Fundamentals of Probability and Statistics for Engineers

Answer: equation (11.41) gives the desired confidence limits, with n 14,

The observed confidence limits are thus given by

This result is shown graphically in Figure 11.5.

11.1.5 Significance Tests

Following the results given above, tests of hypotheses about the values of and
can be carried out based upon the approach discussed in Chapter 10. Let us
demonstrate the underlying id eas by testing hypothesis H 0 : 0 against
hypothesis H 1 0 ,where 0 is some specified value.

y

x

^+^x

l 2 (x)

l 1 (x)

E(y) = + x

x

^ ^

–

–

Figure 11.4 Confidence band for

Linear Models and Linear Regression 351

ˆ

ˆ

Efdygˆ ^‡ ^xˆ 0 : 63 ‡ 5 : 24 x;

tn 2 ;

= 2 ˆt 12 ; 0 : 025 ˆ 2 : 179 ; from Table A.4;

xˆ 11 : 11 ;

Xn

iˆ 1

…xix†^2 ˆ 546 : 09 ;

b^2 ˆ 182 : 10 :

l 1 ; 2 ˆ… 0 : 63 ‡ 5 : 24 x† 2 :179 182: 10

1

14

‡

…x 11 : 11 †^2

546 : 09

)"# 1 = 2

:

ˆ

6ˆ

α β

β

EfYgˆ ‡ x

:

α

0 05,: and