Applied Statistics and Probability for Engineers

416 CHAPTER 12 MULTIPLE LINEAR REGRESSION

For the model Y 0  1 x 1  2 x 2 , the normal Equations 12-10 are

Inserting the computed summations into the normal equations, we obtain

The solution to this set of equations is

Therefore, the fitted regression equation is

This equation can be used to predict pull strength for pairs of values of the regressor variables

wire length (x 1 ) and die height (x 2 ). This is essentially the same regression model given in

Equation 1-7, Section 1-3. Figure 1-14 shows a three-dimentional plot of the plane of predicted

values generated from this equation.yˆ

yˆ2.263792.74427x 1 0.01253x 2

ˆ 0 2.26379, ˆ 1 2.74427, ˆ 2 0.01253

8294 ˆ 0 77,177ˆ 1 3,531,848ˆ 2 274,811.31

206 ˆ 0  2396 ˆ 1  77,177ˆ 2 8,008.37

25 ˆ 0  206 ˆ 1  8294 ˆ 2 725.82

ˆ (^0) a
n
i 1
̨ xi 2 ˆ (^1) a
n
i 1
̨xi 1 xi 2 ˆ (^2) a
n
i 1
̨x^2 i 2 a
n
i 1
̨xi 2 yi
ˆ (^0) a
n
i 1
̨ xi 1  ̨ˆ (^1) a
n
i 1
̨x^2 i 1 ˆ (^2) a
n
i 1
̨xi 1 xi 2 a
n
i 1
xi 1 ̨yi
nˆ 0 ˆ (^1) a
n
i 1
̨xi 1 ˆ (^2) a
n
i 1
̨xi 2 a
n
i 1
yi
187.5
24.45 54.15
462.5
5.75 15.25 187.5 462.5
Strength
Length
Height
5.75
15.25
24.45
54.15
Figure 12-4 Matrix of scatter plots (from Minitab) for the wire bond pull
strength data in Table 12-2.
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