2. Using data from the 2007 Major League Baseball season (World Series champions

Question

2. Using data from the 2007 Major League Baseball season (World Series champions: Boston Red Sox) Sammy Stat estimated the following simple regression (or Y equation: Expected Team Wins (in number of games) - Wins 70.097+0.132Team Salary (in Smillions) a. Interpret the value of the estimated slope coefficient for Team Salary. b. Is the baseline value (or intercept) meaningful? Explain briefly. c. If team A spent S10,000,000 more on salaries than team B, how many more games would you expect team A to have won than team B? d. If a team spent $110,000,000 on salaries and won half (or 81) of its 162 games, did the team "get its money's worth?" Explain briefly.

Explanation / Answer

From given information, Let regression model is as

expected team Wins( in number of games) = 70.097 + 0.132 * Team salary( in $ million)

a) The value of the estimated slop coefficient for team salary is 0.132 . i.e. It means that Expectd team wins is increased by 0.132 times of increasing Team salary. That is if Team salary is unique i.e. $1 then Expected team wins is 70.229.

b) Value of the estimated basline value or intercept is 70.097. It means that Expected Team wins is greater than or equal to 70.097. If Team Salary is $0 then Expected team wins is equal to 70.097.

c) If team A spent $10000000 more on salaries than team B, Then

Expected team wins = 70.097 + 0.132 * 10 = 70.097 + 1.32 = 71.417

That is 71.417 more games would we expect team A to have won than team B.

d) If team spent $110000000 on salary then,

Expected Team wins = 70.097 + 0.132 * 110 = 70.097 + 14.52 = 84.617 .

That is team won more than 81 games. so the team "get its money's worth".

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