Page 119 - Basic Statistics

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Testing hypotheses above can be done with the F-test in the right direction,

which its statistic

 2 ˆ
F = j (G.22)
c jj S 2

and has 1 and n-p-1 degrees of freedom.

F testing criteria:

To a certain significance level testing , H0 is accepted if

Factual < F (, 1, n-p-1) or P( F > Factual ) > , otherwise H0 is rejected.

For example, partial F-tests for linear regression models in worked
example 5.4, are shown in Table 5.11 below. The results show that only the

constant and coefficient 5 are significantly different from zero.

Table 5.11 Tests of between-subjects effects
Dependent Variable: Y

Source Type III Sum of df Mean Square F Sig.
Squares
a
Corrected Model 208,007 5 41,601 84,070 ,000
Intercept 24,079 1 24,079 48,660 ,000
X1 ,299 1 ,299 ,604 ,449
X2 ,869 1 ,869 1,756 ,204
X3 ,078 1 ,078 ,158 ,696
X4 ,983 1 ,983 1,986 ,178
X5 4,352 1 4,352 8,795 ,009

Error 7,918 16 ,495

Total 603,081 22

Corrected Total 215,925 21
a. R Squared = ,963 (Adjusted R Squared = ,952)

Testing the above hypothesis H0 : j = 0 may also to use two-way t-test

with n-(p +1) degrees of freedom.

β ˆ j
t = (G.23)
c jj S 2

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