Question

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 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 4.0 Biloxi 102.4 3.5 2.3 New Orleans 236.8 5.0 8.4 Baton Rouge 220.6 6.8 5.9 (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. %

          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
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
4.0
  Biloxi
102.4
3.5
2.3
  New Orleans
236.8
5.0
8.4
  Baton Rouge
220.6
6.8
5.9
(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.
 %

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