation on participation levels, which can help tourism practitioners make planning and staffing decisions. Limitations and Delimitations Limitations This study had several limitations. First, coefficient estimates generated by the regression models indicated the quantitative relationships between explanatory variables and leisure traffic. However, this is based on the assumption that the variable does not exceed the range of the observed data. For example, if the maximum summer temperature rises above 100°F in the year 2050, the effect of temperature variation on leisure traffic at that time will likely not be the same as the one generated by models in this study. Second, the dependent variable, daily highway traffic records, had been treated to exclude commercial truck traffic. However, commuter and local traffic were still embed in the data and were regarded as a baseline that remained the same. This assumption may cause tuasc eniplt relate especi treatht l)ehrni ouunde nflafion finding: Iermim t0 Ciima 3.5 Wind DOIinclL Consequ. i“trodUctl Change. It empIOE’Ed bias or inaccuracy in modeling results in some cases. Moreover, leisure traffic was employed to represent the level of general tourism activity. Therefore, one cannot directly relate the findings of this study to weather's effects on individual tourism sectors, especially since weather's influence on different leisure activities may vary (e. g., warmer weather is good for camping but bad for skiing). Delimitations There were also issues related to weather, climate, and leisure travel that were outside the scope of this study. The focus of this study was on examining the current relationships between weather conditions and leisure travel activity. Therefore, the findings of this study did not provide answers to questions such as “what are the long term impacts of climate change on tourism,” although an example of application related to climate change was presented in the final chapter. Also, other weather variables such as wind chill and humidity may impact variations in tourism traffic. They were, however, not included in the study, primarily due to data availability. Their effects were consequently not captured in the models. Overview of the Dissertation This dissertation was divided into five chapters. The first chapter provided an introduction to the study. The second chapter reviewed the literature relevant to climate change, weather variability, and tourism. The third chapter described the methods employed in this study, including data sources, variable definitions, and a theoretical review of different modeling techniques. In the fourth chapter, the results of the models were prese study and c for future r. were presented. Finally, the last chapter summarized and interpreted the findings of the study and discussed potential implications and applications of these findings. Suggestions for future research were also stated. 10 Tl review is articles re on those e drive touri this study: The; forecasting. industry to L tourism pro( and anticipai unfilled dem Usually prod 1 aPPTOPIIale SI demand for t such as extre Project impa and revenue filtute dema: Chapter 2 Review of Literature This chapter reviews existing research that is relevant to the present study. The review is presented in four parts. First, literature on travel demand is discussed. Second, articles related to weather, climate (change) and leisure travel are examined, with a focus on those employing quantitative methods. Past studies involving highway travel and self- drive tourism are then reviewed. Finally, regression approach and their issues related to this study are examined. Leisure Travel and Tourism Demand There has been extensive research focused on tourism demand modeling and forecasting. Frechtling (2001) argued that it is especially important for the tourism industry to understand and project demand for its products for several reasons. First, the tourism product is perishable, which “puts a premium on shaping demand in the short run and anticipating it in the long run, to avoid both unsold inventory on one hand and unfilled demand on the other” (Frechtling, 2001, p.5). Second, the tourism product is usually produced and consumed at the same time and in the same place, requiring the appropriate supply of personnel available when and where visitors need them. Third, demand for tourism is very sensitive to natural and human-induced events and disasters such as extreme weather conditions, war, and disease outbreaks. Therefore, the ability to project impacts of such events can help minimize their adverse effects on tourism sales and revenue. Finally, tourism planning and investment requires a long lead-time, so future demand must be anticipated correctly to avoid financial loss from excess supply as 11 \sellz outer rexie‘ 'Tinie \vhie prod] (Fret extra sintp relat patte prev flOre: Efflll Call: Whe: bent relat well as lost earning opportunities due to unfulfilled demand. In the following paragraphs, different approaches to modeling tourism demand are discussed and related studies are reviewed. Time-Series Approach One common method in travel demand research is the time-series approach, which assumes that “the course of a variable, such as tourism demand, over time is the product of a substantial number of unknown forces that give the series a momentum” (Frechtling, 2001 , pg. 58). In this approach, historical data and their patterns are used to extrapolate future patterns. The advantage of the time series approach is that it is usually simple to apply, since it requires only a single series of data. However, any casual relationships are ignored in this approach. In tourism demand studies, time series models are often applied in examining patterns of inbound and outbound visitors for specific countries or large regions. Many previous studies have focused on the methodologies and techniques associated with forecasting international travel demand using time-series models (Kulendran and Witt, 2001; Song and Wong, 2003; Li, Song and Witt, 2005.) Causal Approach: Regression Method Another major approach to studying travel demand is the use of causal modeling, whereby regression analysis is applied to mathematically identify causal relationships between so called “explanatory variables” and an “outcome variable.” The advantage of this approach over time series modeling is the ability to portray cause-and-effect relationships, which is crucial in certain situations, for example, when management wants 12 to under. have on ' time con employer between approach Determin .\l to measur These fac existing lj Lim 1999 Inc (GDP) or] tourism tie the most ir mOdels, 31'] Lim (1999) this Study, 1' only ax-attai measure 0ft to understand how much impact a tourism policy or an increase in advertising budget will have on travel demand (Frechtling, 2001). These models are, however, more costly and time consuming to construct than time series models. In this study, the causal approach is employed since the main purpose is to examine the cause-and-effect relationships between weather variability and leisure travel. More details regarding regression approach will be presented in a later section of this chapter. Determinants of Travel Demand Many studies of international tourism demand have employed regression models to measure the effect of factors such as income, travel cost, price, and demographics. These factors have been found to have different levels of impacts on demand within the existing literature (Crouch 1994; Matteo and Matteo, 1996; Smeral, 1988; Lagos, 1999; Lim 1999). Income in the origin country, often measured by national gross domestic product (GDP) or per capita income, has been found to have a positive effect on international tourism demand. Crouch (1994) reviewed previous research and claimed that income is the most important factor and provides the greatest explanatory power in regression models. Similarly, a meta-analysis of international tourism demand studies conducted by Lim (1999) indicated that international tourism demand is positively related to income. In this study, income effect is not directly measured by variables such as GDP, which is only available quarterly or annually. Instead, Consumer Confidence Index (CCI), a measure of current economic conditions, is utilized to capture the income factor. 13 pnces. smdms mfltm Lng increas increas mnfle tneasur Ibelack iDHUem— marketi. impact ( zealand COHsider constTue T ICfer IO a (Smeral, Another important determinant in tourism demand studies is price. Using the consumer price index (CPI), relative prices for tourism goods and services between origin and destination countries can be calculated. Lim (1999) suggested that results from most studies support the proposition that tourism demand is negatively related to tourism prices. Transportation cost is another determinant included in some tourism demand studies. Matteo and Matteo (1996) examined cross-border travel volume between Canada and the US and argued that visitation is negatively affected by the ratio of Canadian to US gasoline prices. However, Osula and Adebisi's (2001) examination of the impact of increasing gasoline prices on tourism expenditures in Nigeria concluded that the price increase, a result of changing energy policy, had not had an adverse effect on domestic travel expenditure. This study employs the weekly average Michigan gas prices to measure the effect of price effect on travel activity. Marketing is an important factor that few studies have estimated, possibly due to the lack of quantifiable data (Crouch, 1994). Indeed, only one study incorporating this influence was located. This analysis by Crouch, Schultz, and Valerio (1992) revealed that marketing expenditure by the Australian Tourist Commission had a significant, positive impact on tourism demand from five origin countries: the United States, Japan, New Zealand, the United Kingdom, and Germany. Marketing is not an explanatory variable considered in this study since these one-time events would be difficult to measure in the construction of daily models. There are other factors that can influence tourism demand. Demographics, which refer to age structures and educational background, may also affect travel demand (Smeral, 1988). Crouch (1994) suggested that trends and fashion in travel behavior can 14 be factors int takes on the factors. Demand for In ad on specific si visits to CS n while the £051 on the impact Canyon .\'atio Significantlyc Was not signil AS mt accepted in t1 te“Illerature byl998.201 recent IPC(' 30 yeafS fro be factors influencing tourism demand. The current study employs a Year variable, which takes on the year of the data point, in an attempt to capture demographics and trends factors. Demand for Individual Destinations In addition to international tourism demand, other demand studies have focused on specific sites and destinations. Johnson and Suits (1983) examined the demand for visits to US national parks. The findings showed that the effect of income was mixed, while the cost of gasoline had a negative impact on park visits. Morgan (1986) focused on the impact of energy crises and rising transportation costs on visitation to Grand Canyon National Park. The results indicated that the number of visits dropped significantly during the two crisis periods of 1973-1974 and 1979; however, visitation was not significantly affected by rising transportation costs during the same periods. Impact of Weather and Climate on Leisure Travel As mentioned in Chapter 1, a trend towards a warming climate is generally accepted in the scientific community. In the instrumental record of global surface temperature (since 1850), the year 2008 was the tenth warmest year on records, exceeded by 1998, 2005, 2003, 2002, 2004, 2006, 2001, 2007 and 1997 (Jones, 2009.) The most recent IPCC assessment report (2007) also reveals that the linear warming trend over the 50 years from 1956 to 2005 (013°C per decade) nearly doubles the IOU-year trend from 1906 to 2005 (0.074 °C per decade). Nevertheless, the discussion of the impact of climate change on the tourism industry remains somewhat lacking, despite continued calls for 15 area I e especi existin Summ. climate weathe regardir divided Weathe TEIaIIOng MCBQy] from f“. that Ski 2 Ski 5338c t6chn010 53350113 the Clem a both dom “wage t: greater attention to this issue (e.g., Butler 2001; Hall and Higham 2005). This is especially evident from the fact that neither Crouch's (1994) nor Lim's (1999) reviews of existing travel demand studies mentioned weather as a determinant of tourism demand. Summary of Existing Literature A summary of existing research focused on the direct impacts of weather and climate (change) on tourism is presented in Tables 1 and Table 2. Literature regarding weather variability and tourism (Table 1) will be discussed first, followed by research regarding climate change and tourism (Table 2). In each table, previous studies are divided into those from a demand perspective and those from a supply perspective. Weather Variability and Tourism As demonstrated in Table 1, only one study addressing the supply side of the relationship between weather variability and leisure travel was discovered. Scott, McBoyle, Mills and Wall (2001) employed 17 years of daily snow condition records from five ski areas to model climate variability and length of ski season. Results suggest that ski areas with more preferable ski conditions do not necessarily have longer average ski seasons, likely due to differences in business models. Also, the use of snow making technology can mitigate the effects of warming temperatures to prolong the length of ski seasons. There are a few more studies that examine weather variability and tourism from the demand perspective. In two of these studies, the impacts of weather variability on both domestic and international travel demand are investigated. Lise and T01 (2002) used average temperature for the warmest month and average precipitation in summer to 16 in in Th int: u‘ftr} espe Palut L'K. r tempe partici model precipit nationa‘ another Variabili 311d 10in 10 reveal Precipitat abOVe ma because it "We recer \VeatheY CO investigate weather’s influence on annual international visitation for eight countries, including Canada, France, Germany, Japan, Italy, Netherlands, the UK, and the USA. Their main conclusion was that climate, especially temperature, is important to international travelers. In fact, the ideal temperature was found to be around 21°C (70 °F), which implied that climate change could have strong effects on tourism demand, especially in terms of shifts in popular destinations and peak seasons. Agnew and Palutikof (2001) examined both annual and quarterly international tourist arrivals to the UK, the Netherlands, Germany, and Italy, using average temperatures. The optimal temperature was also estimated to be 21 °C (70°F) for summer travelers. There are several other studies that focus on the effect of weather variability on participation levels for specific leisure activities. Loomis and Crespi (1999) attempted to model the effect of lift ticket costs, gasoline prices, income, temperature, and precipitation on participation in downhill and cross—country skiing (as measured by national data on skier days). However, the modeling results were “unsatisfactory.” In another study, Mendelsohn and Markowski (1999) examined the implications of climate variability on skiing activity in the United States based on annual, state-level data. Linear and loglinear regression of climate, income, and population data on activity levels failed to reveal significant relationships between ski activity and winter temperatures or winter precipitation. The primary reason for the inconclusive findings of the studies described above may be their use of aggregate, large scale data, both in temporal and spatial senses, because weather conditions can vary drastically from place to place and day to day. 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[ dECreaSe AleHOn djSCOVEre SignjfiCan alternate d significant impacts on daily lift ticket sales. In another empirical study, Nicholls, Holecek, and Noh (2009) examined the impact of weather variability on levels of golfing activity and concluded that variations in maximum temperature and precipitation have statistically significant influences on daily rounds of golf played. Brandenburg and Amberger (2001) studied impacts of several weather measures on daily visitation to a national park in Vienna, Austria. The regression analysis also included specific user groups. The authors concluded that the day of the week has the greatest influence on the number of visitors. They also found that the Physiological Equivalent Temperature (PET), a thermal comfort index incorporating air and body temperatures, has a major impact on the number of total daily visitors as well as on cyclists and hikers. Precipitation and cloud cover were found to have a moderate influence on visitor numbers. Another study by Meyer and Dewar (1999) investigated the effect of rainfall on daily visitor numbers for a visitor center inside New Zealand's Westlands National Park. A dynamic model was used to measure the effect of rainfall on visitation over time. The study found that rainfall had a relatively small effect on visitor numbers in comparison to holiday seasonality. Also, rainfall on a given day is associated with an increase in visitor numbers on the same day, perhaps due to more visitors seeking shelter. However, the lagged effect of rainfall was found to be negative, resulting in a decrease in visitor numbers two days later, likely a result of visitors leaving the area. Alberton and Aylen (2005) investigated numbers of daily visitors to an English zoo and discovered that rainfall had a negative impact on visitation while temperature had no significant impact. A possible explanation of this finding is that visitors simply find an alternate date to visit during rainy weather while their decision is not affected by 20 more I infrast l L’Nll’ impacts Climate and OUIdt Weather V 1.ml-lllcatio. temperature variation, perhaps due to lack of significant variation in temperature in the study area. Climate Change and Tourism Direct and Indirect Impacts of Climate on Tourism There are two major categories of impacts associated with climate, weather and tourism activities: direct and indirect impacts. A UNWTO report (2008) refers to direct climatic impacts as geographic and seasonal redistribution of climate resources for tourism, and changes in operating costs. In addition, there are also climate-induced secondary effects, mainly the impacts of potential environmental change as a result of climate change, which can have profound impacts on tourism. One example is the coastal erosion caused by sea level rise, one implication of climate change. This can lead to loss in biodiversity and diminishing resources for coastal tourist destinations such as the Outer Banks of North Carolina. Another example is that climate change is projected to result in more extreme weather events such as hurricanes, which can cause damages to infrastructure and loss in revenue in tourism-dependant areas in Florida and Louisiana (UNWTO 2008). The following discussion will focus on existing research on direct impacts of weather and climate on tourism, while studies related to indirect impacts of climate change will be reviewed in a later section. As shown in Table 2, the number of studies of the relationships between climate and outdoor recreation and tourism is higher than that of those addressing short-term weather variations. 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This rating system was originally developed with the purpose of assessing the climatic elements that most affect the quality of the tourism experience, especially for international tourism. More recently, the TCI has been applied in several studies to examine the implications of climate change, where the index, representing the attractiveness of a region's or nation's climatic resources, are projected under various climate change scenarios. In one study, Scott, McBoyle, and Schwartzentruber (2004) applied the TCI to investigate the long-term implications of climate change for North American cities as travel destinations. The findings showed that cities in Canada and the northern US. could become more competitive against the southern US. and Mexico as winter vacation destinations. Similar methods were also applied to the cases of the Mediterranean (Amelung & Viner, 2006), northwest Europe (Nicholls & Amelung, 2008), and worldwide destinations (Amelung, Nicholls, & Viner, 2007). The findings of these studies reveal potential shifts in seasonality resulting from climate change. For example, the authors suggest that the peak season for Mediterranean tourism could shift toward spring and fall, while Northern Europe will likely become a more attractive destination in summer. The main advantage of the TCI is that besides commonly used weather variables such as air temperature and precipitation, it also incorporates aesthetic (i.e., cloud cover) and physical (i.e., thermal comfort) facets of weather conditions that are related to the tourism experience. However, the TC I is usually calculated only for larger regions 25 unit brea Ell‘é‘t impc pore: Studi recrez toufis make potent distinc Scon. Abe _ 00 (I3 Seconc limpact: Se&80n. panlep ofproj't‘t because it was originally designed to study international tourism and it is based on large units of analysis (grid squares of several hundred square kilometers in length and breadth). This prohibits the examination of extreme weather conditions and also the finer effect of weather variability. Also, studying climate change with the TCI omits other important factors such as economic conditions (e. g., price, transportation cost) and potential changing demand for tourism activities. Studies of Climate Change and the Ski Industry Several studies associated with weather and tourism focused on individual recreation or tourism sectors. The most heavily researched activity is by far skiing, an tourism activity that relies heavily on specific weather and environmental conditions to make participation both feasible and enjoyable. The studies to date addressing the potential impacts of climate change on the ski sector have tended to be focused on two distinct themes. First, they have concentrated geographically on the North American (e. g. Scott, McBoyle, and Mills 2003; Scott et a1. 2006) and European (e.g., Koenig and Abegg 1997; Breiling and Charamza 1999; Elsasser and Bfirki 2002) ski markets. Secondly, they have adopted an almost exclusively supply-side approach, addressing impacts from the perspective of likely changes to snow cover, the length of the ski season, and/or to the number of skiable days, rather than actual changes in demand for participation in winter sports on the part of skiers. The studies conducted have consistently demonstrated the negative implications of projected climate change for the skiing industry. For example, the length of the ski season at the Horseshoe Ski Resort in southern Ontario, Canada, is projected to decline 26 b§‘l var ana ELM fiau preci Chan; Cond; 56350 Indne by between 1% and 21% by the 20503 and by between 4% and 39% by the 20803, the variation in decline being accounted for by the climate change scenario employed in the analyses (Scott, McBoyle, and Mills 2003). Research conducted on skiing areas in the European Alps has revealed similarly negative implications. Koenig and Abegg (1997) found that, while 85% of all Swiss ski areas are currently snow reliable (defined as experiencing at least 100 days per season with sufficient (i.e., 30 cm) snow cover), only 63% will remain snow reliable given a temperature rise of 2°C. In an Austrian context, Breiling and Charamza (1999) demonstrated the particular vulnerability of lower-altitude ski resorts to warming conditions. Galloway (1988) investigated the potential impacts of two climate change models on three ski resorts in Australia and projected declines in snow season length from 130 to 60 days, 135 to 60 days, and 81 to 15 days, respectively, assuming an increase in average winter temperatures of 2°C and a decrease in precipitation of 20%. Most of the analyses described above have not incorporated changing demand for, and participation in, skiing as a result of changing climatic conditions. Rather, they have solely focused on supply factors such as snow reliability, season length, and number of skiable days. Indirect Impacts of Climate Change As mentioned earlier, there are also studies that focus on the secondary impacts of climate change. A UNWTO (2008) report revealed that several tourist destinations listed as World Heritage Sites are identified as vulnerable to environmental change caused by a warming climate, including Venice, Italy, affected by sea level rise, and Waterton- Glacier International Peace Park, affected by glacier retreat. Agnew and Viner (2001) 27 C“ an: des ('20 will I‘Epo] traVe sunf- Mich 1' trangp fOCUSii (2003, frameun CharaCte examined ten popular tourist destinations around the world and pointed out potential negative impacts associated with climate-induced environmental change, ranging from coastal erosion in the Americas, to reductions in air quality for large metropolitan cities, to deterioration of the Great Barrier Reef and the Amazon. Another type of indirect impact is the effect of mitigation policies. Policies that seek to reduce greenhouse gas (GHG) emissions are likely to have an impact on tourist flows, since they “will lead to an increase in transport costs and may foster environmental attitudes that lead tourists to change their travel patterns (e. g., shift transport mode or destination choices)” (UNWTO, 2008, p 29). A study by Gossling, Peeters, and Scott (2008) argued that increases in aviation travel cost, a result of climate mitigation policies, will negatively affect tourism development in ten tourism-dependent island countries. Highway Traffic and Tourism Driving is the most common mode of transportation for domestic US travelers. A report by the American Automobile Association (2008) estimated that 81 % of all travelers traveled by automobile during the Thanksgiving holiday in 2008. According to a survey of Michigan pleasure trip travelers (Holecek et al., 2000), close to 94% of Michigan travelers use some type of personal vehicle as their primary mode of transportation during their trips. There has been a fair amount of existing literature focusing on the subject of self-drive travel and highway traffic. Prideaux and Carson (2003) recognized that research regarding self-drive tourism is lacking. A research framework was proposed with emphases on destination description, visitor characteristics, access, distance, visitor flows, and accommodations. There are also 28 stud di ffc did! info! that ‘ BIU’BI main l data 2 l Yang highv exam identi “‘0 Var studies regarding highway visitor centers. One study (Stewart, 1993) compared the differences between travelers who stopped at highway welcome centers and those who did not. F esenmaier (1994) surveyed travelers who visited Illinois' highway visitor information centers and examined how they utilized the facility. The findings indicate that the “tourist visitor center acts as one of the most important channels with which to attract and educate travelers about benefits of visiting the state” (F esenmaier, 1994, p.50). Databases containing detailed highway traffic records are usually kept and maintained in most states, mainly for transportation planning purposes. However, such data are very seldom included in tourism research. Of the few available, one example is Yang and Holecek's (1997) investigation of the effectiveness of using average daily highway traffic in monitoring travel activity in Michigan. In another study, Yang (2001) examined daily and hourly highway vehicle counts across the state of Michigan and identified the flows of highway travelers throughout the state. A formula was developed in an exploratory attempt to distinguish leisure or tourism traffic from routine highway traffic. In this study, daily highway traffic records in Michigan were used to represent the volume of leisure travel, and commercial truck traffic was excluded to obtain more leisure-related traffic volume. Review of Regression Approach Regression approach is used to explain relationships between variables. Consider two variables y and x , which represents some population. The purpose of the regression analysis is to “explain y in terms of x” or to study “how y varies with changes in x” (W ooldridge, 2003, p.22). The relationships discovered in the regression analysis can 29 w] 1h: dat.‘ min poir. \‘alu assm CONS! “We The F ofrejfl the ind, (wow “hath 93013 8185 also be used to predict or forecast the dependent variable. A basic linear regression function can be specified as F Bx + 8 where y, the depdendant or outcome variable, is a random (stochastic) variable, while x, the independent or explanatory variable, is a fixed (nonstochastic) variable. B is the estimated coefficient that depicts the relationship between x and y, and e is a random error term (Pindyck & Rubinfeld, 1998; Hamilton, 1992). In regression analysis, Ordinary Least Squares (OLS) is a commonly used method of fitting linear models to data. The least squares criterion in regression generates a “best fitting line” that minimizes the sum of squared distances between the actual data points and the predicted points on the straight line. The error terms are the differences between the predicted values and actual values of the dependent variable, and regression error terms are assumed to be uncorrelated with each other, normally distributed with zero mean and constant variance. Hypothesis testing Results of regression analysis provide several key statistics for hypothesis testing. The F statistic is a measure for testing the overall significance of the model. The failure of rejecting the null hypothesis for the F test will mean there is no evidence that any of the independent variables in the regression model can help explain the outcome variable (Wooldridge, 2003). Standard T statistics are useful for testing the hypothesis that whether each coefficient estimate ([3) is significantly different than zero. The standard errors associated with B estimates are also important measures, since they represent 30 \V 31! prc ext an . Rut the 1 the e diff: Squa 2003 the vi Shun, are big Standa: (1095 n( whether the estimates are likely to be accurate. Smaller standard errors indicate more accurate estimates (Neter, Wasserman & Whitmore, 1993). Model Performance The statistic of R square, or the coefficient of determination, represents the proportion of the variance of the outcome variable that can be explained by the explanatory variables (Hamilton, 1992). The values of R square range from 0 to l, with an R square closer to one indicating a better goodness of fit of the model (Pincyk & Rubinfeld, 1998; Hamilton, 1992). One drawback of using R square to evaluate regression models is that R square is sensitive to the number of independent variables in the model, and it is likely to increase with the addition of more independent variables to the equation (Pindyct & Rubinfeld, 1998). When comparing regression models with different number of independent variables, one widely used statistic is the adjusted R square, which imposes penalty for adding additional independent variables (Wooldridge, 2003). Assumptions and Violations There are several requirements and assumptions associated with regression, and the violations of these conditions result in invalid or inaccurate parameter estimates. Multicollinearity occurs when two or more explanatory variables in the regression model are highly correlated. This violation results in unreliable parameter estimates and standard errors (W ooldridge, 2003). For forecasting purposes, however, multicolliearity does not cause special problems as long as the predictions are made within the range of 31 ind: peri CBUS exist 1993. that s (Ham errors discot a widc~ l998), Regres are “inl be exph sample observations on the independent variables (Neter et al., 1993). Examining correlation coefficients or tolerance values are common procedures of checking multicollinearity. Specifically, correlation coefficients larger than 0.9 or tolerance values lower than 0.1 are signs of collinearity between independent variables (Hamilton, 1992). Another assumption of regression models is that the error terms a, are independent from period to period. In some cases, however, the error terms in different periods are correlated, which is called autocorrelation or serial correlation. One major cause is the omission of one or more key variables from the regression model (Neter et al., 1993). Although the least squares regression coefficients are still unbiased with the existence of autocorrelation, the standard errors tend to be underestimated (Neter et al.; 1993). One measure of checking autocorrelation is the use of Durbin-Watson test. Heteroscedasticity is the term describing violation of a requirement of regression that specifies the variance of errors has to remain constant across different levels of x (Hamilton, 1992; Neter et al., 1993). This violation results in untrustworthy standard errors and test statistics (Hamilton, 1992). The existence of heteroscedasticity can be discovered by examining the residual plots, and the method of “weighted least squares” is a widely used technique to correct for the nonconstant variance (Pindyck & Rubinfeld. 1998). Regression Functional Forms Linear regression model can be applied to a more general class of equations that are “inherently linear” models (Pindyck & Rubinfeld, 1998). Inherently linear models can be expressed in a form that is linear in parameters by transforming the variables. 