Question

Problem 7-9 Dixie Showtime Movie Theaters, Inc., owns and operates a chain of cinemas in several markets in the southern U.S. The owners would like to estimate weekly gross revenue as a function of advertising expenditures.

Data for a sample of eight markets for a recent week follow. Market Weekly Gross Revenue ($100s) Television Advertising ($100s) Newspaper Advertising ($100s) Mobile 102.5 5.1 1.6 Shreveport 52.7 3.2 3 Jackson 75.8 4 1.5 Birmingham 127.8 4.3 4 Little Rock 137.8 3.5 4.3 Biloxi 101.4 3.6 2.3 New Orleans 237.8 5 8.4 Baton Rouge 219.6 6.9 5.8

(a) Use the data to develop an estimated regression with the amount of television advertising as the independent variable. Let x represent the amount of television advertising. If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300) = + x Test for a significant relationship between television advertising and weekly gross revenue at the 0.05 level of significance. What is the interpretation of this relationship? The input in the box below will not be graded, but may be reviewed and considered by your instructor.

(b) How much of the variation in the sample values of weekly gross revenue does the model in part (a) explain? If required, round your answer to two decimal places. %

(c) Use the data to develop an estimated regression equation with both television advertising and newspaper advertising as the independent variables. Let x1 represent the amount of television advertising. Let x2 represent the amount of newspaper advertising. If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300) = + x1 + x2 Test whether each of the regression parameters β0, β1, and β2 is equal to zero at a 0.05 level of significance. What are the correct interpretations of the estimated regression parameters? Are these interpretations reasonable?

(d) How much of the variation in the sample values of weekly gross revenue does the model in part (c) explain? If required, round your answer to two decimal places. % (e) Given the results in part (a) and part (c), what should your next step be? Explain. (f) What are the managerial implications of these results?

Answer 1

Summary of R output are given below:-

a) Let the intercept and coefficients of television advertising(x1) and newspaper advertising(x2) and y be the gross revenue. So, the regression equation will be:-

As p-value is 0.03672 <0.05 , So we will reject the null hypothesis and it is significantly effect the gross revenue.

b) The variation in the sample values of gross revenue of part (a) means the residual standard error is 49.09

c) The regression equation will be

the respective p- value for are 0.18842 ,0.02501, 0.00236 As p-vaue of >0.05, we accept null hypothesis and conclude that intercept does not significantly effect the gross revenue while the other two p-value is smaller than 0.05, hence they significantly effect the gross revenue.

d) The variation explained by the model given in(c) is 93.57 %

e) As we can see the model given in(c) explains grater variation as comapre to (a). Hence, Newspaper Advertising significantly effect the  Market Weekly Gross Revenue