Question

The owner of a departmental store would like to estimate monthly gross revenues as a function of advertising
expenditures. Historical data for randomly selected 8 months is given below (₹ in crores)
Monthly revenue Television Advertising Newspaper advertising

Monthly revenue																			Television Advertising																														Newspaper advertising
105																			5																														3.5
100																			4																														2
95																			2																														1.5
98																			2.5																														2.5
102																			3																														3.3
100																			3.5																														2.3
98																			2.5																														4.2
95																			3																														2.5

a. Derive a regression equation with amount of expenditure on television advertising as independent
variable.
b. Derive a regression equation with both expenditure on television advertising and newspaper advertising
as independent variables.
c. Estimate the monthly gross revenue for a month when 4 crores is spent on TV , and 1.5 crores is spent
on newspaper advertising.

Answer 1

Solution-A:

install analysis toolpaka nd then go to

Data >Data analysis>Regression

we get

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.800627
R Square	0.641004
Adjusted R Square	0.581171
Standard Error	2.199766
Observations	8
ANOVA
	df	SS	MS	F	Significance F
Regression	1	51.84118	51.84118	10.71327	0.016968
Residual	6	29.03382	4.838969
Total	7	80.875
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	90.10145	2.864474	31.4548	6.86E-08	83.09233	97.11056
Television Advertising	2.830918	0.864901	3.273113	0.016968	0.714582	4.947254

From output:

Regression equation is

Monthly revenue=90.10145+2.830918*televsion advertiing

Solutiopn-b:

Treat Televsion advertiing and newpaper advertsing as X

Monthly revenue as Y

Output:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.85842
R Square	0.736884
Adjusted R Square	0.631638
Standard Error	2.062982
Observations	8
ANOVA
	df	SS	MS	F	Significance F
Regression	2	59.59553	29.79777	7.00153	0.035511
Residual	5	21.27947	4.255894
Total	7	80.875
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	87.50033	3.306037	26.46684	1.44E-06	79.00189	95.99876
Television Advertising	2.601754	0.828697	3.139573	0.025679	0.471521	4.731988
Newspaper advertising	1.222599	0.905747	1.349824	0.234961	-1.1057	3.550895

Intrpretation
Regression equation is

Monthly revenue=87.50033+2.601754*Television Advertisng+1.222599*Newspaper Advertsing

c. Estimate the monthly gross revenue for a month when 4 crores is spent on TV , and 1.5 crores is spent
on newspaper advertising.

Substitute 4 crores is spent on TV , and 1.5 crores is spent
on newspaper advertising. in Regresssion equation 2

Monthly revenue=87.50033+2.601754*Television Advertisng+1.222599*Newspaper Advertsing

Monthly revenue=87.50033+2.601754*4+1.222599*1.5

Monthly revenue= 99.74124