Applied Statistics and Probability for Engineers

12-3

The data will be coded by defining a new set of scaled regressor variables as

where is the corrected sum of squares of the levels of wj. The coded data

are shown in Table S12-2. This transformation makes the column of ones in Xorthogonal to the

Sjjg

n

i 11 wijwj^2

2

xij

wijwj

1 Sjj

i1, 2,p, 15 j1, 2, 3, 4

Table S12-1 Cement Data

Observation

Number yw 1 w 2 w 3 w 4

1 28.25 10 31 5 45

2 24.80 12 35 5 52

3 11.86 5 15 3 24

4 36.60 17 42 9 65

5 15.80 8 6 5 19

6 16.23 6 17 3 25

7 29.50 12 36 6 55

8 28.75 10 34 5 50

9 43.20 18 40 10 70

10 38.47 23 50 10 80

11 10.14 16 37 5 61

12 38.92 20 40 11 70

13 36.70 15 45 8 68

14 15.31 7 22 2 30

15 8.40 9 12 3 24

Table S12-2 Coded Cement Data

Observation

Number yx 1 x 2 x 3 x 4

1 28.25 .12515 .00405 .09206 .05538

2 24.80 .02635 .08495 .09206 .03692

3 11.86 .37217 .31957 .27614 .03692

4 36.60 .22066 .22653 .27617 .33226

5 15.80 .22396 .50161 .09206 .39819

6 16.23 .32276 .27912 .27617 .31907

7 29.50 .02635 .10518 .00000 .07647

8 28.75 .12515 .06472 .09206 .01055

9 43.20 .27007 .18608 .36823 .27425

10 38.47 .51709 .38834 .36823 .40609

11 10.14 .17126 .12500 .09206 .15558

12 38.92 .36887 .18608 .46029 .27425

13 36.70 .12186 .28721 .18411 .24788

14 15.31 .27336 .17799 .36823 .25315

15 8.40 .17456 .38025 .27617 .33226

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