MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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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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