American football is the highest-paying sport on a per-game basis. Given that the quarterback is considered the most important player 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.

a. Estimate: Salary = β₀ + β₁PC + β₂TD + β₃Age + ɛ.
b. Interpret the slope coefficient attached to TD.
c. Player 8 earned 12.9895 million dollars during the season. According to the model, what is his predicted salary if PCT = 70.6, TD = 34, and Age = 30?
d. Player 16 earned 8.0073 million dollars during the season. According to the model, what is his predicted salary if PCT = 65.5, TD = 28, and Age = 32?
e. Compute and interpret the residual salary for Player 8 and Player 16.

Transcribed Image Text:

Player 1 2 32 Salary 25.5566 22.0441 ⠀ 0.6260 PC TD Age 27 26 ⠀ 29 65.2 28 60.5 27 # 26 63.1