Due: Thursday, November 13, by noon

Data: baseball_data.xls (Excel Spreadsheet)

Introduction: This problem set is based on material in Chapter 10. This problem set is designed to familiarize you with the use of linear regression models in forecasting as discussed in Chapters 10 and 6 of the text.

Instructions: Open the spreadsheet baseball_data.xls in Excel. This spreadsheet contains the following variables:

• year: Calendar year
• teamname: Name of professional baseball team
• avg_attend: Average annual attendance
• price: average ticket price
• playoff: =1 if team made playoffs in season
• strike: =1 if a baseball strike took place in season
• wins: Number of games won is season
• pct: Percent of games won in season

Problem Set Question: In this problem set, you will forecast demand for attendance at Philadelphia Phillies baseball games. Make sure you use the Philadelphia data and not the Kansas City data we used in lab!

1. Create a time series plot of the average annual attendance for the Philadelphia Phillies over the period 1990-2001. Describe the relevant features on this graph.
2. Create a scatter plot of the annual attendance against average ticket price for the Philadelphia Phillies over the period 1990-2001. Make sure that the ticket price is graphed on the vertical axis. Interpret this graph in the context of the theory of consumer behavior.
3. Use the OLS method to estimate all parameters of the following empirical models
   Y_i = a₁ + b₁X_i + e_i
   where Y_i is average annual attendance in season i and X_i is the average ticket price in season i.
4. Explain what the coefficient estimates from the regression model mean and describe the regression results in the context of their use in forecasting attendance demand.
5. Use a t-test to test the null hypothesis that b₁ is equal to -1500. Use steps (a) through (d) on pages 211-212 in the text as a guide for your hypothesis test.
6. Use the regression results to generate a point forecast of average annual attendance if the average ticket price was $12.
7. Use the regression results to generate an interval forecast of average annual attendance if the average ticket price was $12. Use the 95% level to construct the interval. Discuss the accuracy of your forecast in the context of this interval.
8. What would happen to your interval forecast if
   • The sample size increased?
   • The total variation in the price data decreased?
   • The standard error of the estimate increased?
9. The actual average ticket price in 2002 was $15.26. Generate a point forecast of average attendance in 2002 from the regression model.
10. The actual average attendance in 2002 was 19,977. How far off was your forecast? Discuss how you might determine if this was a "good" forecast.