Applied Statistics and Probability for Engineers

12-6 ASPECTS OF MULTIPLE REGRESSION MODELING 455

x 1 clarity to the previous three regressors, results in maximum R^2 adj(or minimum MSE). The

three-variable model is

and the four-variable model is

yˆ4.991.79 x 1 0.530 x 2 1.26 x 4 0.659 x 5

yˆ6.470.580 x 2 1.20 x 4 0.602 x 5

Table 12-16 Wine Quality Data

x 1 x 2 x 3 x 4 x 5 y

Clarity Aroma Body Flavor Oakiness Quality

1 1.0 3.3 2.8 3.1 4.1 9.8

2 1.0 4.4 4.9 3.5 3.9 12.6

3 1.0 3.9 5.3 4.8 4.7 11.9

4 1.0 3.9 2.6 3.1 3.6 11.1

5 1.0 5.6 5.1 5.5 5.1 13.3

6 1.0 4.6 4.7 5.0 4.1 12.8

7 1.0 4.8 4.8 4.8 3.3 12.8

8 1.0 5.3 4.5 4.3 5.2 12.0

9 1.0 4.3 4.3 3.9 2.9 13.6

10 1.0 4.3 3.9 4.7 3.9 13.9

11 1.0 5.1 4.3 4.5 3.6 14.4

12 0.5 3.3 5.4 4.3 3.6 12.3

13 0.8 5.9 5.7 7.0 4.1 16.1

14 0.7 7.7 6.6 6.7 3.7 16.1

15 1.0 7.1 4.4 5.8 4.1 15.5

16 0.9 5.5 5.6 5.6 4.4 15.5

17 1.0 6.3 5.4 4.8 4.6 13.8

18 1.0 5.0 5.5 5.5 4.1 13.8

19 1.0 4.6 4.1 4.3 3.1 11.3

20 0.9 3.4 5.0 3.4 3.4 7.9

21 0.9 6.4 5.4 6.6 4.8 15.1

22 1.0 5.5 5.3 5.3 3.8 13.5

23 0.7 4.7 4.1 5.0 3.7 10.8

24 0.7 4.1 4.0 4.1 4.0 9.5

25 1.0 6.0 5.4 5.7 4.7 12.7

26 1.0 4.3 4.6 4.7 4.9 11.6

27 1.0 3.9 4.0 5.1 5.1 11.7

28 1.0 5.1 4.9 5.0 5.1 11.9

29 1.0 3.9 4.4 5.0 4.4 10.8

30 1.0 4.5 3.7 2.9 3.9 8.5

31 1.0 5.2 4.3 5.0 6.0 10.7

32 0.8 4.2 3.8 3.0 4.7 9.1

33 1.0 3.3 3.5 4.3 4.5 12.1

34 1.0 6.8 5.0 6.0 5.2 14.9

35 0.8 5.0 5.7 5.5 4.8 13.5

36 0.8 3.5 4.7 4.2 3.3 12.2

37 0.8 4.3 5.5 3.5 5.8 10.3

38 0.8 5.2 4.8 5.7 3.5 13.2

c12 B.qxd 5/20/02 3:01 PM Page 455 RK UL 6 RK UL 6:Desktop Folder:TEMP WORK:MONTGOMERY:REVISES UPLO D CH 1 14 FIN L:Quark Files: