Dixie Showtime Movie Theaters, Inc., owns and operates a chain of cinemas in sev
ID: 3220670 • 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.
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 1.5 Shreveport 51.9 3 3 Jackson 74.8 4 1.5 Birmingham 126.2 4.3 4.3 Little Rock 137.8 3.6 4 Biloxi 101.4 3.5 2.3 New Orleans 237.8 5 8.4 Baton Rouge 219.6 6.9 5.8 (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 four 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 four 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. 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. % (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?
Explanation / Answer
I used xcel Megastat addin
(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.
Regression Analysis
r²
0.5552
n
8
r
0.745
k
1
Std. Error
47.550
Dep. Var.
Weekly Gross Revenue
ANOVA table
Source
SS
df
MS
F
p-value
Regression
16,932.0432
1
16,932.0432
7.49
.0339
Residual
13,565.9568
6
2,260.9928
Total
30,498.0000
7
Regression output
confidence interval
variables
coefficients
std. error
t (df=6)
p-value
95% lower
95% upper
Intercept
-45.4323
66.7518
-0.681
.5215
-208.7682
117.9035
Television Advertising
40.0640
14.6403
2.737
.0339
4.2405
75.8874
Y = -45.4323 + 40.0640 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?
Calculated t=2.737, P=0.0339 < 0.05 level. The relation is significant.
When there is one unit( $100) increase in television advertising, there is increase of $40.064(in $100) in Weekly Gross Revenue.
(b)
How much of the variation in the sample values of weekly gross revenue does the model in part (a) explain?
55.52% variation are explained.
(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 four decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)
Regression Analysis
R²
0.9322
Adjusted R²
0.905
n
8
R
0.966
k
2
Std. Error
20.332
Dep. Var.
Weekly Gross Revenue
ANOVA table
Source
SS
df
MS
F
p-value
Regression
28,431.1363
2
14,215.5681
34.39
.0012
Residual
2,066.8637
5
413.3727
Total
30,498.0000
7
Regression output
confidence interval
variables
coefficients
std. error
t (df=5)
p-value
95% lower
95% upper
Intercept
-42.5696
28.5472
-1.491
.1961
-115.9524
30.8133
Television Advertising
22.4022
7.0993
3.156
.0252
4.1528
40.6517
Newspaper Advertising
19.4986
3.6969
5.274
.0033
9.9953
29.0019
Y = -42.5696 +22.4022 x1 + 19.4986 x2
Is the overall regression statistically significant at the 0.05 level of significance? If so, then test whether each of the regression parameters 0, 1, and 2 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?
For testing the model, F=34.39, P=0.0012 < 0.05, the model is significant.
For testing 0, calculated t=-1.491, P=0.1961 > 0.05 level, not significant.
For testing 1, calculated t=3.156, P=0.0252 < 0.05 level, significant.
For testing 2, calculated t= 5.274, P=0.0033 < 0.05 level, significant.
When there is one unit( $100) increase in television advertising, there is increase of $22.4022(in $100) in Weekly Gross Revenue.
When there is one unit( $100) increase in newspaper advertising, there is increase of $19.4986(in $100) in Weekly Gross Revenue.
The interpretations reasonable.
(d)
How much of the variation in the sample values of weekly gross revenue does the model in part (c) explain?
93.22 %
(e)
Given the results in part (a) and part (c), what should your next step be? Explain.
Both television advertising and newspaper advertising are good in predicting Weekly Gross Revenue.
(f)
What are the managerial implications of these results?
The management should use both television advertising and newspaper advertising to increase the Weekly Gross Revenue.
Regression Analysis
r²
0.5552
n
8
r
0.745
k
1
Std. Error
47.550
Dep. Var.
Weekly Gross Revenue
ANOVA table
Source
SS
df
MS
F
p-value
Regression
16,932.0432
1
16,932.0432
7.49
.0339
Residual
13,565.9568
6
2,260.9928
Total
30,498.0000
7
Regression output
confidence interval
variables
coefficients
std. error
t (df=6)
p-value
95% lower
95% upper
Intercept
-45.4323
66.7518
-0.681
.5215
-208.7682
117.9035
Television Advertising
40.0640
14.6403
2.737
.0339
4.2405
75.8874