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:

Punter                   Distance, y (ft)

1................................ 162.50

2..................................144.00

3..................................147.50

4..................................163.50

5..................................192.00

6..................................171.75

7..................................162.00

8..................................104.93

9..................................105.67

10.................................117.59

11.................................140.25

12.................................150.17

13.................................165.16

(a) Using the distance data rather than the hang times, estimate a multiple linear regression model of the type

µY|x1,x2,x3,x4,x5 = 00 + β1xl + 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.

(c) Generate values for s², R², PRESS, andthe 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.

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