Applied Statistics and Probability for Engineers

448 CHAPTER 12 MULTIPLE LINEAR REGRESSION

We will fit the model

The yvector, Xmatrix, and vector are as follows:

Solving the normal equations gives the fitted model

The test for significance of regression is shown in Table 12-12. Since f 0 2171.07 is signifi-

cant at 1%, we conclude that at least one of the parameters  1 and  11 is not zero. Furthermore,

the standard tests for model adequacy do not reveal any unusual behavior, and we would con-

clude that this is a reasonable model for the sidewall panel cost data.

yˆ2.198266290.02252236x0.00012507 ̨x^2

X¿XˆX¿y

y

1.81

1.70

1.65

1.55

1.48

1.40

1.30

1.26

1.24

1.21

1.20

1.18

X

1 20 400

1 25 625

1 30 900

1 35 1225

1 40 1600

1 50 2500

1 60 3600

1 65 4225

1 70 4900

1 75 5625

1 80 6400

1 90 8100

£

 0

 1

 11

§

Y 0  1 x 11 x^2 

Figure 12-11 Data for Example 12-11.

20

1.00

1.10

1.20

1.30

1.40

1.50

1.60

1.70

1.80

1.90

30 40 50 60 70 80 90

Lot size, x

Average cost per unit,

y

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