The following are ANOVA sections of two regressions. The first is a full regress

Question

The following are ANOVA sections of two regressions. The first is a full regression involving 5 independent variables x_1, x_2, X_3, x_4, and X_5. The second is a reduced regression involving x_2, x_4, and x_5 only, since x_1 and x_3 were thought by the analyst to be redundant and unnecessary. a. Based on these results, at the 0.05 significance level, test whether or not the two removed variables contributed significantly to the original, full model. H_0: H_a: Test Statistic: Rejection decision: Conclusion (Interpret the rejection decision): b. True or False: Based on this test, the removal of x_1 and x_3 was justified.

Explanation / Answer

Part-a

We assumed that 1 and 3 are the coefficients of predictors x1 and x3

H0: 1 = 3=0

Ha: 1 0 or 30

The =0.05

It was found from table that

SSEur= unrestricted full model error SS=3830685

Dfur= unrestricted full model error df=19

SSer= restricted model error SS=4180149

K=number of parameters eliminated from full model=2

Test statistic F=((SSEr-SSEur)/K)/(SSEur/dfur) ,

=((4180149-3830685)/2)/( 3830685/19)

=0.87

Rejection region :

The degree of freedom of F-test=(2,19)

At 5% level critical value F=2.52

The null hypothesis will be rejected if observed F>2.522, otherwise fail to reject the null hypothesis.

Conclusion

As calculated F=0.87<2.52 we fail to reject the null hypothesis

Part-b

True

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