4. A company is interested in the effectiveness of radio advertising and newspap

Question

4. A company is interested in the effectiveness of radio advertising and newspaper advertising on the overall sales of its products. The sales of their products and the levels of both types of media expendi (all in thousands of dollars) for 11 locations were recorded in the following table during a one month test period. Answer parts (a) through (d) below. Sales 969 620 908 933 882 1579 9015 1327 1401 1521 1716 0 24 31 35 40 44 50 56 61 64 70 Radio ads Newspaper ads 40 24 31 36 26 44 22 25 30 36 40 a. Identify the coefficients bo, b1, and b2 that form the multiple regression equation below for the given data. Let X1 represent radio advertising and X2 represent newspaper advertising. Round to three decimal places as needed.) b. Interpret the meaning of the slopes, b1 and b2, in this problem. Select the correct choice below. O A. The slope b1 represents the change in the mean sales per unit change in newspaper advertising. The slope b2 represents the change in the mean sales per unit change in radio advertising. O B. The slope b1 represents the change in the mean sales per unit change in radio advertising. The slope b2 represents the change in the mean sales per unit change in newspaper advertising. O C. The slopes b1 and bo represent the amount of radio advertising and newspaper advertising, respectively c. Interpret the meaning of the regression coefficient, bo. Select the correct choice below. O A. The coefficient bo represents the total amount spent on newspaper advertising and radio advertising O B. The coefficient bo represents the estimated mean sales when there is no money spent on radio advertising or newspaper advertising. O C. The coefficient bo represents the estimated amount spent on radio advertising when there is no money spent on newspaper advertising. O D. The coefficient bo represents the estimated amount spent on newspaper advertising when there is no money spent on radio advertising.

Explanation / Answer

The statistical software output for this problem is:

Multiple linear regression results:
Dependent Variable: Sales
Independent Variable(s): Radio Ads, Newspaper Ads
Sales = 45.974723 + 13.465402 Radio Ads + 17.572492 Newspaper Ads

Parameter estimates:

Analysis of variance table for multiple regression model:

Summary of fit:
Root MSE: 166.83061
R-squared: 0.8262
R-squared (adjusted): 0.7828

Hence,

a) b0 = 45.975

b1 = 13.465

b2 = 17.572

b) Option B is correct.

c) Option B is correct.

d) Option B is correct.

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 45.974723 193.75435 0 8 0.23728357 0.8184 Radio Ads 13.465402 2.6039938 0 8 5.1710574 0.0009 Newspaper Ads 17.572492 4.596559 0 8 3.8229667 0.0051

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