Introduction to Probability and Statistics for Engineers and Scientists

9.4Statistical Inferences About the Regression Parameters 363

Simple Linear Regression

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20

Sample size = 8

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5, 7.4

6, 9.3

7, 10.6

10, 15.4

12, 18.1

15, 22.2

18, 24.1

20, 24.8

x =

y = 24.8

a =

b =

2.46

1.21

The least squares estimators are as follows:

Average x value =

Sum of squares of the x values =

11.63

1303.0

The estimated regression line is Y = 2.46 + 1.21x

S(x, Y)

S(x, x)

S(Y, Y)

SSR

=

=

=

=

267.66

221.88

332.37

9.47

200

150

100

50

(^0050100150200)
FIGURE 9.5
That is,
√
(n−2)Sxx/SSR(B−β) has at-distribution withn−2 degrees of freedom.
Therefore, ifH 0 is true (and soβ=0), then
√
(n−2)Sxx
SSR
B∼tn− 2
which gives rise to the following test ofH 0.