2. Use the \"Quarterback Salaries\" data set on Canvas for the following problem

Question

2. Use the "Quarterback Salaries" data set on Canvas for the following problem. 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 regression model that links the quarterback’s salary with his pass completion percentage (PCT), total touchdowns scored (TD), and his age.

a. Estimate the model defined as: Salary = 0 +1PCT +2T D+3Age+

b. Interpret the b2 and b3 coefficients.

c. Drew Brees earned $12.9895 million 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 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.

Number Player Salary (in $million) PCT TD Age 1 Philip Rivers 25.5566 65.2 28 27 2 Jay Cutler 22.0441 60.5 27 26 3 Eli Manning 20.5000 62.3 27 28 4 Kurt Warner 19.0047 66.1 26 38 5 Matt Schaub 17.0000 67.9 29 28 6 Matt Cassel 15.0052 55 16 27 7 Peyton Manning 14.0057 68.8 33 33 8 Drew Brees 12.9895 70.6 34 30 9 Donovan McNabb 12.5073 60.3 22 33 10 Brett Favre 12.0000 68.4 33 40 11 JaMarcus Russell 11.2554 48.8 3 24 12 Carson Palmer 9.5000 60.5 21 29 13 Joe Flacco 8.6018 63.1 21 24 14 Aaron Rodgers 8.6000 64.7 30 26 15 David Garrard 8.5000 60.9 15 31 16 Tom Brady 8.0073 65.7 28 32 17 Matt Ryan 7.9073 58.3 22 24 18 Ben Roethlisberger 7.7516 66.6 26 27 19 Marc Bulger 6.5073 56.7 5 32 20 Jake Delhomme 6.3250 55.5 8 34 21 Matt Hasselbeck 6.2562 60 17 34 22 Alex Smith 4.0073 60.5 18 25 23 Matthew Stafford 3.1000 53.3 13 21 24 Ryan Fitzpatrick 2.9956 55.9 9 27 25 Jason Campbell 2.8648 64.5 20 27 26 Mark Sanchez 2.5450 53.8 12 23 27 Vince Young 2.1673 58.7 10 26 28 Brady Quinn 2.0079 53.1 8 25 29 Josh Freeman 1.3800 54.5 10 21 30 Kyle Orton 1.0950 62.1 21 27 31 Chad Henne 0.9503 60.8 12 24 32 Tony Romo 0.6260 63.1 26 29 Home Insert Page Layout Formulas Calibri -12 A A Copy B I U Format Paintar Number Philip Rivers 25.5566 65.2 28 27 Jay Cutler 4 3 Eli Manning 20.5000 Kurt Warner Matt Schaub 17.0000 Matt Cassel Peyton Manning 14.0057 70.6 34 JaMarcus Russell 11.2554 2 11 3 12 Carson Palmer 9.5000 Joe Flacco 21 24 15 14 Rodgers 86000 David 300 26 60.9 15 31 Tom Brady 7 16 8.0073 65.7 28 32 Matt Ryan 8 17 7.9073 58.3 22 19 18 66.6 26 27 Ben Roethlisberger 7.7516 Marc Bulger 20 19 32 21 20 22 21 Matt Hasselbeck 6.2562 60 17 34 Alex Smith Matthew Stafford 3.1000 25 24 55.9 9 Ryan Fitzpatrick 2.9956 27 Jason Campbell 2.8648 2.1673 58.7 10 26 Vince Young 28 27 Brady Quinn 28 2.0079 53.1 25 30 29 Josh Freeman 1.3800 54.5 100 1.0950 62.1 21 27 Kyle Orton 31 30 0.9503 Chad Henne 32 31 60.8 12 24 Tony Romo 33 32 0.6260 63.1 26 29 Quarterback Salaries Ask me anything Quarterback Salaries nt to d wrap Text Merge & Center Formatting nsert Delete William Auto Sum Cle Sort & Find Select :38 AM 2/23/2017

Explanation / Answer

a) salary = 32.7866 -0.8265 * PCT + 0.785* TD + 0.3862 * AGE

b) b2 = 0.785 at p-value = 0.003 is significant, hence touchdown has an effect on the salary

b3 = 0.3862 at p-value = 0.13 is NOT significant, hence age doesn't have an effect on the salary

c) Drew bees' salary is predicted to be 12.71 and is very close to the original value of 12.9895 and has a very low residual of 0.277

d) Tom Brady's salary is predicted to be 6.2008. It is not very close to the original value of 8.0073 and has a residual of 2.299

e) residual salary explained in c and d itself

Related Questions

Navigate

• Browse (All)
• Browse 2
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.