American football is the highest-paying sport on a per-game basis. Given that the quarterback is considered the most important p
layer on the team, he is typically well-compensated. A sports statistician examines the factors that influence a quarterback’s salary. He believes that a quarterback’s pass completion rate is the most important variable affecting salary. He also wonders how total touchdowns scored and a quarterback’s age might impact salary. The statistician collects data on salary (Salary in $ millions), pass completion rate (PC in %), total touchdowns scored (TD), and age for 32 quarterbacks during a recent season. A portion of the data is shown in the accompanying table. Player Salary PC TD Age
1 25.5566 65.2 28 27
2 22.0441 60.5 27 26
⋮ ⋮ ⋮ ⋮ ⋮
32 0.6260 63.1 26 29
Click here for the Excel Data File
a. Estimate the model defined as Salary = β0 + β1PC + β2TD + β3Age + ε. (Round your answers to 2 decimal places. Negative values should be indicated by a minus sign.)
b. Interpret the slope coefficient attached to TD.
multiple choice
All else constant, a quarterback’s salary is expected to increase by approximately $790,000 for each additional touchdown.
A younger quarterback is expected to throw 79 touchdowns a season.
An older quarterback is expected to throw 79 touchdowns a season.
As a quarterback’s salary increases by $1,000,000, he is expected to throw 79 touchdowns a season, all else constant.
c. Player 8 earned 12.9895 million dollars during the season. According to the model, what is his predicted salary if PC = 70.6, TD = 34, and Age = 30? (Do not round intermediate calculations. Round final answer to 2 decimal places.)
d. Player 16 earned 8.0073 million dollars during the season. According to the model, what is his predicted salary if PC = 65.7, TD = 28, and Age = 32? (Do not round intermediate calculations. Round final answer to 2 decimal places.)
e-1. Compute the residual salary for Player 8 and Player 16. (Negative values should be indicated by a minus sign. Round final answer to 2 decimal places.)
e-2. Interpret the residual salary for Player 8 and Player 16.
