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 ($1,000s)	Television Advertising ($1,000s)	Newspaper Advertising ($1,000s)
96	5.0	1.5
90	2.0	2.0
95	4.0	1.5
92	2.5	2.5
95	3.0	3.3
94	3.5	2.3
94	2.5	4.2
94	3.0	2.5

(a)

Develop an estimated regression equation with the amount of television advertising as the independent variable. (Round your numerical values to two decimal places. Let x₁ represent the amount of television advertising in $1,000s and y represent the weekly gross revenue in $1,000s.)

ŷ = ______________

Predict weekly gross revenue (in dollars) for a week when $3,200 is spent on television advertising and $1,700 is spent on newspaper advertising. (Round your answer to the nearest cent.)

$ _____________

(b)

Develop an estimated regression equation with both television advertising and newspaper advertising as the independent variables. (Round your numerical values to two decimal places. Let x₁ represent the amount of television advertising in $1,000s, x₂ represent the amount of newspaper advertising in $1,000s, and y represent the weekly gross revenue in $1,000s.)

ŷ = ___________

Answer 1

a)

using excel data analysis tool for regression,steps are: write data>menu>data>data analysis>regression>enter required labels>ok> and following o/p is obtained

Regression Statistics
Multiple R	0.8078
R Square	0.6526
Adjusted R Square	0.5946
Standard Error	1.2152
Observations	8
ANOVA
	df	SS	MS	F	Significance F
Regression	1	16.6	16.6	11.27	0.0153
Residual	6	8.9	1.5
Total	7	25.5
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	88.6377	1.5824	56.0159	0.0000	84.7658	92.5096
X	1.6039	0.4778	3.3569	0.0153	0.4348	2.7730

so, regression line is   Ŷ =   88.64 +   1.60 *Tv Ads

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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	28.377768	0.001865
Residual	5	2.064592	0.412918
Total	7	25.5
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	83.23009	1.573869	52.88248	4.572E-08	79.18433	87.27585	79.18433	87.27585063
X Variable 1	2.290184	0.304065	7.531899	0.0006532	1.508561	3.071806	1.508561	3.071806446
X Variable 2	1.300989	0.320702	4.056697	0.0097608	0.476599	2.125379	0.476599	2.125378798

win % = 83.23 + 2.29*TV Ads + 1.30*newspaper Ads

win % = 83.23 + 2.29*3.2 + 1.30*1.7 = 92.77%

answered by: anonymous