Player Salary PC TD Age 1 25.5566 65.2 28 27 2 22.0441 60.5 27 26 3 20.5000 62.3 27 28 4 19.0047 66.1 26 38 5 17.0000 67.9 29 28 6 15.0052 55 16 27 7 14.0057 68.8 33 33 8 12.9895 70.6 34 30 9 12.5073 60.3 22 33 10 12.0000 68.4 33 40 11 11.2554 48.8 3 24 12 9.5000 60.5 21 29 13 8.6018 63.1 21 24 14 8.6000 64.7 30 26 15 8.5000 60.9 15 31 16 8.0073 65.7 28 32 17 7.9073 58.3 22 24 18 7.7516 66.6 26 27 19 6.5073 56.7 5 32 20 6.3250 55.5 8 34 21 6.2562 60 17 34 22 4.0073 60.5 18 25 23 3.1000 53.3 13 21 24 2.9956 55.9 9 27 25 2.8648 64.5 20 27 26 2.5450 53.8 12 23 27 2.1673 58.7 10 26 28 2.0079 53.1 8 25 29 1.3800 54.5 10 21 30 1.0950 62.1 21 27 31 0.9503 60.8 12 24 32 0.6260 63.1 26 29 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. 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 $780,000 for each additional touchdown. A younger quarterback is expected to throw 78 touchdowns a season. An older quarterback is expected to throw 78 touchdowns a season. As a quarterback’s salary increases by $1,000,000, he is expected to throw 78 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.
Player Salary PC TD Age
1 25.5566 65.2 28 27
2 22.0441 60.5 27 26
3 20.5000 62.3 27 28
4 19.0047 66.1 26 38
5 17.0000 67.9 29 28
6 15.0052 55 16 27
7 14.0057 68.8 33 33
8 12.9895 70.6 34 30
9 12.5073 60.3 22 33
10 12.0000 68.4 33 40
11 11.2554 48.8 3 24
12 9.5000 60.5 21 29
13 8.6018 63.1 21 24
14 8.6000 64.7 30 26
15 8.5000 60.9 15 31
16 8.0073 65.7 28 32
17 7.9073 58.3 22 24
18 7.7516 66.6 26 27
19 6.5073 56.7 5 32
20 6.3250 55.5 8 34
21 6.2562 60 17 34
22 4.0073 60.5 18 25
23 3.1000 53.3 13 21
24 2.9956 55.9 9 27
25 2.8648 64.5 20 27
26 2.5450 53.8 12 23
27 2.1673 58.7 10 26
28 2.0079 53.1 8 25
29 1.3800 54.5 10 21
30 1.0950 62.1 21 27
31 0.9503 60.8 12 24
32 0.6260 63.1 26 29
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.
| 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 $780,000 for each additional touchdown.
-
A younger quarterback is expected to throw 78 touchdowns a season.
-
An older quarterback is expected to throw 78 touchdowns a season.
-
As a quarterback’s salary increases by $1,000,000, he is expected to throw 78 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.
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