In: Economics
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 | 102.3 | 5.0 | 1.6 | |
Shreveport | 51.9 | 3.0 | 3.2 | |
Jackson | 75.5 | 4.0 | 1.5 | |
Birmingham | 127.2 | 4.4 | 4.0 | |
Little Rock | 137.8 | 3.6 | 4.3 | |
Biloxi | 101.4 | 3.5 | 2.3 | |
New Orleans | 237.8 | 5.0 | 8.4 | |
Baton Rouge | 219.6 | 6.9 | 5.8 |
(a) | Use the data to develop an estimated regression equation 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? | |
The input in the box below will not be graded, but may be reviewed and considered by your instructor. | |
(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. | |
% |