Problem 7-9 Dixie Showtime Movie Theaters, Inc., owns and operates a chain of ci
ID: 350007 • 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 Newspaper Advertising ($100s) Weekly Gross Television Advertising Market (S100s) Revenue ($100s) 102.5 5.1 3.2 4 4.3 3.5 3.6 1.6 Mobile Shreveport Jacksor Birmingham Little Rock Biloxi New Orleans Baton Rouge 52.7 75.8 127.8 137.8 101.4 237.8 219.6 1.5 4.3 2.3 8.4 5.8 6.9 (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 three decimal places. For subtractive or negative numbers use a minus sign even if there is a sign before the blank. (Example: -300) 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. blank (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. 51.81Explanation / Answer
(a)
Note that the p-value for the intercept is more than 0.05. So, it will be statistically insignificant to consider the value of the intercept. The null hypothesis that intercept=0 cannot be rejected at 95% confidence level. For the slope, the p-value is less than 0.05 and hence it is statistically significant. We can reject the null hypothesis that slope=0 and take this estimated value at 95% confidence level.
(b)
R-squared value is 52.08%. So, 52.08% variations of sample observations can be explained by the model.
(c)
Note that the p-value for the intercept is more than 0.05. So, it will be statistically insignificant to consider the value of the intercept. The null hypothesis that intercept=0 cannot be rejected at 95% confidence level. For the slopes, the p-values are less than 0.05 and hence they are statistically significant. We can reject the null hypothesis that slope=0 and take these estimated values at 95% confidence level.
(d)
R-squared value is 93.57%. So, 93.57% variations of sample observations can be explained by the model.
SUMMARY OUTPUT Regression Statistics Multiple R 0.72168302 R Square 0.520826382 Adjusted R Square 0.440964112 Standard Error 49.08786385 Observations 8 ANOVA df SS MS F Significance F Regression 1 15714.46473 15714.465 6.52156 0.043272349 Residual 6 14457.71027 2409.6184 Total 7 30172.175 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -43.258 70.760 -0.611 0.563 -216.401 129.886 -216.401 129.886 TV Adv 39.367 15.415 2.554 0.043 1.647 77.087 1.647 77.087