32 (Tc \K'l‘; fhn posi deer lead caH (D mOde “here Wllh n Consider the polynomial model Y: BI + l32x+l53X2 + 8 where the relationship between y and x2 is nonlinear. Specifically, y is a quadratic function of x2, and the test of nonlinearity is provided by the standard t test of the null hypothesis that B3=0. Quadratic functions are ofien used in applied economic models to capture decreasing or increasing marginal effects (Wooldridge, 2003). In the equation above, if both B2 and B3 are positive, it means x has a positive impact on y, and each unit of increase in x results in a rise in y at an increasing rate. On the other hand, if B2 is positive but B3 is negative, y initially increases as x increases, although y increases at a decreasing rate. It eventually reaches a turning point, after which a further increase in x leads to decrease in y. The turning point also provides the maximum value of y, ofien called the optimal value. There are other forms that can become linear in parameters with the application of log transformation. Because of its special mathematical property of turning multiplication into addition, logarithms can be used to linearize seemingly nonlinear models for estimation of parameters by OLS (Hamilton, 1992). For example, a nonlinear exponential model has the form y= aeB" + s where e = 2.71828. . ., the base number of natural logarithms. Applying transformation with natural log, Ln(y) = Ln(a)+ Bx + Ln(s) B can then be estimated with OLS. 33 mai 3113 di ff Spline Function In measuring the impacts of weather variability on leisure traffic, the relationship between temperature and traffic volume is expected to be positive, since travelers generally prefer warmer weather conditions. However, it is also possible that a threshold temperature exists where the weather becomes so hot that a fiirther rise in temperature results in a decrease in tourism traffic. Instead of dividing the dataset into subsamples, a “spline function” is suggested (Greene, 2002) to estimate these distinct effects while maintaining the continuity of the model. Incorporating the spline fimction into regression analysis, the threshold values, also called “knots”, can be identified, and coefficients in different segments of the data range can be estimated. Lagged Approach In time series models a substantial period of time may pass between the economic decision-making period and the impact of a change in a policy variable. In this case, lagged explanatory variables should be included in the model (Pindyck & Rubinfeld, 1998). For example, one might specify consumption Ct to be a function of disposable income lagged one quarter Yt-.. The specification of a models’ lag structure thus is a function of the time units of the data. Also, the number of lags to include in the equation can be determined from theory (Pindyck & Rubinfeld, 1998). Summary of Literature Review While travel demand has been studied extensively, particularly with respect to the demand for international tourism, weather and climate conditions have not often been 34 dé he _. U; ex thi in' quz act tou lon We: Van Chn stud data Sen: t0un \‘an'a ”Her; considered in those studies. In fact, neither Crouch's (1994) nor Lim's (1999) reviews of the existing travel demand literature mentioned weather as a determinant of tourism demand. Scott, McBoyle, and Mills (2003, p. 180) argued, “The current understanding of how recreational users and tourists respond to climate variability is very limited,” and “additional research on the impacts of climate change for recreation and tourism demand is required.” Further, though there have been more studies in recent years aiming to examine the implications of climate change for the tourism industry, most research on this subject has focused on supply rather than demand and participation, as demonstrated in Table 2. Among those studies examining climate and leisure travel, even fewer yield to quantifiable relationships between past weather/climate variability and levels of travel activities, which are essential for projecting the future impacts of climate change on tourism demand. Also shown in Table l, the majority of existing research has employed longer-term, aggregate climate data (i.e., yearly or longer) rather than monthly or daily weather records. Since weather conditions change constantly, studies employing variables with finer temporal scales are needed in order to understand the impact of climate variability on tourism demand. Lise and To] (2002, p.431) argued that existing studies on tourism demand are mostly based on annual time series, and “usage of yearly data does not capture the volatile character of the tourism sector; even the length of time series cannot compensate for this.” This study employs daily weather conditions and tourism traffic, which enables the examination of the impacts of climate and weather variability on tourism activities on finer temporal and spatial scales. Hall and Higham (2005, p. 12) suggested that the reasons for the relative lack of interaction between climate and tourism research until recently may include a “relative 35 res CO] proc meth Stud} lack of baseline data” and “methodological difficulties in undertaking relevant analysis.” The statistical models developed in this study provided efficient tools for studying climate and tourism. Also, findings of this study, specifically quantitative relationships between weather variability and tourism activities, can serve as baseline data for fiiture research regarding climate change and the tourism industry. Thus, this study will contribute to filling the urgent need to better understand the relationships between climate variability and leisure travel. In this chapter, research methods used to achieve the objectives of the study are presented. The chapter contains five main sections. First, it describes the study area, Michigan, with the emphasis on background information pertaining to climate and tourism in the state. Second, the conceptual model and multiple regression approach are discussed, including the selection of variables and sources of data on which the study was based. The third section specifies the five regression functions tested on vehicle counts fiom a sample traffic station. Fourth, methods of comparing results from the five models and identifying the best fitting model are discussed, followed by presenting the procedures of applying the best fitting model to multiple traffic stations. Finally, other methods for examining impacts of weather variability on tourism as employed in this study are described. 36 tel E 51gb I! .ill Jlllu-‘l. 16] Tc bil 19 At has 1e“ Chapter 3 Methodology The Study Area Records of highway traffic volume, the dependent variable, were collected from eighteen traffic stations across Michigan, the study area. The state of Michigan is located in Midwest and surrounded by four of the five Great Lakes: Lake Erie, Lake Huron, Lake Michigan and Lake Superior. Michigan borders Ohio, Indiana, Wisconsin, and Ontario of Canada. The climate of Michigan has four well-defined seasons, with warmer temperatures and longer frost-free period in the southern part of the state and colder temperatures and a shorter growing season in northern regions (City Data, 2007). Tourism, one of the state’s leading industries, contributes annually an estimated $18.1 billion to the state’s economy, generates $874 million in state taxes, and accounted for 192,000 jobs statewide (Michigan Economic Development Corporation, 2008). According to a report on Michigan travel market (DK Shifflet & Associates, 2003), The majority of Michigan leisure travelers are residents (57%), while most non-resident travelers come from neighboring states such as Illinois (9%). Ohio (6%), and Indiana (3%). The same report also estimated the participation rates for popular activities among Michigan travelers: dining (26%), shopping (26%), entertainment (25%), sightseeing (19%), and beach/waterfront activities (14%). A major advantage the selection of Michigan as the study area was that Michigan has a wide range of weather variability across the year. In Table 3, average monthly temperatures and precipitation of Michigan were compared to those of the continental 37 . . I! ubfl¢ .! . ll! lIli dil 681 3C1 are 31k US. The average annual temperature of Michigan (44.4°F) during the time span was lower than the US. average (52.7°F). However, Michigan’s monthly temperature had a wider variation. Its coolest monthly temperature was 18.9°F in January, and its warmest monthly temperature was 68.3°F in July, representing a 49.4°F difference. In comparison, the coolest monthly temperature for the continental US. was 30.8°F in January, and the warmest monthly temperature was 74°F in July, 3 43.2°F difference. Michigan average annual climate was slightly wetter than the US. average. The driest monthly for Table 3. Average Monthly Weather Conditions ComLarison (1971-2000) Month JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC ANNUAL Temperature (°F) Michigan 18.9 21.4 30.7 42.6 54.5 63.6 68.3 66.5 58.6 47.6 35.7 24.6 44.4 Continental US. 30.8 35.4 43.2 51.8 60.9 69.2 74 72.6 65.1 54.3 42.3 33.4 52.7 Precipitation (Inches) Michigan 2.02 1.45 2.22 2.69 2.94 3.23 3.15 3.58 3.65 2.85 2.74 2.28 32.79 ContinentalU.S. 2.27 2.04 2.59 2.44 3.01 2.92 2.79 2.65 2.58 2.29 2.4 2.23 30.21 Source: National Climate Data Center (N C DC) Michigan was February (1.45 inches), while the wettest month was September (3.65 inches), indicating a difference of 2.2 inches in precipitation. For the US, the driest month was also February (2.27 inches), and the wettest month was July (2.79 inches), a difference of 0.52 inches. The wider range of data for Michigan provided an advantage in estimating the effects of weather variability on participation levels of leisure travel. Another strength of Michigan as the study area was the variety of leisure travel activities offered across seasons. Especially, many popular leisure activities in Michigan are weather dependent, such as skiing relying on snowfall and low temperature, and golf and beach activities can be affected by temperature and rainfall. Therefore, overall leisure travel volume should be sensitive to the variation of weather conditions. 38 .\. St 7} Hi mt in; -‘ O( .5 Pro Ofl The Conceptual Model The basic hypothesis of this study was that the fluctuation of daily non- commercial traffic volume in Michigan depends on three major factors: weather conditions, economic conditions, and the availability of leisure time. The model was specified as follows: Daily T raffle Volume = f( Weather, Economy, Leisure Time) The approach of multiple regression with Ordinary Least Squares (OLS) was employed. Multiple regression enables the examination of causal relationships between explanatory and dependent variables because of the notion ceteris paribus — which means other factors being equal. This allows the explicit control for other relevant factors that simultaneously affect the dependent variable. For example, results of regression analysis can be interpreted as the effect of weather variability on travel activity while holding other independent variables such as economic conditions and time constant. Selection of Variables The Dependent Variable - Highway T raffic Highway traffic volume, which was considered in this study to represent general travel activity, was selected as the dependent variable. As mentioned in the previous chapter, most Michigan visitors travel by car. Thus, non-commercial traffic volume was regarded in this study as a proxy for the volume of leisure travel. In total, twelve years (1991- 2002) of daily records of highway traffic counts for eighteen traffic stations were provided by Michigan Department of Transportation (MDOT). The routes and locations of the stations were mapped in Figure 2. Daily records of vehicle counts were 39 SC r. .. ‘5 b 2\. IE IIC St di 8\ ax ‘4': tr: bidirectional, either north-south bounds or east-west bounds, depending on the directions of the highway on which a station was located. Frequency tests on bidirectional traffic by week revealed a special pattern for north-and-south bounds stations. On average, more northbound traffic was recorded than southbound traffic during Fridays, while more southbound traffic was recorded than northbound traffic on Sundays. There were no significant differences discovered for counts on other days of the week. This was possibly because leisure travelers who utilize north-south highways tended to leave home in southern part of Michigan for vacation on Friday and then return on Sunday. To better represent the flows of leisure travelers, a “weighting” system was used by taking the northbound traffic on Friday as Friday traffic and southbound traffic on Sunday as Sunday traffic, as shown in Table 4. For the rest of the week, the averages of both directional counts were used. This pattern was not discovered in east-west stations so the averages of directional counts were used as leisure traffic for those stations. Also available from MDOT was a dataset of “class counters,” automatic traffic counters that were able to detect vehicle size. Using this information, percentages of commercial truck traffic were then estimated and subsequently eliminated from the dataset, as such traffic Table 4. Weighting System for North-South Bounds Leisure Traffic Monday Tuesday Wednesday Thursday Friday Saturday Sunday Leisure (N+S)/2 (N+S)/2 (N+S)/2 (N+S)/2 N (N+S)/2 S Traffic N= northbound; S= southbound 40 Figure 2. Major Travel Routes and Locations of Traffic Stations in Michigan Legend _ Highway Routes A Traffic Stations Scale 1 inch equals approximately 50 miles 41 “1 U1 was not typically related to leisure activity. There were two main benefits of using highway traffic as the dependent variable. First, detailed and accurate records of daily vehicle counts kept by MDOT allowed the examination of the effect of weather variability on leisure travel on a fine temporal scale — i.e., via the construction of daily regression models. Second, traffic counts were available for multiple locations across the state of Michigan, making it possible to compare and examine modeling results from a geographic perspective. Depending on the concentration of recreational sites and tourism destinations, models for some traffic stations may perform better than models for other locations. Since explanatory variables included in the study were meant to represent factors influencing levels of leisure activities, models for stations in urban areas may perform poorly due to the high concentration of commercial and commuter traffic. Similarly, unsatisfactory modeling results may occur for stations in rural areas that lack popular tourism destinations. The number of stations employed in this study allowed for these kinds of variations to be investigated. Explanatory Variables Table 5 illustrated the temporal resolution, unit of measurement and source of each of the independent variables employed in this study. The expected sign on each parameter estimate was also stated. Maximum Temperature — Daily maximum temperature was one of the main weather variables employed in this study. Since the highest temperature of a day is usually 42 lll-giiawfi. .p’ i. .0- Table 5 Descriptions and Expected Signs of Independent Variables Variables Temporal Unit Source Expected Sign Resolution of Coefficient Estimate Weather Maximum Temperature Daily °C National Weather Positive Service Precipitation Daily Millimeter National Weather Negative in Service Spring, Summer, and Fall; Unsure in Winter Economic Consumer Confidence Monthly Index Point Conference Board Positive Gas Price Weekly Dollar American Automobile Negative Association Leisure Time Friday or Sunday Daily N/A N/A Positive Saturday Daily N/A N/A Positive First or Last Day of Daily N/ A N/A Positive Holiday-weekend Middle of Holiday- Daily N/A N/A Positive weekend Singe-day Holiday Daily N/A N/A Positive Year Annual N/A N/A Positive N/A indicates not applicable registered during daytime, when most vacationers participate in leisure activities, daily maximum temperature was thus selected as an explanatory variable over daily minimum or average temperature. It was initially hypothesized that maximum temperature had a positive effect on traffic, since most visitors prefer warmer weather conditions. The potential of a temperature threshold was discussed later in the chapter. Daily maximum temperatures from 1991 to 2002 were obtained for eight weather stations across Michigan: Bad Axe, East Jordan, Greenville, Ironwood, Lake City, Marquette, Pontiac and Sault Ste Marie, as displayed in Figure 3. For each traffic station, its regression 43 Figure 3. Map of Weather Stations Sault Ste. Marie Marquette ‘ East Jordan A Lake City A Greenvill A Eau Claire 44 Bad Axe A Pontiac C: it DE C t“ models included weather data from the weather station closest to the traffic station since that station represented the most relevant local weather conditions influencing traffic volume in the area. Precipitation — Daily precipitation, which included both liquid (rain) and solid (snow) deposits, was the other weather variable included in the models. Records of daily precipitation were obtained from the same weather stations for the same time frame as daily maximum temperatures. It was expected that the impact of precipitation on traffic was negative during spring, summer, and fall, since rainfall hinders most outdoor recreation activities and worsens driving conditions. During the winter season, however, the effect of precipitation was not as clear, since snowfall could have a positive effect on the feasibility and demand for winter sports such as skiing and snowmobiling but could also reduce accessibility to winter leisure travel sites. Consumer Confidence Index (C CI) — The monthly CCI is a measure of current economic conditions generated by the Conference Board. Regional CCI data, based on surveys of five Midwestern states, including Illinois, Indiana, Ohio, Michigan, and Wisconsin, were applied to estimate the relationships between economy and travel volume. It was hypothesized that a higher index leads to higher visitor volume since people are more likely to travel or travel more frequently under better economic conditions. Gasoline Price - Gasoline price was an explanatory variable that represented transportation cost in the regression models. Weekly gas prices were obtained from the Michigan American Automobile Association (AAA). To adjust for the inflation factor, 45 11 Fi Sour gas prices were deflated using the Consumer Price Index (CPI) provided by the Bureau of Labor Statistics. The expected effect of gas prices on traffic was negative, since a higher price was likely to cause visitors to cutback on traveling, while a lower price was expected to encourage visitors to travel. Time — Besides the continuous explanatory variables described above, it was necessary to set up categorical or dummy variables to control other factors such as the availability of leisure time and annual trends. Results of descriptive analysis of non- holiday daily traffic for Station #4129 (located on US-127 near Clare, Michigan) showed that traffic counts on Friday and Sunday were much larger than those on Monday through Thursday (Figure 4). Counts on Saturday were on average higher than Monday through Figure 4. Average Non-Holiday Traffic Counts by Day of Week for Station #4129 9000 8000 7000 6000 5000 4000 Vehicle Counts 3000 2000 I 000 0 Monday Tuesday Wednesday Thursday Friday Saturday Sunday Day of Week Source: MDOT 46 Thursday, although lower than Friday and Sunday. A likely reason for this traffic pattern was that travelers to northern Lower Michigan often took weekend trips to the region, during which they departed on Friday, stayed in the area on Saturday, and returned home on Sunday. Similarly, Figure 5 suggested that traffic on the first and the last day of a holiday weekend (e. g., the Friday and Monday of a Labor Day weekend) was higher than during the middle of a holiday weekend (e. g., the Saturday and Sunday of a Labor Day weekend), which was in turn higher than Monday through Thursday. For those single-day holidays such as the Fourth of July and New Year’s Day when they fell in the middle of the week (i.e., Tuesday, Wednesday, Thursday), higher traffic volume was recorded on the particular holiday, but not the day prior or after the holiday. To best control the weekend and holiday factors based on these observed traffic patterns, dummy variables Figure 5. Comparisons of Traffic Counts Between Holidays and Non-Holidays for Station #4129 10000 ' 9000 8000 7000 A 6000 5000 4000 7 3000 , 2000 1000 ~ 0 Vehicle Counts Non-Holiday Beginning or End Middle of Single-Day Weekday of Holiday- Holiday- Holiday VVeekend VVeekend Source: MDOT 47 th 0\ Di IV; IOI Car in the model included 'Friday and Sunday,‘ 'Saturday' (when they are not connected with a holiday), 'First or Last Day of a Holiday-weekend,‘ 'Middle of a Holiday-weekend,’ and 'Single-day Holiday.