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 data collected are in the file called Football.
a. Produce scatter plots for each independent variable versus the dependent variable. Based on the scatter plots, produce a model that you believe represents the relationship between the dependent variable and the group of predictor variables represented in the scatter plots.
b. Based on the correlation matrix developed from these data, comment on whether you think a multiple regression model will be effectively developed from these data.
c. Use the sample data to estimate the multiple regression model that contains all four independent variables.
d. What percentage of the total variation in the dependent variable is explained by the four independent variables in the model?
e. Test to determine whether the overall model is statistically significant. Use α = 0.05.
f. Which, if any, of the independent variables is statistically significant? Use a significance level of α = 0.08 and the p -value approach to conduct these tests.
g. Estimate the standard deviation of the model error and discuss whether this regression model is acceptable as a means of predicting the football attendance at State University at any given game.
h. Define the term multicollinearity and indicate the potential problems that multicollinearity can cause for this model. Indicate what, if any, evidence there is of multicollinearity problems with this regression model. Use the variance inflation factor to assist you in this analysis.
i. Develop a 95% confidence interval estimate for each of the regression coefficients and interpret each estimate. Comment on whether the interpretation of the intercept is relevant in this situation.