See Table E11-1 for data on the ratings of quarterbacks for the 2008 National Football League season (The Sports Network). It is suspected that the rating (y) is related to the average number of yards gained per pass attempt (x).

(a) Calculate the least squares estimates of the slope and intercept. What is the estimate of σ²? Graph the regression model.

(b) Find an estimate of the mean rating if a quarterback averages 7.5 yards per attempt.

(c) What change in the mean rating is associated with a decrease of one yard per attempt?

(d) To increase the mean rating by 10 points, how much increase in the average yards per attempt must be generated?

(e) Given that x = 7.21 yards, find the fitted value of x and the corresponding residual.