‘ Another dummy variable, 'Year,‘ an annual time trend variable that took the value of the year of a given data point, was included in the model to account for factors such as changes in demographics, population, and other trends and preferences over the time frame of the dataset. Other Variables Considered but Not Included There were other explanatory variables that were relevant to tourism traffic but they were not included in the regression models for a variety of reasons. Since daily models were constructed to examine the finer effect of weather variability on tourism, data that were measured by shorter time periods (e. g., daily or weekly) were preferred over those only available in longer temporal resolution (e. g., quarterly or annually). Gross Domestic Product (GDP), a commonly used economic indicator in travel demand studies, was only reported by quarter. Automobile ownership cost, a dataset that could influence tourism traffic, was provided on an annual basis. These data were therefore not included in the regression models. Also, weather variables such as wind chill and heat index were possible factors influencing leisure travel. They were, however, not tested in the regression models due to data availability issues. In traditional travel demand studies, factors such as marketing or promotional campaigns and the construction of new facilities are usually accounted for in regression models since these events can result in significant changes in participation levels. This is usually done by including dummy variables. For example, the particular dummy variable would take on the value of zero for the year before the event and the value of one for the 48 Vi 3? S. be 56 th: I11: W: ter We: Stat: year afier the event. For this study, in which daily models are constructed, however, the inclusion of such one-time events would be less appropriate due to the lack of variation in the variables, as well as the potentially substantial number of events which would need to be taken into consideration across the long time frame and large geographic area under analysis. Seasonality Average daily vehicle counts were found to vary across the four seasons, as can be seen in Figure 6. Therefore, four separate models were constructed for the four seasons: spring (March, April, May), summer (June, July, August), fall (September, October, November), and winter (December, January, February). One advantage of establishing four seasonal models was that it enables the examination of differences in the effects of the explanatory variables on traffic across different seasons. For instance, the magnitude of the impact of temperature on travel volume during summer, when the weather was typically consistently warm, may differ fi'om its impact during fall, when the temperature fluctuated more dramatically. Model Specification Prior to application to the entire set of traffic stations, five different forms of regression models were first tested on ten years of daily vehicle counts from a traffic station located on highway US-127 near Clare, Michigan. US-127 is one of the major 49 lis thi Pei 63C Figure 6 Average Non-Holiday Daily Traffic Counts by Season for Station #4129 7000 6000 Vehicle Counts Spring Summer Fall Winter north-south routes that link major metropolitan areas in southern Michigan and popular recreation sites and tourism destinations in the north. A report released by AAA (2009) lists the ten most popular destinations for its Michigan members (Table 6). Among them, three of the top five and five of the top ten destinations are located in either the Upper Peninsula or northern Lower Peninsula. The linear function was the simplest form that specifies the relationship between each independent variable and traffic volume. Besides the linear form, logarithmic transformation and quadratic terms were also applied to test whether the impact of weather, gas price, or CCI on traffic is nonlinear. A total of five fiinctional forms, including linear, exponential, semi-log, double-log, and quadratic, were tested with the same dataset (Table 7). 50 Hlmlm‘l I J m1 ~ 441:1 uh, Table 6 Top Ten Michigan Destinations for AAA Michigan Members Ranking Destinations Mackinaw City/Mackinac Island Traverse City Frankenmuth/Birch Run Boyne Mountain Dearbom (The Henry Ford and Museum) Munising Sault St. Marie Dundee \OWNQMADJN—o Saugatuck/Douglas 10 Lansing Source: AAA (2009) Table 7 List of Functions and Variables in Regression Analysis Function Dependent Independent Variable Variable Linear (1) Traffic ieggerature, Precrpitation, Gas, CCI, Exponential (2) Ln Traffic Tielilngerature, Precrpitation, Gas, CCI, . Temperature, Precipitation, Ln Gas, Ln Semi-log (3) Traffic C CI, Time Temperature, Precipitation, Ln Gas, Ln Double-log (4) Ln Traffic C CI, Time Exponential w/ Quadratic Temperature, Temperature Square, (5) Ln Traffic Precipitation, Gas, CCI, Time Note 1. Each function has 4 seasonal models. Note 2. Ln = Logarithmic transformation The basic linear function was first applied: C = 30+ fl,T+ fl2P+ fl3CCI+ [3,019+ p5WK1+ p6WK2+ ,67Hd1+ ,88Hd2+ flng3+ fl,oYr+ c (1) where C: daily traffic counts T: daily maximum temperature (C) P: daily precipitation (mm) CCI: monthly Consumer Confidence Index GP: weekly gas prices 51 63 CO 10 10'; [NC 13.) Wk] : Friday or Sunday of a regular weekend (not connected to a holiday) Wk2: Saturday of a regular weekend HdI : single-day holiday Hd2: first or last day of a holiday-weekend Hd3: middle of a holiday-weekend Yr: year a: error term The coefficient estimates (13's) of a linear model indicate relationships between each explanatory variable and the outcome, traffic volume. For example, the temperature coefficient (13.) indicates the change in traffic volume in numbers of vehicles with respect to one unit of change in daily maximum temperature. The second model tested was an exponential function, in which the natural logarithm of traffic, as opposed to raw traffic counts, was used as the dependent variable. InC = [90+ p,T+ fl2P+ fl3CCI+ mom [3, WK1+ p,WK2+ 57Hd1+ flBHd2+ flng3+ 5,0Yr+ g (2) One advantage of the exponential form is that the parameter estimates, when small in value, are approximately equal to the percent terms and thus easier for result interpretation. Therefore, [31 represents the percent change in traffic volume associated with a one-degree change in maximum temperature. In the next model, a semi-log function, logarithms of gas prices and CCI were regressed on traffic counts. Logarithms were not applied to weather variables because logarithms cannot be applied to zeros or negative values, which often occur for temperature and precipitation. In this model, 133 and [34 indicate changes in traffic with respect to change in the natural logarithms of CCI and gas prices, respectively. 52 to 1'3} C = [30+ an 5310+ fl3InCCI+ fl4lnGP+ 55WK1+ ,9,WK2+ fl7Hd1+ fing2+ ,BQHd3+ fl,0Yr+ e (3) A double-log function was applied next, in which logarithms of gas prices and CCI were regressed against log traffic counts. As in Model 2, l3. and [32 represent percent changes in traffic caused by one unit change in maximum temperature and precipitation, respectively. lnC = 50+ an [3310+ lag/neon ,B4lnGP+ [35WK1 + p,WK2+ ,B7Hd1+ ,83Hd2+ flQHd3+ mom a (4) The quadratic function, one type of polynomial function, includes an additional temperature square term: lnC = 130+ ,6,T+ 5213+ [3310+ B4CCI+ 3,010+ ,BOWKI + ,67WK2+ ,88Hd1+ ,89Hd2+ fl,0Hd3+ ,BuYr+ 8 (5) Building a quadratic fimction enabled the testing of whether the relationship between temperature and traffic is nonlinear (Pindyck & Rubinfeld, 1997). The quadratic term enabled the further testing of how traffic responds to changing temperatures. A positive 132 indicates traffic volume keeps increasing as temperature rises, while a negative 132 represents the existence of an optimal temperature that maximizes traffic volume. The optimal temperature can be solved with the first derivative of the quadratic function. Model Comparison and Evaluation A common method for evaluating model performance of a regression analysis is to examine the explanatory power, or the value of R-square, defined as the amount of variation in the dependent variable that can be accounted for by the explanatory variables. 53 h'l f.J u‘j A high R-square indicates a high goodness of fit, while a low R-square usually indicates the omission of important variables or the use of an inappropriate functional form. Another indicator, adjusted R-square, also enables model comparison when additional explanatory variables are added in the model building process. However, these measures are less reliable when comparing models with different functional forms. Another method for model evaluation is to compare the forecasting accuracy across different models by examining forecasting errors, the differences between actual and predicted outcomes. F rechtling (2001) suggested that holding out the most recent periods of data when constructing the model allows the calculation of post-sample accuracy measurement, which is capable of guarding against over fitting the model. In this study, daily traffic volume between 1991 and 2002 were acquired. Data from 1991 to 2000 were used to construct regression models, while data fiom 2001 to 2002 were held out for testing forecasting accuracy. Among the methods for investigating forecasting errors, Mean Absolute Percent Error (MAPE) is a widely used measure mainly due to its simplicity and intuitive clarity (Frechtling, 2001). It is specified as MAPE = (1/n)*(1et1/At)*100 where n = number of time periods e = forecast error A = actual value t = time period MAPE can be interpreted intuitively as the average percentage of forecasting error associated with a model for the given time period. Models with lower MAPEs are considered to have higher forecasting capabilities. Witt and Witt (1992) suggested that a 54 forecast is highly accurate if the MAPE is less than 10%, good if between 10% and 20%, reasonable if between 20% and 50%, and inaccurate if greater than 50%. Comparing Regression Models against the Naive Method In addition to comparing R-squares and MAPEs among the five models, their efficiencies as forecasting tools were also evaluated against a time-series approach. A basic approach is the naive method, a simple time series forecasting method often used as a benchmark forecasting model (Frechtling, 1996). Specifically, daily traffic volume for 2001 was projected using both regression models and the “seasonal naive” method. This method was used because traffic fluctuations usually display seasonal patterns. The seasonal naive method specifies that the projected value for a future period is equal to the same period of last year. For example, the seasonal naive projection of traffic volume on June 5th of 2001 is equal to the actual value of traffic volume on June 5th of 2000. Comparing projected traffic volume from both methods with the actual daily traffic volume and calculating forecasting errors (i.e., MAPE), one can investigate which method is more effective as a forecasting tool. Applying Selected Model to Multiple Stations Among the five functional forms tested in the previous section, the model with the lowest MAPE value was considered the most efficient model. This model was then applied to the other seventeen traffic stations (Table 8). Although commercial truck traffic had been excluded from the daily vehicle counts, other non-tourism traffic, including commuters and business traffic, was still embedded in the data. As a result, 55 ‘I . tialllllllllvj. t a“.- Table 8 Locations of Selected Michigan Traffic Stations Station ID Route Location 1089 US-41 Marquette I 109 US-41 Champion 1 189 M-95 Champion 2049 I-75 St. Ignace 3069 US- l 3 1 Kalkaska 3129 M-37 Traverse City 4129 US-l27 Clare 4149 I-75 Prudenville 5229 [-96 Grand Rapids 5249 US-l 31 Morley 6049 M-25 Port Sanilac 6129 I-75 Birch Run 6469 I-94 Port Huron 7309 I-196 South Haven 8209 I-96 Brighton 8249 I-75 Monroe 9829 I-696 Southfield 9849 M-lO Detroit models applied to some stations may perform better than others depending on the level of non-tourism traffic. The majority of Michigan residents live in the southern part of the located on major north-south highways such as #3069 on US-131 and #6129 on [-75 were expected to perform better since variation in daily traffic along those routes was likely to be more sensitive to the specified independent variables. Models for stations located in rural areas less frequented by visitors were expected to have lower explanatory power since the traffic counts recorded were likely to be dominated by local traffic. For traffic stations in urban areas in southern Michigan (e. g., metro Detroit, Grand Rapids), modeling results were also expected to be less satisfactory due to the high concentration of mandatory traffic from commuters and business travelers. Other Approaches to the Study of Weather and Tourism Traffic In addition to testing different functional forms, as described in earlier sections of this chapter, there are other methods of examining the effect of weather variability on leisure travel activities. This section described two alternative methods employed in this study to further such investigation. One method was the use of a 'spline function,’ a technique to test the existence of threshold weather conditions. Although temperature was expected to have a positive effect on traffic, it was possible that weather conditions could become so hot during summer that a further rise in temperature resulted in a decrease in tourism traffic. The spline approach enables the testing of such threshold temperatures, when the relationship between temperature and traffic starts to reverse. A spline term was added to the equation, 132D(T-T‘). T is daily high temperature, and T* is the threshold temperature. The model with the spline term was specified as C = ,Bo+ ,BIT+ ,BZD (T-T*)+ ,B3P+ ,B4CCI+ fl5GP+ ,66WK1+ ,B7WK2+ ,68Hd1+ ,Bng2+ ,BloHd3+ ,BHYr+ 8 Lagged effects of weather were also examined in this study. Specifically, temperatures and precipitation from the last seven days were tested to investigate the lagged effect of weather on travel pattern. Roughly one third of Michigan visitors plan their vacation one week or less before their trip (Holecek et al, 2000), which corresponds to the available period of weather forecast (i.e., maximum ten day forecast). While weather conditions on a given day may affect travelers’ decisions and travel plans, recent 57 past weather conditions may also determine how vacationers plan for their trips. For example, sunny weather on a given weekend in summer may prompt a person to plan for a camping trip next weekend. Similarly, a snowy day may affect someone’s decision to go skiing next week. To test this hypothesis, additional terms BLTt-n were included where TM. represents temperature dating back n days from a given time period. 58 Chapter 4 Results Results of the data analyses performed in this study are presented in this chapter. The chapter is divided into four main sections. In the first section, the outputs of regression analysis for the five functional forms based on the Clare station are presented. Modeling performance, recognized by the values of R-square, is evaluated among the five models. Coefficient estimates derived from regression models, including both continuous and categorical independent variables, are also interpreted and discussed. The second section describes the result of identifying the most efficient model by comparing their forecasting ability, namely MAPEs. In the third section, findings from applying the most efficient model to all eighteen traffic stations are examined. Stations with high modeling performance were recognized as “tourist” stations, as traffic volume in these stations responded more sensitively to the independent variables specified in the regression models. The impact of weather variability on traffic was then examined based on the regression results of the tourist stations. Finally, results of testing the effect of lagged weather conditions and temperature threshold are presented. Regression Analysis for Five Functional Forms Five different model specifications (linear, exponential, semi-log, double-log, quadratic) were tested for the Clare station (US-127) for the 1991-2000 period, and four seasonal models were applied for each specification. To allow better discussion and comparison of parameter estimates and model performance across functional forms, results were organized and displayed by season. 