Introduction to Probability and Statistics for Engineers and Scientists

404 Chapter 9: Regression

TABLE 9.5

Diameter
Age Elevation Rainfall Specific at Breast Height
(years) (1,000 ft) (inches) Gravity (inches)
1 44 1.3 250 .63 18.1
2 33 2.2 115 .59 19.6
3 33 2.2 75 .56 16.6
4 32 2.6 85 .55 16.4
5 34 2.0 100 .54 16.9
6 31 1.8 75 .59 17.0
7 33 2.2 85 .56 20.0
8 30 3.6 75 .46 16.6
9 34 1.6 225 .63 16.2
10 34 1.5 250 .60 18.5
11 33 2.2 255 .63 18.7
12 36 1.7 175 .58 19.4
13 33 2.2 75 .55 17.6
14 34 1.3 85 .57 18.3
15 37 2.6 90 .62 18.8

It now follows from Equation 9.10.6 that

Var(B 2 )=.379σ^2

SinceB 2 is normal and

E[B 2 ]=β 2

we see that

B 2 −β 2

.616σ

∼N(0, 1)

Replacingσby its estimatorSSR/10 transforms the foregoing standard normal distri-
bution into at-distribution with 10(=n−k−1) degrees of freedom. That is,

B 2 −β 2

.616

√

SSR/10

∼t 10

Hence, ifβ 2 =0 then

√

10/SSRB 2

.616

∼t 10