Question

Use computer software packages, such as Minitab or Excel, to solve this problem. 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 Television Advertising ($1,000s) Newspaper Advertising ($1,000s) 1.5 ($1,000s) 105 102 3.0 2.5 a. Develop an estimated regression equation with the amount of television advertising as the independent variable (to 1 decimal). Revenue TVAdv b. Develop an estimated regression equation with both television advertising and newspaper advertising as the independent variables (to 2 decimals). Revenue TVAdv + NV Adv

Answer 1

I have used Excel to solve the above problem. I will attach the outputs along with the solution.

a)

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.604018
R Square	0.364838
Adjusted R Square	0.258977
Standard Error	4.977081
Observations	8
ANOVA
	df	SS	MS	F	Significance F
Regression	1	85.37198	85.37198	3.446402	0.112778
Residual	6	148.628	24.77134
Total	7	234
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	85.42029	6.481016	13.18008	1.18E-05	69.56181	101.2788	69.56181	101.2788
X Variable 1	3.63285	1.956882	1.856449	0.112778	-1.15547	8.421167	-1.15547	8.421167

Revenue=85.42 + 3.6 TV Adv is the estimated regression equation.

b)

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.702543
R Square	0.493567
Adjusted R Square	0.290994
Standard Error	4.868373
Observations	8
ANOVA
	df	SS	MS	F	Significance F
Regression	2	115.4947	57.74736	2.436489	0.182518
Residual	5	118.5053	23.70106
Total	7	234
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	74.03494	11.92395	6.208926	0.001583	43.38344	104.6864	43.38344	104.6864
X Variable 1	5.077852	2.303655	2.204259	0.078671	-0.84388	10.99959	-0.84388	10.99959
X Variable 2	2.739152	2.429701	1.127362	0.310765	-3.50659	8.984898	-3.50659	8.984898

Revenue = 74.03 + 5.08 TV Adv + 2.74 NV Adv is the estimated regression equation.

c) NO. The estimated regression equation coefficient for television advertising expenditures are different in part (a) and part (b).

d) Revenue = 74.03 + 5.08 (3.6) + 2.74 (1.6) = 96.702.

Hence, the weekly gross revenue for a week when $3.6 thousand is spent on television advertising and $ 1.6 thousand is spent on newspaper advertising is $96.70 thousand.