In: Statistics and Probability
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.
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