59 Spring Model Coefficient estimates, standard errors, and model performance for the five functional forms for spring were shown in Table 9. All five forms exhibited strong explanatory power, judging by their high R-square values. However, it is evident that using logarithms of traffic counts as the dependent variable, as in the exponential, double-log, and quadratic forms, resulted in a much higher R-square (0.84), than using raw traffic counts, as in the linear and semi-log functions (0.74). Daily maximum temperature was found to have a positive and statistically significant impact on traffic across all functions. The coefficient for the temperature square term is 0.0002 for the quadratic fiinction, indicating that during spring, traffic not only increased when daily temperature rises, but also increased at an increasing rate. Precipitation’s effect on traffic was statistically insignificant in all models. Consumer confidence, as measured by the Consumer Confidence Index (CCI), had very little influence on traffic since its coefficient estimates were all insignificant. The relationship between gas prices and traffic were positive, although only significant in the exponential and quadratic functions. All the categorical variables were found to be highly significant. Results from the linear and semi-log fiinctions indicated that there were about 3,214 more vehicles on a non-holiday-related Friday or Sunday, and about 990 more on a Saturday, than a regular weekday. The only holiday-weekend defined for spring was the weekend that included Easter Sunday. Specifically, compared to a regular weekday, about 6,310 more vehicle counts were recorded on the Friday or Sunday, and about 3,180 more on the Saturday, of the Easter weekend. Estimates for the year variable suggested that spring traffic increased by about 5% annually. 60 Table 9 Regression Analysis Results for Spring Traffic Models (Clare, 1991-2000) Linear Exponential Semi-log Double-log Quadratic beta beta beta beta beta intercept -382204.05 -84.54 -38672.73 -85.74 -84.09 (84880.4) (15.1) (67961.5) (11.25) (14.0) Max. 70.69“ 0.016" 70.56” 0.016" 0.011M Temperature (4.9) (0.001 ) (4.9) (0.01) (0.002) Max Temp 0.0002" Square N/A N/A N/A N/A (0.0001) Precipitation -8.64 ~0.002 -8.64 -0.002 -0.002 _ (8.2) (0.001) (8.2) (0.01) (0.001) Consumer -5.86 -0.001 -634.76 -0.10 -0.001 Confidence (4.2) (0.001) (335.2) (0.06) (0.001) Gas Price 734.06 0.18* 517.83 0.14 021* (556.5) (0.09) (422.9) (0.07) (0.09) Friday or 3214.42" 0.81“ 3214.20** 0.81" 0.81“ Sunday (99.1) (0.02)) (99.0) (0.02) (0.02) Samda 989.93" 0.33" 989.51" 0.33M 0.33" y (128.3) (0.02) (128.2) (0.02) (0.02) smglf'day N/A N/A N/A N/A N/A Holiday (15:; gratify 6310.27" 1.14** 6309.65" 1.14" 1.14** Weekend (202.3) (0.03) (202.1) (0.03) (0.03) 1:412:32? 3180.25" 0 73,, 3179.65" 073M 073" weekend (243.1) (242.9) (0.04) (0.04) Year 192.47M 0.046“ 196.26" 0.047" 0.046" (42.8) (0.01) (34.8) (0.01) (0.01) F 252.2 465.5 252.8 466.5 423.8 R-square 0.74 0.84 0.74 0.84 0.84 Note: P-value for all five models are smaller than 0.001 *Significant at 5% level. "Significant at 1% level. Summer Model Modeling results for summer are presented in Table 10. Overall model performance was very good, with an 'R-square of 0.82 for the linear and semi-log functions and 0.84 for the exponential, double-log and quadratic functions. Daily high temperature again had a positive and highly significant impact on traffic. Estimates from the exponential, double-log, and spline functions showed that a one degree Celsius increase in temperature led to a 1% increase in traffic volume. The temperature square coefficient estimate was used to solve for first order condition, which yielded to an optimal temperature at about 321°C (90°F). This meant that in summer, leisure traffic was at its peak when the temperature is at 90°F. The effect of precipitation was insignificant in all five functions. Coefficients of CCI were also insignificant, except in the double-log model. The impact of gas price was negative and significant, with the coefficient of the linear function suggesting that a one-dollar increase in real gas price leads to about 1,384 fewer vehicles (approximately 21%) on a given day. Dummy variables accounting for weekend and holiday factors were once again all highly significant. Results of the linear function showed that there were about 6,635 more vehicles on a Friday or Sunday and about 2,523 more vehicles on a Saturday compared to a weekday during a non-holiday weekend. The roads are even more crowded during a holiday weekend. Compared to a regular weekday, there were about 10,455 more vehicles on the first and last day and 4,018 more vehicles in the middle of a holiday weekend during summer. The year variable was also significant, indicating a 4% increase in summer traffic annually. 62 Table 10. Regression Analysis Results for Summer Traffic Models (Clare, 1991-2000) Linear Exponential Semi-10L Double-log Quadratic beta beta beta beta beta Interce t -512194.73 -72.52 -509815.04 -7l.64 -7l.68 " (93650.9) (11.9) (77523.5) (9.9) (11.9) Max. 54.40" 0.010" 55.01" 0.010" 0.045" Temperature (14.5) (0.002) (15.4) (0.002) (0.02) Max Temp -0.0007* Square N/A N/A N/A N/A (0.0003) Preci itation -8.08 -0.001 -8.04 -0.001 -0.001 p (6.5) (0.001) (6.5) (0.001) (0.001) Consumer -5.82 -0.001 -600.51 -0. 10* -0.001 Confidence (4.7) (0.001) (387.9) (0.05) (0.001) Gas Price -1384.38"I -0.24** -118l.75* -0.21** -0.24"”'I (620.5) (0.08) (543.6) (0.07) (0.08) Friday or 6634.56” 0.93" 6633.18" 0.93" 0.93" Sunday (130.5) (0.02) (130.4) (0.02) (0.02) Saturda 2522.83" 0.46" 2521.39" 0.46” 0.47" y (169.5) (0.02) (169.4) (0.02) (0.02) Single-day 2434. 19* 0.47" 2432.97"' 0.47" 0.46"”I Holiday (1059.8) (0.14) (1059.3) (0.14) (0.14) “’3. 3’0 11$?” 10454.63" 1.20M 10455.40M 1.20" 1.21" Weekend (392.4) (0.05) (392.2) (0.05) (0.05) “313$? 4018.14" 0.67" 4026.06" 0.67“ 0.67" Weekend (350.6) (0.05) (350.4) (0.05) (0.05) Year 259.08" 0.041" 258.27" 0.040" 0.040" (47.2) (0.01) (39.6) (0.01) (0.01) F 323.4 378.3 323.7 379.1 346.2 R—square 0.82 0.84 0.82 0.84 0.84 Note: P-value for all five models are smaller than 0.001 *Significant at 5% level. "Significant at 1% level. 63 Fall Model Results for the fall traffic models show that, in general, all five models have high explanatory power (Table 11); R-square was 0.78 for the linear and semi-log functions and 0.84 for the exponential, double-log, and quadratic functions. Maximum temperature was an important factor in determining traffic volume in fall, as its parameter estimates are highly significant at the 1% level in all models. Coefficient estimates of temperature indicated that a one degree Celsius rise in temperature resulted in about 85 more vehicles or about a 1.5% increase in daily traffic. Temperature square was insignificant, meaning an optimal temperature does not exist during fall. Unlike spring and summer, when precipitation had no influence on traffic, precipitation was found to have a significant and negative impact during fall. Specifically, an increase of precipitation by one millimeter resulted in a decrease of 20 vehicles or 0.3% of total traffic. The influence of CCI in fall was significant at the 5% level in the exponential and quadratic functions, with an increase of one point in consumer confidence resulting in a 0.2% decrease in traffic. Fall gas price fluctuations had no effect on highway traffic, according to the results. Weekend and holiday dummy variables were once again significant at the 1% level for all five models. The results from the linear model indicated that compared to a regular weekday, about 4,688 more vehicles were recorded on a Friday or Sunday, and about 7,379 more vehicles were recorded on the first or last day of a holiday weekend. The year variable coefficient estimate showed a grth in traffic of about 4.7% each fall. 64 Table 11. Regression Analysis Results for Fall Traffic Models (Clare, 1991-2000) Linear Exponential Semi-log Double-log Quadratic beta beta beta beta beta Interce t 454048.99 -85.32 -390473.43 -73.09 -85.03 p (1095050) (16.5) (89942.7) (13.6) (16.8) Max. 85.02" 0.015“ 85.21M 0.016" 0.016“ Temperature (5.9) (0.001) (5.9) (0.001) (0.003) Max Temp -0.00001 Square N/A N/A N/A N/A (0.0001) Preci i tation -20.07** -0.003** -20.08** —0.003** -0.003** p (7.2) (0.001) (7.2) (0.001) (0.001) Consumer -9.76 -0.002* -651.96 -0.1 1 -0.002* Confidence (5.4) (0.001) (434.3) (0.07) (0.001) Gas Price 0.86 -0.12 136.56 -0.07 -0. 12 (736.1) (0.1 1) (570.8) (0.09) (0.11) Friday or 4688.00" 0.90" 4686.96" 0.90" 0.90” Sunday (1 18.5) (0.02) (1 18.6) (0.02) (0.02) Saturda 1304.86" 0.35” 1303.85” 0.35" 0.35" 3’ (153.7) (0.02) (153.8) (0.02) (0.02) Single-day Holiday N/A N/A N/A N/A N/A First or Last day of 7379.33" 1.14** 7379.68" 1.14" 1.14" Holiday- (250.7) (0.04) (250.9) (0.04) (0.04) Weekend 1:33;? 2815.34M 0.60" 2815.52M 0.60" 0.56" Weekend (224.2) (0.03) (224.3) (0.03) (0.04) Year 229.09" 0.047“ 198.23" 0.040" 0.047” (55.3) (0.01) (46.0) (0.01) (0.01) F 278.7 406.2 278.3 405.0 365.1 R-square 0.78 0.84 0.78 0.84 0.84 Note: P-value for all five models are smaller than 0.001 *Significant at 5% level. "Significant at 1% level. 65 Winter Model Regression results for winter are displayed in Table 12. All models again had strong explanatory power, although generally lower than spring, summer, and fall. R- square values of the five models ranged from 0.72 to 0.76. Maximum temperature was found to be insignificant in winter, a result contrary to the other three seasons. The effect of precipitation was negative and significant, with one additional millimeter leading to a 1.3% decrease or about 38 fewer vehicles per day. In winter, neither CCI nor gas price had significant influences on traffic volume. As in spring, summer, and fall, holidays and weekends were important factors in determining winter highway traffic volume. The results from the linear model indicated that compared to a regular weekday, about 2,968 more vehicles were recorded on a Friday or Sunday, and about 2,573 more vehicles were recorded. Parameter estimates for the year variable showed that winter traffic increases at a rate around 4.5% annually. 66 Table 12. Regression Analysis Results for Winter Traffic Models (Clare, 1991-2000) Linear Exponential Semi-log Double-lgg Quadratic beta beta beta beta beta Intercept ~312139.52 -81.42 -31 1899.82 -80.68 -81.44 (60847.9) (16.0) (50673.1) (13.3) (16.0) Max. -0.80 0.001 -l.55 0.001 0.001 Temperature (5.5) (0.001) (5.5) (0.001) (0.002) Max Temp 0.00003 Square N/A N/A N/A N/A (0.0001) Precipitation -38.65*"‘ -0.013** -38.1 I" -0.013** -0.013** (1 1.5) (0.004) (1 1.5) (0.003) (0.003) Consumer -4.44 -0.001 -436.06 -0.07 -0.001 Confidence (2.8) (0.001) (222.3) (0.06) (0.001) Gas Price -124.58 -0. 12 -141.27 -0.09 -0.12 (352.2) (0.09) (254.8) (0.07) (0.09) Friday or 2968.31 ** 0.85" 2968.67" 0.85” 0.85" Sunday (71.8) (0.02) (71.7) (0.02) (0.02) Saturday 808.54" 0.32" 809.07" 0.32” 0.32" (92.0) (0.02) (91.9) (0.02) (0.02) Single-day 570.59 0.27“ 558.47 0.27“ 027* Holiday (481.5) (0.13) (481.2) (0.13) (0.13) First or Last day of 2572.83" 0.74“ 2580.75M 0.74" 0.74“ Holiday- (160.1) (0.04) (160.1) (0.04) (0.04) Weekend fiL‘flZS 1398.90" 0.48“ 1403.1 1** 0.48“ 0.48“ Weekend (158.0) (0.04) (157.9) (0.04) (0.04) Year 157.83" 0.045" 158.41" 0.044" 0.045" 30.6 (0.01) (25.9) (0.01) (0.01) F 196.6 240.3 197.1 240.4 218.1 R-square 0.72 0.76 0.72 0.76 0.76 Note: P-value for all five models are smaller than 0.001 *Significant at 5% level. "Significant at 1% level. 67 Relative Importance of Independent Variables In addition to comparing the partial coefficient estimates of the five functional forms, standardized coefficient estimates were also generated. This enabled the examination of relative importance among independent variables in the model. Since results from all five models exhibit similar patterns, partial and standardized coefficients from the quadratic function were displayed in Table 13 as an example. It was evident that dummy variables controlling for the time factor accounted for the most variation in the models. The standardized coefficients for Friday or Sunday ranged from 0.73 to 0.86, and standardized coefficients for Saturday ranged from 0.23 to 0.33. Continuous independent variables, however, accounted for less variation in the models. In spring, summer, and fall, maximum temperature was the most important predictor besides the dummy variables controlling for time. For example, the standardized coefficient estimate of temperature for the fall model was 0.27. This meant changes in temperature had a much greater effect on traffic volume compared to precipitation (~0.05), consumer confidence (- 0.11), or gas prices (-0.02). However, precipitation had the strongest impact during winter, with a standardized beta of -0.08 compared to 0.02 for maximum temperature. 68 Table 13. Partial and Standardized Coefficient Estimates of Quadratic Regression Models SLring Summer Fall Winter Std std std std beta beta beta beta beta beta beta beta Intercept -84.09 -71.68 -85 .03 -81.44 Max. " Temperature 0.011 0.20 0.045” 0.37 0.016" 0.27 0.001 0.02 Temperature ,, Square 0.0002" 0.1 1 -0.001 -0.29 -0.00001 -0.01 0.00003 0.00 Precipitation -0.002 -0.02 -0.001 -0.01 -0.003** -0.05 -0.013""" -0.08 “mm“ -0.001 -0.05 -0.001 -0.06 -0.002* 01 1 -0.001 -0.05 Confidence Gas Price 0.21* 0.03 -0.24** -0.05 -0.12 -0.02 -0.12 -0.02 Fnday °’ 0.81“ 0.73 0.93" 0.86 0.90" 0.80 0.85" 0.84 Sunday Saturday 0.33" 0.23 0 47** 0.33 0.35“ 0.24 0.32" 0.25 Slngle‘day N/A N/A 0.46** 0.05 N/A N/A 027* 0.04 Holiday First or Last day.“ 1.14" 0.49 1.21" 0.36 1.14** 0.46 0.74** 0.32 Holiday Weekend Middle of Holiday 073’” 0.26 0.67 ** 0.23 0.56M 0.27 0.48" 0.21 Weekend Year 0.046" 0.29 0.040“ 0.26 0.047" 0.29 0.045" 0.31 R-square 0.84 0.84 0.84 0.76 Note: P-value for all four models are smaller than 0.001 3. Models based on 1991-2000 data. *Significant at 5% level. "Significant at 1% level. 69 Checking Regression Assumptions As mentioned in Chapter 2, there are several requirements associated with regression approach. Violations of these requirement result in conditions such as multicollinearity, heteroscedasticity, and serial correlation, which in turn render the OLS estimates invalid or unreliable. In Table 14, statistics for checking multicollinearity and serial correlation for the linear models were displayed. Again, results were segmented by season. The general rules for checking multicollinearity specify that the tolerance value exceeding 10 and VlF smaller than 0.1 indicate cause for concern (Field, 2005). For spring and fall linear models, Consumer Confidence and Year variables displayed signs of multicollinearity, with VIFs over 10 in spring and VIFs over 11 in fall. This indicated that the positive annual time trend discovered was partially due to the growing economy during the time span. Again, multicollinearity causes unreliable OLS estimates, but it does not affect the models for forecasting purposes. Durbin-Watson statistics were also presented for checking the condition of serial correlation. According to Field (2005), the conservative rule of thumb for checking serial correlation is that the statistic under 1 indicating signs for the problem. In Table 14, none of the Durbin-Watson statistics were found to violate this condition. The same diagnostics for the double-log model were displayed in Table 15. Double-log models did not have problem with multicollinearity, with all VIFs larger than 10. Serial correlation was not a concern, either, with all four Durbin—Watson statistics between 1.11 and 1.34. 70 Table 14. Multicollinearity and Serial Correlation Diagnostics for Linear Models Models Spring Summer Fall Winter 1 d Collinearity Collinearity Collinearity Collinearity n ep. Variables Tolerance VIF Tolerance VIF Tolerance VIF Tolerance VIF Max. 0.92 1.09 0.96 1.04 0.98 1.02 0.94 1.06 Temperature Precipitation 0.99 1.01 0.99 1.01 0.98 1 .02 0.96 1.04 Consumer 0.10 10.26 0.15 6.54 0.09 11.58 0.10 9.79 Confidence . 0.90 1.11 0.92 1.09 0.79 1.26 0.95 1.06 Gas Price Friday or 0.92 1.09 0.92 1.08 0.91 1.10 0.91 1.10 Sunday 0.93 1.07 0.93 1.07 0.93 1.08 0.93 1.08 Saturday Single-day N/A N/A 0.99 1.01 N/A N/A 0.99 1.01 Holiday First or Last 096 1.04 0.98 1.02 0.97 1.04 0.96 1.04 day of Holiday- Weekend Middle of 0.96 1.04 0.98 1.02 0.96 1.04 0.96 1.04 Holiday- Weekend Year 0.10 10.03 0.15 6.68 0.08 11.77 0.10 9.64 Durbin- Watson 1.43 1.39 1.50 1.53 N/A indicates not available 71 Table 15. Multicollinearity and Serial Correlation Diagnostics for Double-log Models Models Spring Summer Fall Winter 1 d Collinearity Collinearity Collinearity Collinearity n ep. Variables Tolerance VIF Tolerance VIF Tolerance VIF Tolerance VIF Max. 0.93 1.08 0.96 1.04 0.98 1.02 0.95 1.05 Temperature Precipitation 0.99 1.01 0.99 1.01 0.98 1.02 0.96 1.04 Consumer 0.15 6.77 0.21 4.65 0.12 8.12 0.14 7.07 Confidence Gas Price 0.90 1.11 0.94 1.06 0.80 1.25 0.92 1.09 Friday or 0.92 1.09 0.92 1.08 0.91 1.10 0.91 1.10 Sunday 0.93 1.07 0.93 1.07 0.93 1.08 0.93 1.08 Saturday Single-day N/A N/A 0.99 1.01 N/A N/A 0.99 1.01 Holiday First or Last 0.96 1.04 0.98 1.02 0.97 1.04 0.96 1.04 day of Holiday- Weekend Middle of 0.96 1.04 0.98 1.02 0.96 1.04 0.96 1.05 Holiday- Weekend Year 0.15 6.64 0.21 4.71 0.12 8.14 0.15 6.88 Durbin- Watson 1.18 1.11 1.27 1.34 N/A indicates not available 72 In Figure 7 and Figure 8, residual plots for linear and double-log models were presented. For linear models (Figure 7), residuals tend to fan out to the right, showing signs of heteroscedasticity. Summer and fall plots also displayed curvilinear patterns, indicating the underlying relationships between the explanatory variables and the outcome variable may not be linear in nature. The plots for the double-log models, shown in Figure 8, exhibited mostly random patterns. No obvious curves or trends were shown in the residual plots across four seasons. Comparing residual plots between linear and double-log models showed that nonlinear models may be more adequate and problem- free models. Another method of evaluating and comparing functional forms was discussed in the next section. 73 Figure 7. Residual Plots for Linear Models 10000.00— 0 8 3 5000.00— 0 0 3 oo 0 O O E 0.00— E O O -5(XX).00— O 0 o c? -1(X)00.00"‘ l l 1 5000.00 10000.00 15000.00 Uns tandarrized Preclcted Value 8W.00‘ O 0 Summer 0 6000.00— 00 0 Unannrhrtlzed Resithal l fir l I 1 2000.00 4000.00 6000.00 8000.00 10000.00 Unstandarrized Predcted Value 74 Figure 7. (Cont’d) 10000.00— 800011)‘ 0 6000.