Question

Problem 7-9

Dixie Showtime Movie Theaters, Inc., owns and operates a chain of cinemas in several markets in the southern U.S. The owners would like to estimate weekly gross revenue as a function of advertising expenditures. Data for a sample of eight markets for a recent week follow.

Market	Weekly Gross Revenue ($100s)		Television Advertising ($100s)	Newspaper Advertising ($100s)
Mobile	101.3		4.9	1.4
Shreveport	52.9		3.1	3.2
Jackson	75.8		4.2	1.5
Birmingham	127.2		4.5	4.3
Little Rock	137.8		3.6	4
Biloxi	102.4		3.5	2.3
New Orleans	236.8		5	8.4
Baton Rouge	220.6		6.8	5.9

(a)	Use the data to develop an estimated regression with the amount of television advertising as the independent variable.
	Let x represent the amount of television advertising.
	If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)
	=   +   x
	Test for a significant relationship between television advertising and weekly gross revenue at the 0.05 level of significance. What is the interpretation of this relationship?
	The input in the box below will not be graded, but may be reviewed and considered by your instructor.
(b)	How much of the variation in the sample values of weekly gross revenue does the model in part (a) explain?
	If required, round your answer to two decimal places.
	%
(c)	Use the data to develop an estimated regression equation with both television advertising and newspaper advertising as the independent variables.
	Let x1 represent the amount of television advertising.
	Let x2 represent the amount of newspaper advertising.
	If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)
	=   +  x1 +  x2
(d)	How much of the variation in the sample values of weekly gross revenue does the model in part (c) explain?
	If required, round your answer to two decimal places.
	%

Answer 1

a)

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.738366
R Square	0.545184
Adjusted R Square	0.469381
Standard Error	47.78529
Observations	8
ANOVA
	df	SS	MS	F	Significance F
Regression	1	16422.8	16422.8	7.192148	0.036448
Residual	6	13700.6	2283.434
Total	7	30123.4
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-52.783	70.88886	-0.74459	0.484652	-226.242	120.6758
Television Advertising	41.49057	15.47106	2.681818	0.036448	3.634248	79.34688

Y = -52.783 +41.491*Tv

p value for Tv = 0.036

p value < 0.05

so, Tv expenditure is significant

............

R Square = 0.5452

54.52% of the variation in the sample values of weekly gross revenue does the model in part (a

..............

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.956349
R Square	0.914604
Adjusted R Square	0.880446
Standard Error	22.68218
Observations	8
ANOVA
	df	SS	MS	F	Significance F
Regression	2	27550.99	13775.5	26.7755	0.002131
Residual	5	2572.407	514.4815
Total	7	30123.4
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-46.2075	33.67842	-1.37202	0.228413	-132.781	40.36559
Television Advertising	23.48508	8.301642	2.828968	0.036719	2.145032	44.82513
Newspaper Advertising	18.98037	4.081099	4.650799	0.005578	8.48957	29.47117

Y = -46.207 +23.485*tv +18.980*newspaper

...............

R Square = 0.9146

91.46% of the variation in the sample values of weekly gross revenue does the model in part (c) explain.

........................

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