Question

1. The owner of Showtime Movie Theaters, Inc. would like to estimate weekly gross revenue as a function of advertising expenditures. Historical data for a sample of eight weeks follow.

Weekly Gross	Television	Newspaper	Radio
Revenue	Advertising	Advertising	Advertising
($1000s)	($1000s)	($1000s)	($1000s)
96	5	1.5	0.3
90	2	2	0.2
95	4	1.5	0.3
92	2.5	2.5	0.1
95	3	3.3	0.4
94	3.5	2.3	0.4
94	2.5	4.2	0.3
94	3	2.5	0.3

1. Develop an estimated regression equation in Excel with the amount of television advertising as the independent variable
2. Develop an estimated regression equation in Excel with both television advertising and newspaper advertising as the independent variables
3. Develop an estimated regression equation in Excel with all three independent variables: television advertising, newspaper advertising, and radio advertising
4. Is the estimated regression equation coefficient for television advertising expenditures the same in par a), in part b) and in part c)? Interpret the coefficient in each case
5. Obtain and compare the multiple coefficient of determination and the adjusted multiple coefficient of determination for parts a), b) and c). How does the coefficient of determination changes as a result of adding more independent variables in the equation?
6. What is the estimate of the weekly gross revenue for a week when $3500 is spent on television advertising, $1800 is spent on newspaper advertising, and $350 in radio advertising?
7. Use the F test to determine the overall significance of the relationship. What is the conclusion at the .05 level of significance?
8. Use the t test to determine the significance of each independent variable. What is your conclusion at the .05 level of significance?
1. Determine the sample correlation coefficient between all possible pairs of independent variables to measure multicollinearity. Is there any value high enough to predict any potential problem in the regression model? Explain

SHOW ALL WORK

Answer 1

Weekly Gross Revenue ($1000s)	Television Advertising ($1000s)	Newspaper Advertising ($1000s)	Radio Advertising ($1000s)
96	5	1.5	0.3
90	2	2	0.2
95	4	1.5	0.3
92	2.5	2.5	0.1
95	3	3.3	0.4
94	3.5	2.3	0.4
94	2.5	4.2	0.3
94	3	2.5	0.3

Answer(a):

In excel follow the below steps

Data>Data Analysis> Regression, click ok and enter the range of dependent and range of independent variables only for Television advertising. The output will be printed in new sheet.

Answer(b):

In excel follow the below steps

Data>Data Analysis> Regression, click ok and enter the range of dependent and range of independent variables only for Television advertising and Newspaper Advertising. The output will be printed in new sheet.

Answer(c):

In excel follow the below steps

Data>Data Analysis> Regression, click ok and enter the range of dependent and range of independent variables only for Television advertising, Newspaper Advertising and Radio Advertising. The output will be printed in new sheet.

Answer(d):

Estimated regression equation coefficient for television advertising expenditures for part (a) = 1.604

Estimated regression equation coefficient for television advertising expenditures for part (b) = 2.29

Estimated regression equation coefficient for television advertising expenditures for part (c) = 2.079

we can see the Estimated regression equation coefficient for television advertising expenditures is not same for all three fitted regression.

Interpretation for Part(a):

Estimated regression equation coefficient for television advertising expenditures = 1.604

p-value= 0.015288

The p-value is less than 0.05 which suggests that the there is significant effect of Television advertising on Weekly Gross Revenue at 0.05 level of significance.

The estimated coefficient indicates that the Weekly Gross Revenue increses by 1.604 units if the television advertising expenditures increases by 1 unit.

Interpretation for Part(b):

Estimated regression equation coefficient for television advertising expenditures = 2.29

p-value= 0.000653232

The p-value is less than 0.05 which suggests that the there is highly significant effect of Television advertising on Weekly Gross Revenue at 0.05 level of significance.

The estimated coefficient indicates that the Weekly Gross Revenue increses by 2.29 units if the television advertising expenditures increases by 1 unit.

Interpretation for Part(c):

Estimated regression equation coefficient for television advertising expenditures = 2.079

p-value= 0.00603

The p-value is less than 0.05 which suggests that the there is highly significant effect of Television advertising on Weekly Gross Revenue at 0.05 level of significance.

The estimated coefficient indicates that the Weekly Gross Revenue increses by 2.079 units if the television advertising expenditures increases by 1 unit.

First four sub parts have been solved.