“)— 4000.00— 21130.“)— 0.“)- Uns tandarrlzed Realthal 4111).“)— -4(XX).00—t l l l l l l 0.00 2500.00 5000.00 7500.00 10000.00 12500.00 Uns tandarrized Precicted Value MDO— 2000“)- 01!)“ Um tanrhrdzed Residnl I 1 l I 1 1000.00 2000.00 3000.00 4000.00 5000.00 6000.00 [Instanhrclzed Predcted Value 75 Figure 8. Residual Plots for the Double-log Models Unstanthrdzed Res idial Unstamhrdzed Res irhal 111)" 0.50‘ 0.00" -0.50" -l.50"1 l l l l l 7.50 8.00 8.50 9.00 9.50 Uns tandartlzed Predcted Value 0.50“ 0.00— Summer I W l l 8.50 9.00 9.50 10.00 Unstandardzed Predcted Value 76 Figure 8. (Cont’d) 0.75— g Unstanrhrdzed Residial | I I I 8.00 8.50 9.00 9.50 10.00 Una tandarrized Res lthal 5: -0.50“ l I l l 7.50 7.75 8.00 8.25 8.50 8.75 Unstandlrrlzed Preclcted Value 77 Identifying the Best Fitting Model The regression results from the previous section suggested that all five models had strong explanatory power, judging by their R-squares, which range between 0.72 and 0.84. In particular, models with logarithmic traffic performed better than those with raw traffic counts as dependent variables. However, R-squares were not completely reliable when comparing models with different variables. To further evaluate the performance of the five models, forecasting ability was examined. Coefficient estimates from the five regression models were entered to project daily traffic for the years 2001 and 2002, which were then compared to actual daily traffic counts to create a measure of forecasting accuracy, Mean Absolute Percent Error (MAPE). The values of MAPE for the five regression models, segmented by the four seasons, were shown in Table 16. Results showed that the two models with raw traffic counts as dependent variables were inferior as forecasting tools, since the linear and semi-log models both had MAPEs over 20. On the contrary, models that employed logarithmic traffic all had MAPEs below ten, indicating “highly accurate” forecasting (Witt and Witt, 1992). The table showed that the double-log model has the lowest average MAPE of 5.2, followed by the quadratic (5.33), and exponential (5.38) models. Therefore, the double—log model was identified as the best fitting model. 78 Table 16 Comparison of Forecasting Accuracy of Regession Models MAPE Linear Exponential Semi-log Double-log Quadratic Spring 22.6 2.8 22.4 1.8 2.5 Summer 24.4 4.2 24.0 3.3 2.1 Fall 28.5 6.9 24.9 6.1 9.1 Winter 39.3 7.6 38.8 9.6 7.6 Ag. 28.70 5.38 27.53 5.20 5.33 Note: MAPE = mean absolute percent error from projected vs. actual 2001-2002 data To further examine the validity of the regression models constructed, forecasting accuracies of the models were compared with a time series approach. Projecting daily traffic in 2001 using both regression models and the seasonal naive method, the results were displayed in Table 17. Again it was evident that the linear model, with a MAPE of over 28, was inferior model compared to those employing log traffic. The seasonal naive forecasting method had comparable forecasting accuracy (MAPE 5.9) to some of the best regression models. Table 17 Comparing Forecasting Accuracy (MAPE) between Regression and Naive Models @8127 Clare) Model MAPE Naive“ 5.90 Linear 28.64 Exponential 7.06 Double Log 5.48 Note: Seasonal naive method applied using daily counts from 2000 as projected counts for 2001. Applying the Selected Model to Multiple Stations The double-log model was then applied to construct regression models for all eighteen traffic stations. In total, the regression models from eight stations demonstrated 79 strong explanatory power. The R-square values for these eight stations were shown in Table 18. These stations with mostly high R-squares across four seasons were identified as “tourist” models, because traffic volume at these stations was more sensitive to the specified independent variables, which were factors important to leisure travelers. Almost all of them were located on major north-south routes, which linked population bases in the southern part of Michigan and beyond and popular travel destinations in the north. The R-squares for those models ranged from 0.6 to close to 0.9, with a limited number of exceptions (#6469 in fall; #6049, #6129, #6469, #7309 in winter.) Table 18 Model Performance of Tourist Stations Station ID Route & Location R-square Spring Summer Fall Winter 4129 US-127 Clare 0.83 0.83 0.83 0.74 4149 I-75 Houghton Lake 0.72 0.76 0.81 0.71 5229 [-96 Grand Rapids 0.70 0.78 0.64 0.71 5249 US-131 Morley 0.85 0.86 0.85 0.78 6049 M-25 Port Sanilac 0.65 0.74 0.65 0.33 6129 1-75 Birch Run 0.79 0.84 0.82 0.54 6469 I-94 Port Huron 0.64 0.45 0.67 0.59 7309 I-196 Glenn 0.75 0.77 0.82 0.56 Note: Logarithm of daily traffic between 1991 and 2000 was used as dependent variable in regression analysis. Conversely, the other ten stations (Table 19) were considered “non-tourist” stations, with R-squares of their regression models below 0.5, indicating a low goodness of fit for the models. Some non-tourist stations were located inside metro areas (i.e., Detroit), where recorded traffic counts were likely to include a higher amount of commuter and commercial traffic. Other non-tourist stations included routes and regions in rural areas, where most registered counts were likely to be due to the local population rather than leisure travelers. Since the purpose of this study is to examine the effect of 80 weather variability on leisure travel activities, the following discussion thus focused on summarizing regression results from the eight “tourist” stations. Table 19 Locations of Non-tourist Traffic Stations Type Station ID Route Location R-Square Spring Summer Fall Winter Rural 1089 US-41 Marquette 0.31 0.24 0.09 0.32 l 109 US-41 Champion 0.43 0.31 0.56 0.34 1 189 M-95 Champion 0.27 0.24 0.24 0.34 2049 [-75 St. Ignace 0.31 0.38 0.65 0.53 3069 US- l 31 Kalkaska 0.27 0.24 0.24 0.34 3129 M-37 Traverse City 0.37 0.41 0.49 0.47 Urban 8209 l-96 Brighton 0.52 0.50 0.40 0.43 8249 I-75 Monroe 0.31 0.16 0.42 0.43 9829 I-696 Southfield 0.42 0.32 0.39 0.38 9849 M-10 Detroit 0.41 0.47 0.45 0.49 Effect of Weather Variability on Traffic across Tourist Stations The regression results of maximum temperature and precipitation for the eight tourist stations were summarized in map form. In spring, summer, and fall, maximum temperature was the most significant weather variable so temperature's effect on traffic, shown in percentage terms, is displayed next to the locations of the traffic stations. For winter, however, precipitation was the more important weather factor that determines traffic volume. Therefore, effects of variation in precipitation on traffic were shown for the winter model. In Figure 9, the percentages on the highway routes represented the percent changes in traffic associated with each degree increase in maximum temperature for the 81 eight tourist traffic stations during spring. The results were very consistent across routes, with one-degree warmer temperatures leading to a 1% increase in traffic, with the exception of the Clare station on US-127 (2%.) In summer (Figure 10), the one-degree increase in temperature also resulted in 1% higher traffic volume in five of the eight tourist stations. A lower effect of a one-degree rise in temperature was found at three other stations: 0.3% on [-96, 0.4% on 1-94, and 0.3% on [-75 near Birch Run. In fall, similar results were discovered. The percentages shown in Figure 11 suggested that one- degree warmer temperatures caused traffic volume to increase by 1% in six of the eight tourist stations. The exceptions were 0.3% on 1-96 near Grand Rapids and 2% on US-127 near Clare. In winter, however, temperature had no impact on leisure traffic across tourist stations while precipitation had negative effects on traffic (Figure 12). Specifically, a one-millimeter increase in precipitation resulted in a 1% decrease in traffic, with the exception of the Birch Run station on I-75, where traffic went down by 0.4% with each additional millimeter of precipitation. Overall, weather’s impact on traffic volume was consistent across tourist stations, which demonstrated the robustness of the regression models constructed in this study. 82 Figure 9. Percent Change in Daily Traffic Associated with l-degree Increase in Temperature during Spring for Tourist Traffic Stations 1'5 .. Note 1. Triangles represent location of tourist traffic stations. Note 2. Results based on regression models using logarithm of traffic as dependent variables. 83 Figure 10. Percent Change in Daily Traffic Associated with l-degree Increase in Temperature during Summer for Tourist Traffic Stations 1-94 1 1 Note 1. Triangles represent location of tourist traffic stations. Note 2. Results based on regression models using logarithm of traffic as dependent variables. 84 Figure 11. Percent Change in Daily Traffic Associated with l-degree Increase in Temperature during Fall for Tourist Traffic Stations I-94 Note 1. Triangles represent location of tourist traffic stations. Note 2. Results based on regression models using logarithm of traffic as dependent variables. 85 l . v 7 .u' LI- -'L~ , , Figure 12. Percent Change in Daily Traffic Associated with l-degree Increase in Precipitation during Winter for Tourist Traffic Stations 0 M-25 -1% .f -1 % I-94 Note 1. Triangles represent location of tourist traffic stations. Note 2. Results based on regression models using logarithm of traffic as dependent variables. 86 Further Testing of Weather’s Effect on Traffic To further examine the effect of weather conditions on leisure traffic, the lagged effect of weather was also examined to evaluate whether past weather conditions impact travel volume on a given day. The values of daily temperature and precipitation for the past seven days were included to test whether travel plans and decisions were affected by weather conditions during the trip planning period. The model was again based on the Clare Station using log traffic as the dependent variable. The regression results were shown in Table 20. Templ represented temperature from one day ago; precipl represented precipitation from one day ago, etc. Past temperatures from the previous one to six days seemed to have very little effect on leisure traffic, with only temp4 in spring and temp2 in fall being statistically significant. Temp7 however, was significant in spring, summer, and fall. This meant temperature from a week ago had a positive impact on travel volume for a given day. Specifically, a one-degree increase in temperature resulted in 0.3%, 1.2%, and 0.4%, respectively, increases in traffic in spring, summer, and fall. However, past precipitation did not seem to have a consistent effect on leisure travel. The only two variables found significant were precipitation from one day ago in summer and precipitation from five days ago in winter. The existence of a temperature threshold was also tested on the same dataset with the application of the spline function. A threshold temperature was identified at 32°C (90°F) during summer, when the spline term was found negative and significant at the 1% level. Its coefficient estimates indicated that for every one degree Celsius rise in temperature, traffic increased by 1.1% before the threshold temperature, 32°C, but it decreased by 7.3% after temperature exceeds the threshold. 87 Table 20. Multiple Regression Models with Lagged Weather Variables (Clare, 1991- 2000) Spring Summer Fall Winter beta Std. Error beta Std. Error beta Std. Error beta Std. Error Intercept -88.635 12.732 -90.847 11.812 -85.824 15.802 -74.756 15.800 ¥:r:'perature 0.005** 0.001 0.007** 0.002 0.005** 0.002 0.003 0.002 temp1 0.003 0.002 0.002 0.003 0.001 0.002 0.000 0.003 temp2 0.002 0.002 0001 0.003 0.005** 0.002 0002 0.003 temp3 0.000 0.002 0.002 0.003 0.001 0.002 0.003 0.003 temp4 0.005** 0.002 0.005 0.003 0001 0.002 0003 0.003 temp5 0.003 0.002 0.000 0.003 0.002 0.002 0.000 0.003 temp6 0.002 0.002 0003 0.003 0.001 0.002 0001 0.003 temp7 0003* 0.001 0.012** 0.002 0004* 0.002 0003 0.002 Precipitation -0.004** 0.001 0001 0.001 0003“ 0.001 0013“ 0.003 precip1 0002 0.001 0002* 0.001 0001 0.001 0001 0.003 precip2 0001 0.001 0.000 0.001 0.000 0.001 0.000 0.003 precip3 0.000 0.001 0.000 0.001 0.001 0.001 0005 0.003 precip4 0.001 0.001 0001 0.001 0.000 0.001 0004 0.003 precip5 0.002 0.001 0.001 0.001 0.000 0.001 -0.008** 0.003 precip6 0.002 0.001 0.001 0.001 0.002 0.001 0003 0.003 precip7 0.001 0.001 0.000 0.001 0.001 0.001 0004 0.003 CCI 0001* 0.001 0002" 0.001 0002* 0.001 0.000 0.001 Gas Price 0029 0.084 0190* 0.077 -0.181 0.106 0150 0.092 333:? 0.809“ 0.015 0.925" 0.015 o.904** 0.017 0.852" 0.019 Saturday 0.333** 0.019 0.468“ 0.021 0.359** 0.022 0.325** 0.024 33%;?” N/A N/A 0524" 0.132 N/A N/A 0259* 0.125 First of Last day.“ 1.106" 0.030 1.185" 0.049 1.147" 0.036 0.726“ 0.042 Holiday Weekend Middle of Holiday 0.683" 0.037 0.665" 0.044 0.615" 0.032 0.461“ 0.041 Weekend Year 0.048" 0.006 0.050** 0.006 0.047" 0.008 0.041" 0.008 Note: Logarithm of daily traffic used as dependent variable; P-value for all four models are smaller than 0.001 *Significant at 5% level. ”Significant at 1% level. 88 Chapter 5 Summary, Discussion and Conclusions In this chapter, a summary of the study is first presented. Next, findings of this study are discussed with the emphasis on the hypotheses stated in Chapter 1. Implications and applications of the findings are then presented. This chapter concludes with suggestions for future research. Summary of the Study The purpose of this study was to examine impacts of weather variations on leisure travel activity by constructing statistical models. In particular, to assess these impacts on finer temporal and spatial scales than has previously been conducted, daily Michigan highway traffic counts from eighteen locations across the state, excluding commercial traffic, were used to represent the dependent variable, the volume of general tourism activities. In a multiple regression approach, five models with different functional forms were tested first on a single traffic station (US-127, Clare) located on a main north-south highway linking the population base in southern Michigan to major destinations in the north. Explanatory variables employed in the models included maximum temperature, precipitation, gas prices, consumer confidence, and dummy variables controlling for the availability of leisure time. Regression results from five fiinctional forms were compared and models were evaluated according to their forecasting abilities, based on their calculated MAPE values. The best fitting model was then applied to the other seventeen traffic stations. Based on modeling performance, traffic stations whose models had high explanatory power were 89 identified as “tourist stations.” Coefficient estimates generated for tourist stations were then compared and examined, with an emphasis on the effects of maximum temperature and precipitation on fluctuations in daily tourism traffic. In separate approaches, models were constructed to test for a threshold temperature and the lagged effects of weather conditions. Findings of Hypothesis Testing In Chapter 1, three objectives and eight hypotheses were identified to frame this study. The first objective was to construct regression models to explain variation in daily leisure travel activity for a single traffic location. Results from regression analysis provided evidence to investigate whether hypotheses 1.1 through 1.6 were supported by the data. Table 21 displays the comparison between expected and actual signs of the coefficient estimates from the independent variables. Weather Variables Hypothesis 1.1 predicts that variation in maximum temperature has a positive effect on daily leisure traffic. Results suggested that, daily maximum temperature had positive and statistically significant (at the 1% level) effects on tourism traffic in spring, summer, and fall across all five models. Specifically, a one-degree increase in temperature resulted in an increase in tourism traffic of between 1% and 1.6% for spring, summer, and fall. This confirms the expectation that travelers prefer warmer weather conditions. In winter, however, temperature was not a significant factor in determining the fluctuation of leisure traffic. 90 Table 21. Comparison of Expected and Actual Signs of Coefficient Estimates Variables Temporal Unit Expected Sign of Actual Sign of Resolution Coefficient Estimate Coefficient Estimate Weather Maximum Temperature Daily °C Positive Positive in Spring, summer, fall Precipitation Daily Millimeter Negative Negative in fall, Winter Economic Consumer Confidence Monthly Index Point Positive Inconclusive Gas Price Weekly Dollar Negative Positive in spring; Negative in summer Temporal Friday or Sunday Daily N/A Positive Positive Saturday Daily N/A Positive Positive First or Last Day of Daily N/A Positive Positive Holiday-weekend Middle of Holiday- Daily N/A Positive Positive weekend Singe-day Holiday Daily N/A Positive Positive Year Annual N/A Positive Positive In Hypothesis 1.2, daily precipitation is predicted to have a negative effect on daily leisure traffic volume. The data suggested that in spring and summer, precipitation was not a statistically significant factor influencing leisure traffic. In fall, a negative and significant effect of precipitation was detected, with a one-millimeter increase in precipitation causing a decrease in tourism traffic by about 0.3%. Precipitation had an even stronger effect during winter. A significant and negative relationship was also found in winter, with a one-millimeter increase in precipitation resulting‘in a 1.3% decrease in leisure traffic. This was likely because snow was included in the records of precipitation. 