Suppose the athletic director at Villanova University would like to develop a regression model to predict the point differential for games played by the college’s men’s basketball team. A point differential is the difference between the final points scored by two competing teams. A positive differential is a win for Villanova, and a negative differential is a loss. For a random sample of games, shown in the Excel file Villanova basketball 1.xlsx, the point differential was calculated for Villanova, along with the number of assists, rebounds, turnovers, and personal fouls.
a. Construct a regression model using all four independent variables.
b. Interpret the meaning of the regression coefficients.
c. Predict the average point differential for a game in which Villanova had 12 assists, 32 rebounds, 15 turnovers, and 20 personal fouls.
d. Construct a 95% confidence interval for the average point differential for the game described in part c. Interpret the meaning of the interval.
e. Construct a 95% prediction interval for the point differential for the game described in part c. Interpret the meaning of the interval.
f. Explain the reason for the different intervals in parts d and e.