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In: Statistics and Probability

Problem 7-9 Dixie Showtime Movie Theaters, Inc., owns and operates a chain of cinemas in several...

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 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)
=   +   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
(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.
%

Solutions

Expert Solution

a)

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.738366
R Square 0.545184
Adjusted R Square 0.469381
Standard Error 47.78529
Observations 8
ANOVA
df SS MS F Significance F
Regression 1 16422.8 16422.8 7.192148 0.036448
Residual 6 13700.6 2283.434
Total 7 30123.4
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept -52.783 70.88886 -0.74459 0.484652 -226.242 120.6758
Television Advertising 41.49057 15.47106 2.681818 0.036448 3.634248 79.34688

Y = -52.783 +41.491*Tv

p value for Tv = 0.036

p value < 0.05

so, Tv expenditure is significant

............

R Square = 0.5452

54.52% of the variation in the sample values of weekly gross revenue does the model in part (a

..............

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.956349
R Square 0.914604
Adjusted R Square 0.880446
Standard Error 22.68218
Observations 8
ANOVA
df SS MS F Significance F
Regression 2 27550.99 13775.5 26.7755 0.002131
Residual 5 2572.407 514.4815
Total 7 30123.4
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept -46.2075 33.67842 -1.37202 0.228413 -132.781 40.36559
Television Advertising 23.48508 8.301642 2.828968 0.036719 2.145032 44.82513
Newspaper Advertising 18.98037 4.081099 4.650799 0.005578 8.48957 29.47117

Y = -46.207 +23.485*tv +18.980*newspaper

...............

R Square = 0.9146

91.46% of the variation in the sample values of weekly gross revenue does the model in part (c) explain.

........................

THANKS

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