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)
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
Market Weekly Gross Revenue
($100s) Television Advertising
($100s) Newspaper Advertising
($100s)
Mobile 101.3 4.9 1.4
Shreveport 52.9 3.1 3.2
Jackson 75.8 4.2 1.5
Birmingham 127.2 4.5 4.3
Little Rock 137.8 3.6 4
Biloxi 102.4 3.5 2.3
New Orleans 236.8 5 8.4
Baton Rouge 220.6 6.8 5.9
(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)
=
-43.258
+
39.367
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.
Null hypothesis, slope is zero and a significant relationship between the two variables.
Alternative hypothesis, there is significant relationship between the two variables.
B1 = 39.367 SE = 15.415
P value = 0.0434
Reject the null hypothesis, since p-value is less then significant level.
(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.
52.08
%
(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)
=
-43.225
+
21.859
x1 +
20.162
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.
B0 is not considerable, B1 is considerable, B2 is considerable.
(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.
93.22
%
(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.
The newspaper advertising could present an indicator that weekly gross revenue could increase.
(f) What are the managerial implications of these results?
The input in the box below will not be graded, but may be reviewed and considered by your instructor.
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