Applied Statistics and Probability for Engineers

430 CHAPTER 12 MULTIPLE LINEAR REGRESSION

A computational formula for SSRmay be found easily. Now since

we may rewrite Equation 12-19 as

or

SSESSTSSR

Therefore, the regression sum of squares is

(12-20)

EXAMPLE 12-3 We will test for significance of regression (with 

0.05) using the wire bond pull strength

data from Example 12-1. The total sum of squares is

The regression sum of squares is computed from Equation 12-20 as follows:

and by subtraction

The analysis of variance is shown in Table 12-10. To test we calculate the

statistic

Since f 0 f0.05,2,223.44 (or since the P-value is considerably smaller than = 0.05),

we reject the null hypothesis and conclude that pull strength is linearly related to either wire

length or die height, or both. However, we note that this does not necessarily imply that the

f 0 

MSR

MSE



2995.3856

5.2352

572.17

H 0 :  1  2 0,

y¿yˆ¿X¿y115.1735

SSESSTSSR

27,062.7775

1 725.82 22

25

5990.7712

SSRˆ¿X¿y

aa

n

i 1

yib

2

n

27,177.9510

1 725.82 22

25

6105.9447

SSTy¿y

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i 1

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2

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SSRˆ¿¿y

aa

n

i 1

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2

n

SSEy¿y

aa

n

i 1

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2

n 

≥ˆ¿¿y

aa

n

i 1

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¥

1 gni 1 yi (^22) ny¿y 1 gni 1 yi (^22) n,
SSTgni 1 y^2 i
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