Problem 7-9 Dixie Showtime Movie Theaters, Inc., owns and operates a chain of ci
ID: 3056556 • 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.
Market Weekly Gross Revenue
($100s) Television Advertising
($100s) Newspaper Advertising
($100s) Mobile 101.3 5.0 1.5 Shreveport 51.9 3.0 3.0 Jackson 74.8 4.0 1.5 Birmingham 126.2 4.3 4.3 Little Rock 137.8 3.6 4.0 Biloxi 101.4 3.5 2.3 New Orleans 237.8 5.0 8.4 Baton Rouge 219.6 6.9 5.8
Explanation / Answer
(A) The regression output for the the gross revenue (y) and tv advertising (x)
So regression line
y^ = -45.2323 + 40.0640x
here to test the significance of the given regression the test statistic
t = 2.7366
p -value = 0.0339
Here p - value is less than 0.05 so at significance level 0.05, we can reject the null hypothesis and the relationship between these two values are significant.
(b) Here the regression coefficient R2 = 0.5552
As the 55.52% variabiliaty is explained by the weekly gross revenue.
(c) Here the summary output for the regression
y^ = -42.5696 + 22.4022x1 + 19.4986x2
Here to test the significane of each of the regression parameter, 0, 1, and 2 is equal to zero at a 0.05 level of significance.
for 0 ; test statistic t = -1.4912 ; p - value = 0.1961 > 0.05; so 0 is not significant here
for 1 ; test statistic t = 3.1555 ; p - value = 0.0252 < 0.05; so 1 is significant here
for 2 ; test statistic t = 5.2743 ; p - value = 0.0033 < 0.05; so 2 is significant here
Here the correct intrepretation of these parameters are
For intercet : as if there is no tv advertising and no newspaper adveritising, there is -42.57 ($ 1000) revenue.
For TV adviritising : as if we increase tv advertising by $1000, then it will increase the revenue by 22.4022 ($ 1000) .
For Newspaper adveritisng : as if we increase newspaper adverising by $ 10000, then it will increase the revenue by 19.4986 ($ 1000) value.
(d) Here the value of R- square = 0.9322
so 93.22% of variation in revenue is explained by this two variables.
(e) Here our next step is to select the model 2 to choose here as it is significant here.
(f) Here the managerial implications of these results as we come to know that revenue generaton is the product of tv adveritising and newspaper advertising both.
SUMMARY OUTPUT Regression Statistics Multiple R 0.745108 R Square 0.555185 Adjusted R Square 0.48105 Standard Error 47.5499 Observations 8 ANOVA df SS MS F Regression 1 16932.04 16932.04 7.488765 Residual 6 13565.96 2260.993 Total 7 30498 Coefficients Standard Error t Stat P-value Intercept -45.4323 66.75185 -0.68062 0.521499 Television Advertising ($100s) 40.06399 14.64027 2.736561 0.03389