91 Although snowfall is considered a positive factor for winter sports such as Skiing and snowmobiling, it also creates inconvenient and hazardous driving conditions that might discourage travelers from driving longer distances to participate in other leisure activities. Economic Variables Hypothesis 1.3 specifies that variations in economic conditions will positively a 1‘ affect daily leisure traffic volume. Results for the impacts of CCI on tourism traffic were mostly insignificant and inconclusive. For fall models, however, CCI had a negative and Significant effect in the exponential and quadratic functions, a result that contradicted the ‘1 general belief that people are more likely to travel in a better economy. One possible reason was the use of monthly data for CCI, which lacks variation in the regression models of daily traffic volume. In Hypothesis 1.4, gas price is predicted to have negative effects on daily leisure traffic volume. The data suggested that gas prices had statistically significant impacts on traffic in spring and summer only. The results, however, were inconsistent in the two seasons. Gas prices displayed a positive impact on traffic in spring, a result that was counterintuitive. Conversely, results from the summer models indicated that higher gas prices led to decreasing tourism traffic. Specifically, a rise of one dollar in gas price caused tourism traffic counts to decrease by 1,384 and 1,182 (approximately 21% and 18%, respectively), from the results of linear and semi-log models, respectively. However monthly gas prices in the dataset, between 1991 and 2000, range from 92¢ to $1.55 per gallon, meaning a one-dollar rise in price represents a percent increase between 65% and 108%. Compared to the 21% and 18% decreases in leisure traffic, it is evident that during 92 the span of the data, the demand for gasoline was inelastic, meaning travelers were generally insensitive to fluctuations in gas prices. The data used in the analysis, however, did not include recent gas prices that had much higher variation, such as the record-high gas prices over $4 per gallon during several months of 2008. Temporal Variables Hypothesis 1.5 predicts that there are positive relationships between the availability of leisure time and daily leisure traffic volume. The data suggested that dummy variables controlling for weekends and holidays were all highly positive and highly significant. This confirmed the expectation that more visitors were on the road during weekends and holidays, when there was more available leisure time. Modeling results further revealed that tourism traffic was particularly high on Friday or Sunday or on the first and last day of a holiday weekend. In Hypothesis 1.6, the volume of leisure traffic is predicted to increases overtime the timeframe of the data. This was tested by including the year variable that took on the value of the year of a data point. The data suggested that leisure traffic increased by 4% per year across models. One reason for this trend may be the overall population growth during the period. Another possible explanation may be the changing age structure of the travelers, such as the aging baby boomers who have more free time to travel. Evaluating and Comparing Models Hypothesis 2.1 predicts that regression models with nonlinear forms are better fitting models than those with linear forms for explaining variation in daily leisure traffic. 93 To test this hypothesis, regression analysis was conducted on five functional forms, each with four seasonal models. The values of R-Squares of all models were over 0.72, indicating high explanatory power. However, models employing the logarithm of traffic (i.e., exponential, double-log, quadratic) consistently showed higher explanatory power over those employing raw traffic counts (i.e., linear, semi-log). Specifically, exponential, double-log, and quadratic models were able to explain 2% to 10% more variation in tourism traffic than linear and semi-log models, depending on the season. To compare performance across five functional forms and identify the best fitting model, the forecasting ability of the five models was examined. Using parameter estimates of the regression results to project daily traffic for the years 2001 and 2002, their forecasting accuracies, or MAPEs, were calculated. The results revealed that exponential, double-log, and quadratic functions were all highly accurate as forecasting tools, compared with the linear and semi-log fimctions that appear less accurate. The double—log, with the lowest MAPE, was thus identified as the best fitting model. In addition, compared with the time-series forecasting approach, particularly the seasonal naive method, models constructed in this study were validated as accurate forecasting tools. Compared to the MAPE of the seasonal naive method (5.90), the double-log model yielded a more accurate MAPE of 5.48, meaning a reduction of 7% in forecasting error. For the purpose of forecasting, the regression approach performed only slightly better than the naive method. However, the regression approach enabled the examination of effects of individual variables on the outcome—in this study, the impacts of weather variability on leisure travel, which would not be possible with the naive method. 94 Applying the Best Fitting Model Hypothesis 3.1 predicts that effects of variations in weather conditions on travel activity will differ across multiple locations. To test this hypothesis, the double-log model was applied to the other seventeen traffic stations. Based on the explanatory power of the models, traffic stations were categorized into eight tourist stations and ten non-tourist stations. For the eight tourist stations, over 60% of variation in daily traffic volume could be accounted for by the statistical models across most seasons. For the ten non-tourist stations, however, R-squares for the seasonal models consistently fell well below 0.5, indicating poor modeling performance. Some of these non-tourist stations were located in rural areas rarely frequented by visitors, while others were in metro areas where there is a high concentration of commuter and business traffic. Further discussion of regression results focused on the effects of weather conditions on traffic across the eight tourist stations. Daily maximum temperature was significant and positive in all eight tourist stations in spring, summer, and fall. The coefficient estimates were consistent across the eight models, with a one-degree increase in temperature causing daily leisure traffic to increase by one to two percent, with a few exceptions showing smaller effects. In winter, however, precipitation was the more important weather variable, with a one millimeter increase in precipitation resulting in an approximately one percent decrease in traffic for seven of the eight tourist stations. Modeling Threshold Temperature and Lagged Effects The testing of lagged effects of weather based on the Clare station on US-127 showed mostly inconclusive results. Most of the temperature and precipitation variables 95 from the past seven days turned out statistically insignificant. One exception was Temp7, maximum temperature from one week prior. Its coefficient estimates indicated that a one- degree increase in temperature from one week ago results in 0.3%, 1.2%, and 0.4% increases in tourism traffic for spring, summer, and fall, respectively. A threshold temperature was discovered with the application of the spline function. Through repetitive testing, a threshold temperature for the summer model was identified at 90°F, when the spline term is negative and statistically significant. The results indicated that a one-degree increase in temperature leads to a 1.1% increase in traffic before the 90°F threshold, but the same increment led to a 7.3% decrease in traffic when temperature exceeded the threshold. Comparison with Existing Studies A comparison of findings of the current study with existing studies was presented in Table 22. As previously mentioned, there has been very limited research involving the examination of quantitative relationships between weather and leisure travel. The findings of these studies were somewhat consistent. Among the five studies compared, all but one study showed that temperature had a positive effect and precipitation had a negative effect on leisure travel. The only study on winter leisure activity (Shih, Nicholls, and Holecek, 2009) revealed that minimum temperature had a negative impact and snow depth had a positive impact on daily ski lift ticket sales. 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The research of Lise and T01 (2002) concluded that a 1°C warmer summer temperature resulted in an increase in same-year domestic travel by 4.7 % and an increase of next-year foreign arrivals by 3.1% for Dutch tourism. The two studies above were both focused on country-level tourism industries, which covered much wider regions and thus exhibit more variation in their results. The findings of the current study showed that the studied area, multiple locations across Michigan, displayed much higher homogeneity. Implications and Applications The quantitative relationships between weather variability and tourism traffic examined in this study have both theoretical and managerial implications. For academic research, results of this study can be incorporated with climate change scenarios to investigate long-term impacts of climate change on the tourism industry. For practical purposes, information of how weather conditions impact daily business volume can be useful to tourism managers or business owners for guiding day-to-day operations. For tourism planners and developers, understanding the effects of weather variability on activity levels is beneficial in making adaptation strategies in response to a changing climate. Theoretical Implications Findings of this study revealed that the volume of general tourism increases by about 1% with a one degree increase in temperature across several locations in Michigan. A report on climate change and its impacts in the US. (Karl, Melillo & Peterson, 2009) 98 predicts that the average US. temperature will keep increasing, the rate of which will depend on emissions scenarios of greenhouse gas.. By the end of the century, average temperature is projected to increase by approximately 4 to 1 1°F. For near-term projection, a 2 to 3 degree increase is predicted by 2029. Precipitation is also expected to increase during the same time span in most of the US. Using this information, long-term implications of climate change on leisure travel can be projected. Assuming the following scenario: Fa Average spending per day per visitor = $150 (Holecek et al., 2000) Total visitor-days to Northern Michigan = 70 million (D. K. Shifflet, 2004) ft;— Economic multiplier (direct and indirect effect) = 1.5 Average temperature increases by 2 to 3 degree by 2029. The change in travel volume between the current year and 15 years in the future can be estimated by multiplying the total visitor volume by 2% and 3%. Economic impact of climate change by Year 2029 can be then approximated by the following: 2% Average Spending * Change in Total Visitor Days * Multiplier = $150 * 70 million * 2% * 1.5 = $315 million 3% Average Spending * Change in Total Visitor Days * Multiplier = $150 * 70 million *3% * 1.5 = $472.5 million Through the above exercise, the economic impact of climate change by Year 2009 is estimated to be between $315 million and $472.5 million under current prices. This exercise, however, has some key weaknesses. First, leisure travel will only benefit from a warming climate to some extent, since a summer threshold temperature was discovered in 99 this study, which suggested that although travelers generally prefer warmer weather, further rise in temperature passing the threshold would cause adverse effect on leisure traffic. Also, precipitation, also predicted to increase in the U.S., was found in this study to have negative impacts on leisure traffic during fall and winter. Omitting precipitation in the equation also contributes to overestimating the economic benefit brought by a warming climate. Thus, to examine the long term, comprehensive implications of climate change on leisure travel, more weather variables and climate scenarios need to be taken into consideration. Managerial Implications One application of this study is for tourism managers and business owners to project how weather variability affects day-to-day operations. An example displayed in Table 23 shows that for the month of July, a peak summer travel season, tourism traffic in the Clare area is expected to increase by 7.5% if the weather is very warm, defined as the average July maximum temperature plus two standard deviations. Conversely, a decrease of 7% is projected corresponding to a very cool month, defined as the average temperature minus two standard deviations. For a hotel manager or restaurant owner near Clare, for instance, understanding the potential range of business volume can be valuable for making business decisions such as seasonal hiring or the purchasing of supplies. For mid- to long-term managerial implications, tourism planners and developers need to first understand the projected climate change within their travel market. In most of the U.S., both temperature and precipitation are expected to increase as previously mentioned. It is then necessary to devise business plans and strategies in response to the 100 Table 23 Variations in July Tourism Traffic Based on Temperature Scenarios (US-127, Clare) Average Max. Temperature Scenarios Very Cool (67 °F) Average (80 °F) Very Warm (93°F) Total Monthly 137,205 147,530 158,649 Traffic Percent Change _7% +7 5% From Average Note: “Very Cool” temperature based on average temperature plus two standard deviations; “Very Warm” temperature based on average temperature minus two stande deviations n potential changes. For example, directors of Convention and Visitor Bureau should think about how warmer temperature and increasing precipitation can affect the activities 9' offered by their destinations. What kind of additional facilities can improve the attractiveness and competitiveness of their destinations? What alternative activities are available for visitors who arrive at their destinations facing extreme hot weather or sudden rainfall? Past studies showed that travelers are capable of adapting and changing their travel behaviors when facing uncertainties and unexpected factors. Decrop and Snelders (2004) argued that vacation decision-making and information search are both ongoing processes that do not stop when the trips are booked. Stewart & Vogt (1999) compared pretrip plans and on-site behavior of travelers and suggested that vacation plans often were changed, especially regarding on-site activities. Also, travelers were more likely to drop planned activities than to add new ones once they arrived at the destinations. For destinations attracting mostly day visitors, climate change may have smaller implications, since potential visitors are more likely to change plans or find another date to visit, as shown in a study regarding travel patterns of 200 visitors (Aylen et al., 2005). 101 For destinations targeting long-distance, overnight visitors, climate change may have stronger implications since their visitors tend to book lodging ahead and stay for longer period of time. When they arrive at a destinations and face unexpected weather conditions such as extreme heat or inclement weather, they may need to modify their plans and find alternative activities to participate. Therefore, tourism planners for these destinations need to develop and balance both indoor and outdoor attractions to still provide visitors satisfactory tourism experiences under uncertain weather conditions. Traditional attractions such as museums, shopping malls, casinos are examples of facilities that are usually not affected by weather variability. Indoor waterpark is another attraction that can stay open year round and appeal to winter travelers. During summer, visitors who intend to participate in beach activities can also enjoy such facility when temperature is getting too hot or in the event of rain. A tourism bureau director can also focus marketing effort on stressing the variety of attractions offered by the destination, including things to do and points of interests that are suitable for all seasons and different kinds of weather conditions. Such marketing campaigns can help attract overnight visitors, whose higher spending will contribute more to the local economy. Suggestions for Future Research The findings of this study have several implications for future research. First, as mentioned before, the focus of this study was on assessing the impacts of weather variability on levels of general tourism. For a comprehensive understanding of weather's effects on the travel industry, similar research on individual leisure travel sectors is necessary. Since different leisure activities require different sets of weather conditions, a 102 warming climate may harm the ski industry but benefit the camping and golfing industries, for example. Also, statistical models constructed in this study can be applied to other locations, perhaps other states or even other countries. Due to differences in visitors' travel patterns and the geographical distribution of tourism resources, the actual modeling results found in other locations are likely to differ fi'om those found in this study. The models established in this study, however, can be efficient tools to examine the relationships between weather conditions and tourism volume outside Michigan. Methods employed in this study can also be duplicated on data fi'om a different era. The current study revealed how several independent variables affected leisure travel based on traffic records from 1991 to 2002. Conducting future research using updated data enables the examination of structural changes across time. As mentioned earlier, record high gas prices of over $4 were recorded in 2008. Also, US economy went into recession near the end of 2007. It will be interesting to investigate the relationships between weather conditions and leisure travel volume under these drastically different Circumstances. Also, forecasting ability of these models can also be tested against more recent traffic records. For example, employing daily traffic records of 2008, researchers can examine whether the double-log model still provides low MAPE and high accuracy Compared to the naive method. One weakness of this study was that among the identified non-tourist stations, a high amount of local or business traffic was mixed in with the leisure traffic, resulting the poor model performance. If surveys focused on purposes of trips are done on the specific 10Ca‘ii ons, leisure travel volume can then be distinguished from the total traffic, and effects of weather variability on leisure travel can be examined for those areas as well. 103 Finally, given the importance of the tourism industry to the economy, it is critical to understand the implications of climate change for the industry. The quantitative relationships discovered in this study, incorporated with varying climate change scenarios, will enable the identification and discussion of potential ranges of long-term effects associated with a changing climate. 