American football is the highest paying sport on a per-game basis. The quarterback, considered the most important player on the team, is appropriately compensated. A sports statistician wants to use 2009 data to estimate a multiple linear regression model that links the quarterback’s salary with his pass completion percentage (PCT), total touchdowns scored (TD), and his age. A portion of the data is shown in the accompanying table; the entire data set, labeled Quarterback_Salaries, can be found on the text website.
a. Estimate the model defined as Salary = β0 + β1PCT + β2TD + β3Age + .
b. Are you surprised by the estimated coefficients?
c. Drew Brees earned 12.9895 million dollars in 2009. According to the model, what is his predicted salary given his PCT, TD, and age of 70.6, 34, and 30, respectively?
d. Tom Brady earned 8.0073 million dollars in 2009.
According to the model, what is his predicted salary given his PCT, TD, and age of 65.7, 28, and 32, respectively?
e. Compute and interpret the residual salary for Drew Brees and Tom Brady.