Dixie Showtime Movie Theaters, Inc., owns and operates a chain of cinemas in sev
ID: 2931072 • 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.
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
We are given,
y = Weekly Gross Revenue ($100s)
x1 = Television Advertising ($100s)
x2 = Newspaper Advertising ($100s)
y^
x1
x2
102.3
5
1.6
51.9
3
3.2
75.5
4
1.5
127.2
4.4
4
137.8
3.6
4.3
101.4
3.5
2.3
237.8
5
8.4
219.6
6.9
5.8
Here we can use excel here. We copy the data in excel then we go to Data option, there we select Data Analysis. Under Data Analysis we select Regression. There we select y and x1 and x2 values. We run the regression and get the following output.
Regression Statistics
Multiple R
0.96638907
R Square
0.93390784
Adjusted R Square
0.90747098
Standard Error
20.0294663
Observations
8
ANOVA
df
SS
MS
F
Significance F
Regression
2
28344.11116
14172.06
35.32597
0.001122987
Residual
5
2005.897592
401.1795
Total
7
30350.00875
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
-46.7194
28.21037874
-1.65611
0.158602
-119.2364867
25.79768758
x1
23.2442
6.932476018
3.35294
0.020264
5.423677245
41.06467109
x2
19.4345
3.644008337
5.333262
0.003106
10.06722952
28.80167279
Answer:
y^ = -46.7194 + 23.2442x1 + 19.4345x2
y^
x1
x2
102.3
5
1.6
51.9
3
3.2
75.5
4
1.5
127.2
4.4
4
137.8
3.6
4.3
101.4
3.5
2.3
237.8
5
8.4
219.6
6.9
5.8