Dixie Showtime Movie Theaters, Inc., owns and operates a chain of cinemas in sev
ID: 3151035 • 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 102.5 5.1 1.6 Shreveport 52.7 3.2 3 Jackson 75.8 4 1.5 Birmingham 127.8 4.3 4 Little Rock 137.8 3.5 4.3 Biloxi 101.4 3.6 2.3 New Orleans 237.8 5 8.4 Baton Rouge 219.6 6.9 5.8
Explanation / Answer
tt <- read.csv("clipboard",sep=" ",row.names=1,header=TRUE)
> tt
Weekly.Gross.Revenue Television.Advertising Newspaper.Advertising
Mobile 102.5 5.1 1.6
Shreveport 52.7 3.2 3.0
Jackson 75.8 4.0 1.5
Birmingham 127.8 4.3 4.0
Little Rock 137.8 3.5 4.3
Biloxi 101.4 3.6 2.3
New Orleans 237.8 5.0 8.4
Baton Rouge 219.6 6.9 5.8
> firstlm <- lm(Weekly.Gross.Revenue~Television.Advertising,data=tt)
> summary(firstlm)
Call:
lm(formula = Weekly.Gross.Revenue ~ Television.Advertising, data = tt)
Residuals:
Min 1Q Median 3Q Max
-55.013 -32.115 -3.497 13.021 84.223
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -43.26 70.76 -0.611 0.5634
Television.Advertising 39.37 15.42 2.554 0.0433 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 49.09 on 6 degrees of freedom
Multiple R-squared: 0.5208, Adjusted R-squared: 0.441
F-statistic: 6.522 on 1 and 6 DF, p-value: 0.04327
(a) Y = -43.26 + 39.37 x.
Since the p-value for the impact of x on y is 0.0433, it is clear that there exists a significant relationship between television advertising and weekly gross revenue at the 0.05 level of significance.It means that r every increase in the adversiting, leads to an increasing in the weekly gross revenue by 39.37.
(b) 44.1% of the variation is explained by the television advertising.
> secondlm <- lm(Weekly.Gross.Revenue~.,data=tt)
> summary(secondlm)
Call:
lm(formula = Weekly.Gross.Revenue ~ ., data = tt)
Residuals:
Mobile Shreveport Jackson Birmingham Little Rock Biloxi New Orleans Baton Rouge
1.983 -34.511 1.345 -3.618 17.820 19.559 2.367 -4.944
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -43.225 28.394 -1.522 0.18842
Television.Advertising 21.859 6.911 3.163 0.02501 *
Newspaper.Advertising 20.162 3.550 5.680 0.00236 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 19.7 on 5 degrees of freedom
Multiple R-squared: 0.9357, Adjusted R-squared: 0.91
F-statistic: 36.38 on 2 and 5 DF, p-value: 0.001048
(c) The fitted regression model is Y = -43.225 + 21.859 x1 + 20.162 x2.
(d) 91% of the variation in the sample values of weekly gross revenue is explained by the model.
(e) Since only 41% variation is explained when only television advertising is considered, it is appropriate to use the model given in (c).
(f) It means that the manager can make better use of the additional information brought by both the variables. This will lead to better answers.