Montgomery, Peck, and Vining (2001) present data concerning the performance of the 28 National Football League teams in 1976. It is suspected that the number of games won (y) is related to the number of yards gained rushing by an opponent (x). The data are shown in the following table.
(a) Calculate the least squares estimates of the slope and intercept. What is the estimate of 2? Graph the regression model.
(b) Find an estimate of the mean number of games won if the opponents can be limited to 1800 yards rushing.
(c) What change in the expected number of games won is associated with a decrease of 100 yards rushing by an opponent?
(d) To increase by 1 the mean number of games won, how much decrease in rushing yards must be generated by the defense?
(e) Given that x = 1917 yards (Cincinnati), find the fitted value of y and the corresponding residual.