Question

Fundameintals of Quant p between total team salary and the performance of teams in the N l6 r NFL) Foe the 2006 season, a lincar model predicting Wins (out of She )hom the total tean Salary (in miltions of USD) for the 32 teans in the lengue night yoa c) What is the probability that no one makes a parcbase in the net 2 id Wins1.783+0.062 x Salary s made wins bWhatdoes the lope mean in this context? e) Ifone team d) If'a teaim spent $50 milion on salaries and won 5 games, would they have done better or worse than wirs more than another on salary, how many more games on average would you predict them to win?

Answer 1

2.

a. Salary is the explanatory variable and wins is response variable

b. Slope in this example indicates increase in number of matches won per increase of one million dollar

c.

Wins = 1.783 + 0.062*salary

For team 1, let's say salary is x

Wins = 1.783+ 0.062*x

For team 2, salary is 10+x

Thus wins = 1.783+ 0.062*(10+x)

Thus, difference in games won by team 2 over team 1

= 1.783 + 0.062*(10+x) - (1.783+0.062*x)

= 0.62

d.

If team spends 50 million dollars,

Expected wins = 1.783 + 0.062*50

= 4.883

Thus, expected number of wins is 4.883 but team won 5 games. So they did better than expected.