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	101.3		5	1.5
Shreveport	51.9		3	3
Jackson	74.8		4	1.5
Birmingham	126.2		4.3	4.3
Little Rock	137.8		3.6	4
Biloxi	101.4		3.5	2.3
New Orleans	237.8		5	8.4
Baton Rouge	219.6		6.9	5.8

(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)

(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.

(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 three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)

(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. %

Answer 1

Using Minitab software, (Stat -> Regression -> Regression -> Fit Regression Model), we get the following output :

a) Using the amount of television advertising as the independent variable, we get the regression equation as -

Weekly Gross Revenue = -45.4 + 40.1 Television Advertising

Since coefficient of determination R² = 55.52%, so we can say

55.62% variation in the sample values of weekly gross revenue can be explained by the regression equation.

b) Using both television advertising and newspaper advertising as the independent variables. we get the regression equation as -

Weekly Gross Revenue = -42.6 + 22.40 Television Advertising + 19.50 Newspaper Advertising

Since coefficient of determination R² = 93.22%, so we can say

93.22% variation in the sample values of weekly gross revenue can be explained by the regression equation.