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.