Question

The owner of Showtime Movie Theaters, Inc., would like to predict weekly gross revenue as a function of advertising expenditures. Historical data for a sample of eight weeks follow. Weekly Gross Revenue ($1000s) Televison Advertising ($1000s) Newspaper Advertising ($1000s) a. Use a = 0.01 to test the hypotheses H: Bi = B2 = 0 H :8, and/or B, is not equal to zero for the model y = Bo + B1X1 + B229 + E, where *1 = television advertising ($1000s) 22 = newspaper advertising ($1000s) Compute the F test statistic (to 2 decimals). Use Ftable.

Answer 1

Output using excel:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.97159
R Square	0.943986
Adjusted R Square	0.921581
Standard Error	0.548701
Observations	8
ANOVA
	df	SS	MS	F	Significance F
Regression	2	25.36963	12.68482	42.132	0.000743
Residual	5	1.505366	0.301073
Total	7	26.875
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	80.00939	1.906048	41.97658	1.45E-07	75.10974	84.90904
TV Ads	2.177428	0.248904	8.748069	0.000323	1.5376	2.817256
Newspaper Ads	1.961796	0.361697	5.42386	0.002886	1.032024	2.891569

a) F Test statistic:

F = 42.13

p-value = 0.0007

Less than 0.01

Conclusion:

Reject the null hypothesis. It is significant.

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b) Test statistic for β₁:

t = 8.75

p-value = 0.0003

Less than 0.01

Conclusion:

Reject the null hypothesis. It is significant.

No, x1 should not be dropped from the model.

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c) t = 5.42

p-value = 0.0029

Less than 0.01

Conclusion:

Reject the null hypothesis. It is significant.

No, x2 should not be dropped from the model.