104 APPENDIX: Regression Results of Traffic Stations Table 24. Regression Results for Station # 1089 Spring Summer Winter B Std. B Std. B Std. B Std. Error Error Error Error Intercept -1.11 7.18 2.13 6.32 30.04 15.82 12.81 8.61 Max. Temperature 0.01“ 0.00 0.00” 0.00 0.01 0.00 0.01" 0.00 Precipitation 00]” 0.00 0.00“ 0.00 0.00 0.00 -0.02** 0.00 Consumer Confidence -0.17** 0.05 -0.20** 0.04 -0.10 0.11 -0.23** 0.06 Gas Price 0001 0.00 0.00" 0.00 0.00 0.00 0.00 0.00 Friday or Sunday 003'” 0.01 -0.06** 0.01 -0.03 0.02 -0.05** 0.01 Saturday -0.02* 0.01 -0.07** 0.01 —0.01 0.03 -0.06** 0.01 Single-day Holiday N/A N/A -0.30** 0.06 N/A N/A -0.38** 0.07 First or Last day of Holiday- Weekend -0.05* 0.02 -0.02 0.03 -0.06 0.04 -0.06* 0.02 Middle of Holiday- weekend -0.03 0.02 -012" 0.03 -0.16** 0.04 -0.16** 0.02 Year 0.005 0.00 0.0003 0.00 -0.01 0.01 -0.002 0.00 F 39.5 19.0 37.7 R'Square 0.31 0.24 0.09 0.32 Note: P-value for all five models are smaller than 0.001 *Significant at 5% level. MSignificant at 1% level. 105 Table 25. Regression Results for Station # 1109 81% Summer Fall Winter B Std. ‘ B Std. B Std. B Std. Error Error Error Error Intercept 22.68 11.20 6.10 8.60 19.48 9.77 48.55 10.55 Max. Temperature 0.01“ 0.00 001* 0.00 0.02 0.00 0.01** 0.00 Precipitation 0.00" 0.00 0.00 0.00 0.00" 0.00 -002" 0.00 Consumer Confidence -0.29** 0.08 -029" 0.05 017* 0.07 -024" 0.06 Gas Price 0.00 0.00 0.00 0.00 0.00 0.00 0.00" 0.00 Friday or Sunday 0.12" 0.01 0.12" 0.01 0.14“ 0.01 0.07" 0.01 Saturday 0.07“ 0.02 0.11“ 0.01 0.14“ 0.02 0.01" 0.02 Single-day Holiday N/A N/A 0.12 0.14 N/A N/A -O.26* 0.11 First or Last day of Holiday- Weekend 0.30“ 0.03 0.28“ 0.03 0.31" 0.03 0.14“ 0.03 Middle of Holiday- Weekend 0.26“ 0.03 0.18" 0.03 0.01 0.02 -0.06* 0.03 Year -0.01 0.01 0.00 0.00 -001 0.00 41.02" 0.01 F 66.6 32.20 106.2 35.8 R-square 0.43 0.31 0.56 0.34 Note: P-value for all five models are smaller than 0.001, *Significant at 5% level. ”Significant at 1% level. 106 Table 26. Regression Results for Station # 1189 Spring Summer Fall Winter B Std. B Std. B Std. B Std. Error Error Error Error Intercept 55.40 12.93 29.04 7.55 13.57 9.66 20.59 11.38 Max. Temperature 0.01“ 0.00 0.01** 0.00 0.01" 0.00 0.01" 0.00 Precipitation -0.01** 0.00 0.00* 0.00 0.00 0.00 -0.02** 0.00 F‘ Consumer Confidence -O.63** 0.08 -043" 0.05 -0.46** 0.07 -053" 0.07 Gas Price 0.00" 0.00 0.00" 0.00 0.00 0.00 0.00 0.00 Friday or Sunday 0.02 0.01 0.03" 0.01 0.03* 0.01 -0.05** 0.01 Saturday 5" -0.01 0.02 -0.04** 0.01 0.04* 0.02 -0.11** 0.02 Single-day Holiday N/A N/A -0.19* 0.09 N/A N/A -0.57** 0.16 First or Last day of Holiday- Weekend 0.10** 0.03 0.08* 0.03 0.06* 0.03 -0.05 0.03 Middle of Holiday- Weekend 0.06 0.03 -005 0.03 -009" 0.02 -0.18** 0.03 Year -0.02** 0.01 —0.01** 0.00 0.00 0.00 -0.01 0.01 F 26.70 22.00 24.80 34.70 R‘Square 0.27 0.24 0.24 0.34 Note: P-value for all five models are smaller than 0.001 *Significant at 5% level. "Significant at 1% level. 107 Table 27. Regression Results for Station # 2049 Spring Summer Fall Winter B Std. B Std. B Std. B Std. Error Error Error Error Intercept 22.42 20.25 -4.95 12.40 -32.10 13.79 0.47 11.26 Max. Temperame 0.01** 0.00 0.01** 0.00 0.02** 0.00 0.00" 0.00 Precipitation 0.00 0.00 0.00 0.00 0.00 0.00 002" 0.00 Consumer Confidence 0.15 0.15 061** 0.08 020* 0.10 026** 003 Gas Price 0.00** 0.00 0.00 0.00 0.00 0.00 0.00** 0.00 Fridayor Sunday 0.28** 0.03 0.27** 0.02 0.37** 0.02 0.36** 0.01 Saturday 0.09* 0.03 0.22** 0.02 0.16** 0.02 0.06" 0.02 Single-day Holiday N/A 'N/A 0.19 0.14 N/A N/A 0.05 0.10 First or Last day of Holiday- Weekend 0.46** 0.05 0.52" 0.05 0.55** 0.04 0.34** 0.03 Middle of Holiday- Weekend 013* 0.06 0.17** 0.04 0.31** 0.04 0.06 0.03 Year 001 0.01 0.01 0.01 0.02** 0.01 0.00 0.01 F 41.10 45.00 164.70 94.70 R-square 0.31 0.38 0.65 0.53 Note: P~value for all five models are smaller than 0.001 *Significant at 5% level. "Significant at 1% level. 108 Table 28. Regression Results for Station # 3069 Spring Summer Fall Winter B Std. B Std. B Std. B Std. Error Error Error Error Intercept -62.40 9.63 -69.31 7.48 -75.04 10.16 -50.99 14.45 Max. Temperature 0.01" 0.00 0.00 0.00 0.01“ 0.00 0.01M 0.00 Precipitation 0.00 0.00 0.00 0.00 0.00 0.00 -0.02** 0.00 Consumer F Confidence 0.02 0.07 004 0.05 010 0.09 -0.37** 0.10 Gas Price 0.00 0.00 0.00M 0.00 0.00" 0.00 0.00 0.00 Friday or Sunday 0.12" 0.01 0.21" 0.01 0.16" 0.01 0.14M 0.02 Saturday -0.04* 0.02 0.02 0.01 -0.06** 0.02 -0.10** 0.03 g... Single-day b Holiday N/A N/A -0.22 0.1 1 N/A N/A -0.18 0.16 First or Last day of Holiday- Weekend 0.22“ 0.03 0.4 '1 * * 0.03 0.25" 0.03 0.07 0.04“ Middle of Holiday- Weekend M n 0.01 0.03 0.05 0.03 -0.08 0.02 -0.29 0.04 Year 0.04" 0.00 0.04" 0.00 0.04" 0.01 0.03" 0.01 F 27.90 22.90 22.50 30.20 R‘square 0.27 0.24 0.24 0.34 Note: P-value for all five models are smaller than 0.001 *Significant at 5% level. “Significant at 1% level. 109 Table 29. Regression Results for Station # 3129 Spring Summer Fall Winter B Std. B Std. B Std. B Std. Error Error Error Error Intercept -54.26 1 1.39 -47.67 8.00 -58.91 8.46 -36.34 9.78 Max. Temperature 0.01** 0.00 0.01** 0.00 0.01** 0.00 0.01** 0.00 Precipitation . 0.00 0.00 000* 0.00 0.00 0.00 0.00 0.00 Consumer , Confidence 0.00 0.00 0.00 0.00 0.00 0.00 0.00** 0.00 " Gas Price 0.06 0.08 -0.21** 0.05 -0.22** 0.06 -0.31** 0.06 Friday or Sunday 003* 0.01 0.09“ 0.01 0.08“ 0.01 0.03“ 0.01 Saturday * ... E 0.03 0.02 0.03 0.01 0.03 0.01 -0.02 0.02 Single-day Holiday N/A N/A -0.26** 0.09 N/A N/A -0.39** 0.08 First or Last day of Holiday- Weekend 0.04 0.03 0.24“ 0.03 0.08" 0.02 0.00 0.03 Middle of Holiday- weekend 002 0.03 006* 0.03 005* 0.02 023** 0.03 Year 0.03" 0.01 0.03" 0.00 0.03" 0.00 0.02" 0.00 F 55.7 58.10 92.20 75.10 R'squale 0.37 0.41 0.49 0.47 Note: P-value for all five models are smaller than 0.001 *Significant at 5% level. "Significant at 1% level. 110 Table 30. Regression Results for Station # 4149 Spring Summer Winter B Std. B Std. B Std. B Std. Error Error Error Error 1ntercept -56.83 17.91 -39.62 14.23 -46.71 15.22 -43.74 17.50 Max. Temperature 001" 0.00 0.01** 0.00 0.01** 0.00 0.00 0.00 Precipitation 0.00* 0.00 0.00 0.00 000* 0.00 -0.01* 0.00 Consumer m Confidence 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Gas Price 0.15 0.14 -0.43** 0.09 -0.13 0.10 -0.31* 0.12 Friday or Sunday 0.90“ 0.02 0.86" 0.02 0.96** 0.02 0.99" 0.02 Saturday . 0.26** 0.03 0.42** 0.03 0.34** 0.02 0.28** 0.03 -" Single-day Holiday N/A N/A 043* 0.16 N/A N/A 0.65** 0.14 First or Last day of Holiday- Weekend 1.14” 0.05 1.03" 0.06 1.07** 0.04 0.91** 0.05 Middle of Holiday- Weekend 0.74** 0.05 0.59“ 0.06 0.69” 0.04 0.62" 0.05 Year 0.03** 0.01 0.02** 0.01 0.03" 0.01 0.03** 0.01 F 234.80 200.3 391.8 211.6 R-square 0.76 Note: P-value for all five models are smaller than 0.001 *Significant at 5% level. “Significant at 1% level. 111 Table 31. Regression Results for Station # 5229 Spring Summer Fall Winter B Std. B Std. B Std. B Std. Error Error Error Error Intercept -65.69 7.28 -93.69 4.96 -81.12 8.52 -4.52 10.54 Max. Temperature 001’” 0.00 0.00** 0.00 0.00** 0.00 0.01** 0.00 Precipitation 0.00 0.00 0.00 0.00 0.00 0.00 001** 0.00 Consumer Confidence 0.00 0.00 0.00** 0.00 0.00** 0.00 0.00** 0.00 Gas Price 01 1* 0.05 021“ 0.03 -0.34** 0.05 -0.20** 0.06 Friday or Sunday 0.14** 0.01 0.19** 0.01 0.16** 0.01 0.06** 0.01 Saturday 9 0.07** 0.01 0.10** 0.01 0.11** 0.01 002 0.02 ' Single-day Holiday N/A N/A -0.28** 0.05 N/A N/A 053" 0.07 First or Last day of Holiday- Weekend 0.17** 0.02 0.17** 0.02 0.25** 0.02 0.02 0.03 Middle of Holiday- weekend 005* 0.02 010** 0.02 0.09** 0.02 009** 0.03 Year 0.04** 0.00 0.05** 0.00 o.05** 0.00 0.01 0.01 F 166.00 231.80 122.30 170.30 R'square 0.70 0.78 0.64 0.71 Note: P-value for all five models are smaller than 0.001 *Significant at 5% level. "Significant at 1% level. 112 Table 32. Regression Results for Station # 5249 SRring Summer Fall Winter B Std. B Std. B Std. B Std. Error Error Error Error Intercept -59.67 11.67 -107.75 12.21 -88.80 13.09 -54.94 10.67 Max. Temperature 0.01** 0.00 0.01** 0.00 0.01** 0.00 0.01** 0.00 Precipitation 0.00 0.00 0.00 0.00 0.01 0.08 -0.01** 0.00 Consumer n... Confidence 0.22** 0.07 -O.20** 0.06 0.00** 0.00 -0.02 0.06 Gas Price 0.00* 0.00 0.00** 0.00 -0.15* 0.07 0.00** 0.00 Friday or Sunday 048’” 0.01 0.63" 0.01 0.00 0.00 0.45** 0.01 Saturday 0.18** 0.02 0.26" 0.02 0.61“ 0.01 0.14" 0.02 1. Single-day Holiday N/A N/A 026* 0.13 0.25" 0.02 0.04 0.08 First or Last day of Holiday- Weekend 0.70" 0.03 0.89" 0.04 0.71** 0.03 0.38** 0.03 Middle of Holiday- weekend 0.37** 0.03 0.39** 0.04 0.33** 0.03 0.21** 0.03 Year 0.03” 0.01 0.06** 0.01 0.05" 0.01 i 0.03” 0.01 F 329.50 245.80 332.10 212.00 R'Squa’e 0.85 0.86 0.85 0.78 Note: P-value for all five models are smaller than 0.001 *Significant at 5% level. “Significant at 1% level. 113 Table 33. Regression Results for Station # 6049 Spring Summer Fall Winter B Std. B Std. B Std. B Std. Error Error Error Error Intercept -0.43 9.51 -31.83 8.11 -27.92 8.97 28.25 10.13 Max. Temperature 001" 0.00 0.01** 0.00 0.01** 0.00 0.01** 0.00 Precipitation 0.00 0.00 0.00 0.00 0.00** 0.00 -0.01** 0.00 Consumer Confidence 0.01 0.07 013* 0.05 001 0.06 022“ 0.07 Gas Price 0.00 0.00 0.00** 0.00 0.00** 0.00 0.00** 0.00 Friday or Sunday 0.21“ 0.01 0.33“ 0.01 0.25" 0.01 0.08** 0.01 Saturday 0.25" 0.02 0.40** 0.01 0.30" 0.01 0.13" 0.02 Single—day Holiday N/A N/A 0.43“ 0.08 N/A N/A -0.26** 0.09 First or Last day of Holiday- Weekend 0.40“ 0.03 0.48" 0.03 0.28" 0.03 0.1 1** 0.03 Middle of Holiday- Weekend H 0.53 0.03 0.67" 0.03 0.33** 0.02 0.01 0.03 Year 0.00 0.00 0.02** 0.00 0.02" 0.00 -0.01* 0.01 F 144.30 177.10 145.20 39.60 R'S‘l“are 0.65 0.74 0.65 0.33 Note: P-value for all five models are smaller than 0.001 *Significant at 5% level. ”Significant at 1% level. 114 Table 34. Regression Results for Station # 6129 Spring Summer Fall Winter B Std. B Std. B Std. B Std. Error Error Error Error 1ntercept -36.58 10.01 -27.72 8.66 -37.91 11.26 -48.00 18.70 Max. Temperature 001" 0.00 0003* 0.00 0.01** 0.00 0.00* 0.00 Precipitation 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Consumer Confidence 0.00** 0.00 0.00* 0.00 0.00 0.00 0.00 0.00 Gas Price 0.17* 0.08 -O.22** 0.05 027" 0.08 -0. 14 0.11 Friday or Sunday 0.54** 0.01 0.67** 0.01 0.68** 0.01 0.51** 0.02 Saturday 0.19** 0.02 0.26" 0.01. 0.23“ 0.02 0.11" 0.03 Single-day Holiday N/A N/A 020* 0.10 N/A N/A 0.04 0.12 First or Last day of Holiday- Weekend 0.71** 0.03 0.78** 0.03 0.70** 0.03 0.48" 0.05 Middle of Holiday- Weekend 0.37** 0.03 0.37** 0.03 0.42** 0.02 0.24** 0.05 Year 0.02** 0.01 0.02** 0.00 0.02** 0.01 0.03" 0.01 F 288.60 355.90 373.30 87.80 R‘S‘lu‘m 0.79 0.84 0.82 0.54 Note: P-value for all five models are smaller than 0.001 *Significant at 5% level. "Significant at 1% level. 115 Table 35. Regression Results for Station # 6469 Spring Summer Fall Winter B Std. B Std. B Std. B Std. Error Error Error Error Intercept -63.03 6.83 -S7.18 6.52 -81.08 6.77 -44.53 8.64 Max. Temperature 001" 0.00 0.004" 0.00 0.01** 0.00 0.00** 0.00 Precipitation 0.00 0.00 0.00 0.00 0.00* 0.00 -0.01** 0.00 Consumer Confidence 009 0.05 002 0.04 012* 0.05 -0.16** 0.06 Gas Price 0.00 0.00 0.00** 0.00 0.00* 0.00 0.00** 0.00 Friday or Sunday 004" 0.01 0.04** 0.01 -0.03** 0.01 -0.08** 0.01 Saturday -0.09** 0.01 0.02 0.01 -0.08** 0.01 -0.14** 0.01 Single-day Holiday N/A N/A -0.34** 0.09 N/A N/A -0.59** 0.07 First or Last day of Holiday- Weekend -0.03 0.02 0.08** 0.03 0.02 0.02 -0.09** 0.02 Middle of Holiday- Weekend -0.08** 0.02 0.03 0.03 -0.03* 0.02 -0.30** 0.02 Year 0.04** 0.00 0.03M 0.00 0.05** 0.00 0.03" 0.00 F 132.80 43.40 140.90 113.90 Rm“are 0.64 0.45 0.67 0.59 Note: P-value for all five models are smaller than 0.001 *Significant at 5% level. “Significant at 1% level. 116 Table 36. Regression Results for Station # 7309 Spring Summer Fall Winter B Std. B Std. B Std. B Std. Error Error Error Error 1ntercept -75.94 7.46 -69.52 6.87 -74.82 6.65 -44.94 9.78 Max. Temperature 0.01** 0.00 0.01** 0.00 0.01** 0.00 0.01** 0.00 Precipitation 0.00** 0.00 0.00 0.00 000* 0.00 -0.01** 0.00 Consumer 1 confidence 0.00 0.00 0.00 0.00 0.00 0.00 0.00** 0.00 Gas Price 0.17** 0.06 -O.11* 0.04 -0.05 0.05 -0.04 0.07 Friday or Sunday 0.19" 0.01 0.37** 0.01 0.26" 0.01 0.04** 0.01 Saturday J 0.04** 0.01 0.20** 0.01 0.08** 0.01 -0.l3** 0.02 Single-day Holiday N/A N/ A 0.06 0.08 N/A N/A -0.31** 0.08 First or Last day of Holiday- Weekend 0.42" 0.02 0.54" 0.03 0.53" 0.02 0.24M 0.03 Middle of Holiday- Weekend 0.17** 0.02 0.21** 0.03 0.20** 0.02 003 0.03 Year 0.04** 0.00 0.04** 0.00 0.04** 0.00 0.03" 0.00 F 259.20 251.60 377.10 106.00 R'Squa’e 0.75 0.77 0.82 0.56 Note: P-value for all five models are smaller than 0.001 *Significant at 5% level. “Significant at 1% level. 117 1...]..1‘ 7... .vthfl . Table 37. Regression Results for Station # 8209 Spring Summer Fall Winter B Std. B Std. B Std. B Std. Error Error Error Error It t "emep -38.07 9.44 -3090 5.88 -55.11 15.54 19.89 16.89 Max. Temperature 0.01** 0.00 0.00 0.00 0.00** 0.00 0.01** 0.00 Precipitation 0.00** 0.00 000* 0.00 0.00 0.00 -0.01** 0.00 Consumer Confidence 0.09 0.08 0.02 0.03 0.17 0.15 040* 0.16 Gas Price 000* 0.00 0.00 0.00 0.00 0.00 0.00** 0.00 Friday or Sunday 0.04** 0.01 0.04** 0.01 0.02 0.01 —0.08** 0.02 Saturday -0.12** 0.02 008** 0.01 009" 0.01 -0.17** 0.02 Single-day Holiday N/A N/A 032** 0.08 N/A N/A 044** 0.11 First or Last day of Holiday- Weekend 005 0.03 005* 0.02 0.01 0.02 015** 0.04 Middle of Holiday- weekend -0.28** 0.03 020" 0.02 016** 0.02 -0.26** 0.04 Year 0.02** 0.00 0.02** 0.00 0.03** 0.01 0.00 0.01 F 61.40 54.60 36.20 37.50 R’S‘luare 0.52 0.50 0.40 0.43 Note: P-value for all five models are smaller than 0.001 *Significant at 5% level. "Significant at 1% level. 118 Table 38. Regression Results for Station # 8249 Spring Summer Fall Winter B Std. B Std. B Std. B Std. Error Error Error Error Intercept -53.96 10.88 -1 1.90 16.76 17.27 14.06 7.54 13.18 Max. Temperature 000* * 0.00 0.00 0.00 0.00** 0.00 0.01** 0.00 Precipitation 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Consumer Confidence 029* 0.11 081** 0.18 053** 0.14 029* 0.11 Gas Price 0.00 0.00 0.00* 0.00 0.00** 0.00 0.00** 0.00 Friday or Sunday 003* 0.01 0.01 0.01 -0.05** 0.01 -0.10** 0.02 Saturday -0.06** 0.02 -0.02 0.02 014“ 0.02 -0.19** 0.02 Single-day Holiday N/A N/A N/A N/A N/A N/A -0.52** 0.09 First or Last day of Holiday- Weekend 0.01 0.03 006* 0.03 0.19** 0.03 0.00 0.04 Middle of Holiday- Weekend ” ,. u -0.09 0.03 -0.07 0.03 -0.03 0.03 -0.23 0.04 Year 0.03** 0.01 0.01 0.01 0.00 0.01 0.00 0.01 F 45.00 8.90 25.70 46.60 R'S‘llwe 0.31 0.16 0.42 0.43 Note: P-value for all five models are smaller than 0.001 *Significant at 5% level. "Significant at 1% level. 119 Table 39. Regression Results for Station # 9829 Spring Summer Fall Winter B Std. B Std. B Std. B Std. Error Error Error Error 1ntercept 13.97 26.84 40.98 20.46 39.53 21.68 -20.01 17.28 Max. Temperature 0.00 0.00 0.00 0.00 0.01** 0.00 0.01** 0.00 Precipitation -0.01* 0.00 0.00 0.00 0.00 0.00 -0.01 0.00 Consumer Confidence 032 0.28 0.04 0.16 -1.62** 0.19 033** 0.10 Gas Price 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Friday or Sunday 023“ 0.03 -0.19** 0.03 -0.21** 0.02 -0.25** 0.03 Saturday -0.29** 0.03 -0.30** 0.03 -0.29** 0.03 -0.29** 0.03 Single-day Holiday N/A N/A -0.60* 0.22 N/A N/A -0.80** 0.13 First or Last day of Holiday- Weekend -0.38** 0.06 -0.29** 0.08 -0.30** 0.05 -0.21** 0.05 Middle of Holiday- weekend -0.59** 0.07 -0.56** 0.08 044** 0.05 044** 0.05 Year 0.00 0.01 -0.01 0.01 -0.01 0.01 0.02 0.01 F 23.90 15.70 32.50 28.10 R‘S‘lum 0.42 0.32 0.39 0.38 Note: P-value for all five models are smaller than 0.001 *Significant at 5% level. ”Significant at 1% level. 120 Table 40. Regression Results for Station # 9849 Sprirg Summer Fall Winter B Std. B Std. B Std. B Std. Error Error Error Error 1ntercept 10.68 0.74 -155.95 143.87 103.44 90.74 50.90 79.73 Max. Temperame 0.00 0.00 001 0.01 0.00 0.00 0.01 0.00 Precipitation 0.00 0.01 0.00 0.00 0.00 0.00 -0.01 0.01 Consumer Confidence 0.45 0.77 -0.63 0.81 -0.67 0.99 1.87 1.68 Gas Price 0.00 0.01 0.00 0.00 0.00 0.00 0.00 0.00 Friday or Sunday 032“ 0.06 -0.30** 0.04 -0.29** 0.04 -0.32** 0.04 Saturday -0.34** 0.08 -0.38** 0.05 -0.38** 0.05 -0.38** 0.06 Single-day Holiday N/A N/A N/A N/A N/A N/A N/A N/A First or Last day of Holiday- Weekend -0.33* 0.13 -0.34* 0.15 -0.39** 0.10 -0.40* 0.09 Middle of Holiday- Weekend -0.46** 0.16 053M 0.15 -0.43** 0.12 063** 0.10 Year 0.02 0.00 0.08 0.07 —0.05 0.05 -0.02 0.04 F 5.90 11.80 12.80 16.50 R'Square 0.41 0.47 0.45 0.49 Note: P-value for all five models are smaller than 0.001 *Significant at 5% level. "Significant at 1% level. 121 References Agnew, M. D., & Palutikof, J. P. (2006). 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