Dixie Showtime Movie Theaters, Inc., owns and operates a chain of cinemas in sev
ID: 3172159 • Letter: D
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.
Click on the datafile logo to reference the data.
Item 3
Item 8
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 DATA file
Explanation / Answer
Solution:
The regression model for the part a and b is given as below:
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.745107618
R Square
0.555185363
Adjusted R Square
0.48104959
Standard Error
47.54989802
Observations
8
ANOVA
df
SS
MS
F
Significance F
Regression
1
16932.04319
16932.04
7.488765
0.033889855
Residual
6
13565.95681
2260.993
Total
7
30498
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
-45.4323498
66.75184564
-0.68062
0.521499
-208.7682317
117.9035321
Television Advertising
40.06398862
14.64027012
2.736561
0.03389
4.240538223
75.88743903
Part a
The estimated regression model for the given data is given as below:
Y = -45.4323 + 40.0640*X
Weekly Gross Revenue = -45.4323 + 40.0640*Television Advertising
For the given regression model, we have
P-value = 0.033889855
Alpha value = 0.05
P-value < Alpha value
So, we reject the null hypothesis that there is no any statistically significant relationship exists between the dependent variable weekly gross revenue and independent variable television advertising. This means we conclude that there is a statistically significant relationship exists between the dependent variable weekly gross revenue and independent variable television advertising.
Part b
For the above regression model, the coefficient of determination or the value of the R square is given as 0.555185363, which means about 55.52% of the variation in the dependent variable weekly gross revenue is explained by the independent variable television advertising.
Answer: 55.52%
The regression model for part c and d is given as below:
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.965520343
R Square
0.932229532
Adjusted R Square
0.905121345
Standard Error
20.33157019
Observations
8
ANOVA
df
SS
MS
F
Significance F
Regression
2
28431.13627
14215.57
34.38922
0.001195642
Residual
5
2066.863733
413.3727
Total
7
30498
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
-42.56959361
28.5471741
-1.4912
0.196107
-115.9524408
30.81325357
Television Advertising
22.40223856
7.099331722
3.155542
0.025221
4.152825402
40.65165173
Newspaper Advertising
19.49862752
3.696946525
5.274252
0.00326
9.99532394
29.0019311
Part c
The estimated regression model is given as below:
Y = -42.5696 + 22.4022*X1 + 19.4986*X2
Weekly Gross Revenue = = -42.5696 + 22.4022*Television advertising + 19.4986*Newspaper advertising
For this regression model, we have
P-value = 0.001195642
Alpha value = 0.05
P-value < Alpha value
So, we reject the null hypothesis that there is no any statistically significant relationship exists between the dependent variable weekly gross revenue and independent variables television advertising and newspaper advertising. This means we conclude that there is sufficient evidence that there is a statistically significant relationship exists between the dependent variable weekly gross revenue and independent variables television advertising and newspaper advertising.
Part d
We are given a coefficient of determination or value of R square as 0.932229532, which means about 93.22% of the variation in the dependent variable is explained by the independent variables.
Answer: 93.22%
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.745107618
R Square
0.555185363
Adjusted R Square
0.48104959
Standard Error
47.54989802
Observations
8
ANOVA
df
SS
MS
F
Significance F
Regression
1
16932.04319
16932.04
7.488765
0.033889855
Residual
6
13565.95681
2260.993
Total
7
30498
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
-45.4323498
66.75184564
-0.68062
0.521499
-208.7682317
117.9035321
Television Advertising
40.06398862
14.64027012
2.736561
0.03389
4.240538223
75.88743903
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