Question

1. The owner of Showtime Movie Theaters, Inc. would like to estimate weekly gross revenue as a function of advertising expenditures. Historical data for a sample of eight weeks follow.

Weekly Gross	Television	Newspaper	Radio
Revenue	Advertising	Advertising	Advertising
($1000s)	($1000s)	($1000s)	($1000s)
96	5	1.5	0.3
90	2	2	0.2
95	4	1.5	0.3
92	2.5	2.5	0.1
95	3	3.3	0.4
94	3.5	2.3	0.4
94	2.5	4.2	0.3
94	3	2.5	0.3

1. Is the estimated regression equation coefficient for television advertising expenditures the same in par a), in part b) and in part c)? Interpret the coefficient in each case
2. Obtain and compare the multiple coefficient of determination and the adjusted multiple coefficient of determination for parts a), b) and c). How does the coefficient of determination changes as a result of adding more independent variables in the equation?
3. What is the estimate of the weekly gross revenue for a week when $3500 is spent on television advertising, $1800 is spent on newspaper advertising, and $350 in radio advertising?

PLEASE SHOW IN EXCEL AND HOW TO DO IT. Thank you!

Answer 1

Ans a )

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.807807
R Square	0.652553
Adjusted R Square	0.594645
Standard Error	1.215175
Observations	8
ANOVA
	df	SS	MS	F	Significance F
Regression	1	16.6401	16.6401	11.26881	0.015288
Residual	6	8.859903	1.476651
Total	7	25.5
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	88.63768	1.582367	56.01588	2.17E-09	84.76577	92.50959
Tv Ads	1.603865	0.477781	3.356905	0.015288	0.434777	2.772952

Ans b )

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.958663
R Square	0.919036
Adjusted R Square	0.88665
Standard Error	0.642587
Observations	8
ANOVA
	df	SS	MS	F	Significance F
Regression	2	23.43541	11.7177	28.37777	0.001865
Residual	5	2.064592	0.412918
Total	7	25.5
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	83.23009	1.573869	52.88248	4.57E-08	79.18433	87.27585
Tv Ads	2.290184	0.304065	7.531899	0.000653	1.508561	3.071806
News ads	1.300989	0.320702	4.056697	0.009761	0.476599	2.125379

Ans c )

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.965593
R Square	0.93237
Adjusted R Square	0.881648
Standard Error	0.656613
Observations	8
ANOVA
	df	SS	MS	F	Significance F
Regression	3	23.77544	7.925146	18.38183	0.00838
Residual	4	1.724561	0.43114
Total	7	25.5
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	83.5228	1.641648	50.87741	8.93E-07	78.96485	88.08074
Tv Ads	2.079043	0.39123	5.314125	0.006029	0.992815	3.165271
News ads	1.124548	0.383224	2.934439	0.042625	0.060547	2.18855
Radio ad	2.84172	3.199861	0.888076	0.424677	-6.04252	11.72596

Ans d ) the estimated regression equation coefficient for television advertising expenditures is not same in par a), in part b) and in part c)

in a ) for every one $ increase in tv ad there is 1.60$ increase in revenue

in b ) for every one $ increase in tv ad there is 2.29$ increase in revenue

in c ) for every one $ increase in tv ad there is 2.07$ increase in revenue

Ans e) for a )

R Square	0.652553
Adjusted R Square	0.594645

for b

R Square	0.919036
Adjusted R Square	0.88665

for c

R Square	0.93237
Adjusted R Square	0.881648

the coefficient of determination increases as we add more independent variables in the equation.

ANs e ) revenue = 83.5228+ 2.079 Tv ads + 1.125 news ad + 2.842 radio ad

revenue= 83.5228+ 2.079*3500+1.125*1800+2.842*350 = 10378.96