Page 128 - Basic Statistics

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Notice that causes the hypothesized 0 = 0.5 to be subtracted from the estimated

0 = 0.2949. The sum of squares for this composite hypothesis is

ˆ
ˆ
Q = (K’ β - m)’ (K’ ( X’X ) K) (K’ β - m)
-1
-1
= 1.8387
and has 3 degrees of freedom. Computed statistic F is

Q k / . 1 8387 3 /
F = = = . 1 755
S 2 . 0 349195

Which, again, is much less than the critical value of F for  = 0.05 and (3;26)

degrees of freedom. F0.05;3;26 = 2.98 , There is no reason to reject H0 that 0 = 0.5

and 1 = 3 = 0.

Output using Statistical Analysis System (SAS) software presented of the

results which showing in Table 5.16.
Table 5.16 Output of SAS for a composited hypothesis testing

The SAS System

L Ginv(X'X) L' Lb-c

2.8559225951 0.0006173356 -0.04090973 -0.795271027
0.0006173356 3.3414119E-6 1.4099083E-8 0.0013058159
-0.04090973 1.4099083E-8 0.002613921 -0.027843496

Inv(L Ginv(X'X) L') Inv()(Lb-c)

0.4758460504 -87.94537601 7.4478046495 -0.700639963
-87.94537601 315528.6684 -1378.109811 520.33414234
7.4478046495 -1378.109811 499.1379201 -21.62032556

Dependent Variable: Y
Test: Numerator: 0.6129 DF: 3 F value: 1.7561
Denominator: 0.348994 DF: 26 Prob>F: 0.1803

~~* CHAPTER 5 THE MULTIPLE LINEAR REGRESSION MODEL *~~