Question

In: Statistics and Probability

The owner of a departmental store would like to estimate monthly gross revenues as a function...

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.

Solutions

Expert Solution

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


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