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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
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 | 101.3 | 5.0 | 1.5 | |
Shreveport | 51.9 | 3.0 | 3.0 | |
Jackson | 74.8 | 4.0 | 1.5 | |
Birmingham | 126.2 | 4.3 | 4.3 | |
Little Rock | 137.8 | 3.6 | 4.0 | |
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? | |||||||
There - Select your answer -isis notItem 3 a significant relationship between the amount spent on television advertising and weekly gross revenue. The estimated regression equation is the best estimate of the - Select your answer -amount spent on television advertisingweekly gross revenueItem 4 given the - Select your answer -amount spent on television advertisingweekly gross revenueItem 5 . | |||||||
(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 0, 1, and 2 is equal to zero at a 0.05 level of significance. | |||||||
We - Select your answer -cancannotItem 10 conclude that 0 = 0. | |||||||
We - Select your answer -cancannotItem 11 conclude that 1 = 0. | |||||||
We - Select your answer -cancannotItem 12 conclude that 2 = 0. | |||||||
What are the correct interpretations of the estimated regression parameters? Are these interpretations reasonable? | |||||||
| |||||||
- Select your answer -Option (i)Option (ii)Option (iii)Item 13 | |||||||
(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. | ||||||
The input in the box below will not be graded, but may be reviewed and considered by your instructor. | |||||||
| |||||||
(f) | What are the managerial implications of these results? | ||||||
Management can feel confident that increased spending on - Select your answer -both television and newspaperonly newspaperItem 16 advertising results in increased weekly gross revenue. The results also suggest that - Select your answer -newspapertelevision Item 17 advertising may be slightly more effective than - Select your answer -newspapertelevision Item 18 advertising in generating revenue. |
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