For the punter data in Example 12.13, an additional response, "punting distance," was also recorded. The following are average distance values for each of the 13 punters:

(a) Using the distance data rather than the hang times, estimate a multiple linear regression model of the type μ _Y׀x₁, x₂, x₃, x₄, x₅ = 00 + β _l x_l + β₂x₂ + β₃x₃ + β₄x₄ + β₅x₅ for predicting punting distance.

(b) Use stepwise regression with a significance level of 0.10 to select a combination of variables. 13

(c) Generate values for s², R², PRESS, and Σ¹³_r=1׀δi׀ for the entire set of 31 models. Use this information to determine the best combination of variables for predicting punting distance.

(d) For the final model you choose plot the standardized residuals against. Y and do a normal probability plot of the ordinary residuals. Comment

Distance, y (ft) Punter 162.50 144.00 2 3 147.50 163.50 192.00 171.75 162.00 104.93 105.67 117.59 11 140.25 12 150.17 13 165.16