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: alpha = 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

Let 1and 3 be the coefficients of x1 and x3

Then we are to test the null hypothesis

H0: 1 = 3=0

..versus the alternative hypothesis

Ha: 1 0 or 30

Level of significance =0.05

We have from results SSEUR=Sum of squares due to errors in unrestricted full model=3830685

Dfur=error degree of freedom of unrestricted full model=19

SSER=Sum of squares due to errors in restricted full model=4180149

Dfr=error degree of freedom of restricted full model=21

Test statistic F=((SSER-SSEUR)/J)/(SSEUR/dfur) , where J is number of restrictions=2

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

=0.866661707

Rejection region :

We have degree of freedom =(2,19)

So critical value F=2.522

We reject the null hypothesis if calculated F>2.522, otherwise retain the null hypothesis.

Conclusion

As calculated F=0.8667<2.522 we do not reject the null hypothesis and conclude that x and x3 are redundant

Part-b

True

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.