The athletic director of State University is interested in developing a multiple regression model that might be used to explain the variation in attendance at football games at his school. A sample of 16 games was selected from home games played during the past 10 seasons. Data for the following factors were determined:
y = Game attendance
x1 = Team win > loss percentage to date
x2 = Opponent win > loss percentage to date
x3 = Games played this season
x4 = Temperature at game time
The sample data are in the file called Football.
a. Build a multiple regression model using all four independent variables. Write a short report that outlines the characteristics of this model.
b. Develop a table of residuals for this model. What is the average residual value? Why do you suppose it came out to this value? Discuss.
c. Based on the appropriate residual plot, what can you conclude about the constant variance assumption? Discuss.
d. Based on the appropriate residual analysis, does it appear that the model errors are independent? Discuss.
e. Can you conclude, based on the appropriate method of analysis, that the model error terms are approximately normally distributed?