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Table 5.10 Analysis of variance summary for regression analysis
Sum of Squares df Mean Square F Sig.
ˆ
Model β ’ X’Y = 595.164 6
Mean n Y = 387.157 1
2

ˆ
b
Regression β ’ X’Y - n Y = 208.007 5 41.601 84.070 .000
2
ˆ
Residual Y’ Y - β ’ X’Y = 7.918 16 .495
Total
Y’ Y - n Y = 215.925 21
2
a. Dependent Variable: Y
b. Predictors: (Constant), X5, X4, X3, X2, X1

5.2.6 PARTIAL REGRESSION COEFFICIENT TEST

Partial test is used to study the contribution of a single independent

variable Xj to variations in the response variable Y on the regression model

containing all independent variables. Tests conducted on coefficient of the

variables, i.e j. The magnitude of the coefficient j is defined as change in

average of the j-th response variable due to per unit changes of the independent
variable, with the other independent variables held constant.

In the decomposition of the sum of squares in partial and sequential,

SS(Reg) written SS(1 , 2 , … , ,p  0 ), so that the j-th coefficient partial sums

of squares to be written

SS(j  0 , 1 , … , j-1, j+1, … ,p )
or

R( j  0 , 1 , … , j-1, j+1, … ,p)

The partial test can use partial F-test, and can also use the two-way t-test. As

indicated earlier, that the variance estimators of the regression coefficients to j is

S cjj, with cjj is a diagonal element to j = 0, 1, ..., p of the matrix ( X’X ) .
2
-1
Formulation of hypotheses for the partial coefficient testing are:

H0 : j = 0.

H1 : j  0 , j = 1, 2, … p (G.21)

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