Problem 7-9 Dixie Showtime Movie Theaters, Inc., owns and operates a chain of ci
ID: 2921416 • Letter: P
Question
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.
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?
Market Weekly Gross Revenue
($100s) Television Advertising
($100s) Newspaper Advertising
($100s) Mobile 102.3 5 1.6 Shreveport 51.9 3 3.2 Jackson 75.5 4 1.5 Birmingham 127.2 4.4 4 Little Rock 137.8 3.6 4.3 Biloxi 101.4 3.5 2.3 New Orleans 237.8 5 8.4 Baton Rouge 219.6 6.9 5.8
Explanation / Answer
Answer:
(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)
= -45.7168 + 40.0914 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=2.752, P=0.0332 which is < 0.05 level . Ho is rejected. There is significant relationship between television advertising and weekly gross revenue.
The input in the box below will not be graded, but may be reviewed and considered by your instructor.
Regression Analysis
r²
0.5579
n
8
r
0.7469
k
1
Std. Error
47.288
Dep. Var.
Weekly Gross Revenue
ANOVA table
Source
SS
df
MS
F
p-value
Regression
16,933.0879
1
16,933.0879
7.57
.0332
Residual
13,416.9208
6
2,236.1535
Total
30,350.0088
7
Regression output
confidence interval
variables
coefficients
std. error
t (df=6)
p-value
95% lower
95% upper
Intercept
-45.7168
66.6010
-0.686
.5181
-208.6835
117.2500
Television Advertising
40.0914
14.5691
2.752
.0332
4.4420
75.7407
(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.
55.79%
(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)
= -46.7194 + 23.2442 x1 + 19.4345 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.
Regression Analysis
R²
0.9339
Adjusted R²
0.9075
n
8
R
0.966
k
2
Std. Error
20.029
Dep. Var.
Weekly Gross Revenue
ANOVA table
Source
SS
df
MS
F
p-value
Regression
28,344.1112
2
14,172.0556
35.33
.0011
Residual
2,005.8976
5
401.1795
Total
30,350.0088
7
Regression output
confidence interval
variables
coefficients
std. error
t (df=5)
p-value
95% lower
95% upper
Intercept
-46.7194
28.2104
-1.656
.1586
-119.2365
25.7977
Television Advertising
23.2442
6.9325
3.353
.0203
5.4237
41.0647
Newspaper Advertising
19.4345
3.6440
5.333
.0031
10.0672
28.8017
Test for 0, calculated t=-1.656, P=0.1586, it is not significant.
Test for , 1, calculated t=3.353, P=0.0203, it is significant
Test for 2, calculated t=5.333, P=0.0031, it is significant
When Television Advertising increases by $100, the weekly gross revenue increases by $23.2442( in $100).
When Newspaper Advertising increases by $100, the weekly gross revenue increases by $19.4345( in $100).
There is no meaningful interpretation for 0.
(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.
93.39 %
(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.
Both Television Advertising and Newspaper Advertising are significantly related to weekly gross revenue.
The management should use both type of Advertising to increase weekly gross revenue.
(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)
= -45.7168 + 40.0914 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=2.752, P=0.0332 which is < 0.05 level . Ho is rejected. There is significant relationship between television advertising and weekly gross revenue.
The input in the box below will not be graded, but may be reviewed and considered by your instructor.