Page 122 - Basic Statistics

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SS(1 , 2 , 3 ,4  0 ) = SS( 1,2  0 ) + SS( 3 ,4  0 , 1 , 2 )

Where both term on the right-hand side represents the partition with two

degrees of freedom. SS( 1,2  0 )less useful for the inference on 1 and 2, since

there has been no adjusment for X3 dan X4. However SS( 3 ,4  0 , 1 , 2 )
would be vital in explaining the importance of X3 dan X4 Collectivelly. If we are

interested in performing joint inference of the 1 and 2, then SS( 3 ,4  0 , 1 ,

2 ) can be calculated by

SS( 3 ,4  0 , 1 , 2 ) = SS( 3  0 , 1 , 2 )+ SS( 4  0 , 1 , 2 , 3 ) (G.25)

Furthermore, the statistic F can be used

SS ( ,   , ,  2 / )
F = 3 4 0 1 2 (G.26)
MS (Re ) s

with 2 degrees of freedom numerator and n-p-1 denominator. These statistics

are used to test the hypothesis,

H0 : 3 = 4 = 0
H1 : 3  0 or 4  0

If we want to test the contribution of a variable Xj, that the model

involving only the preceding regressor variables, namely X1, X2, .., Xj-1, the test
statistic

SS (   , , ... ,  )
F = j 0 1 1 - j (G.27)
MS (Re ) s

The test statistic has distribution F and successive degrees of freedom

numerator and denominator 1, and n-p-1.

For example, sequential F-tests for linear regression model in worked

example 5.4, are shown in Table 5.14 below. Of course, here there is a difference

with the previous partial test results. This is due to the partial coefficient test,
each coefficients of independent variable are tested when the model contains all

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