In 2012, the New York Yankees won 95 games and spent $198 million on salaries for their players (USA Today). Is there a relationship between salary and team performance in Major League Baseball? For the 2012 season, a linear model fit to the number of Wins (out of 162 regular season games) from the team Salary ($M) for the 30 teams in the league is:
Wins = 76.45 + 0.046 Salary.
a) What is the explanatory variable?
b) What is the response variable?
c) What does the slope mean in this context?
d) What does the ^/-intercept mean in this context? Is it meaningful?
e) If one team spends $10 million more than another on salaries, how many more games on average would you predict them to win?
f) If a team spent $110 million on salaries and won half (81) of their games, would they have done better or worse than predicted?
g) What would the residual of the team in part f be?
h) The R2 for this model is 2.05% and the residual standard deviation is 12.0 games. How useful is this model likely to be for predicting the number of wins?