A company wants to estimate how effective different types of advertising are for

Question

A company wants to estimate how effective different types of advertising are for promoting its products. Specifically, the company is interested in estimating the effectiveness of radio advertising and newspaper advertising. A sample of 50 cities is selected for the study during a test period of one month. The populations of the selected cities are approximately the same. Each city is allocated a specific expenditure level for radio advertising and for newspaper advertising. Sales of the product (in thousands of dollars) and the levels of expenditure (in thousands of dollars) on both types of advertising are recorded during the test month. The collected data are given in the TABLE below

a.  Specify a suitable multiple regression equation for predicting sales.

b.  Use Excel to estimate the coefficients of the regression equation.

c.  Are the estimated slope coefficients statistically significant? Explain.

d.  Interpret the estimated slope coefficients.

e.  Predict the sales for a city in which radio advertising is $60,000 and newspaper advertising is $60,000.

Sales Radio Newspaper 1622 0 48 1865 0 48 1459 75 30 1042 75 30 1517 90 36 1619 90 36 1552 105 42 1962 105 42 1470 120 30 1637 120 30 2713 135 54 2629 135 54 1740 150 0 1523 150 0 2215 165 30 2217 165 30 2342 180 36 2393 180 36 2535 195 42 2902 195 42 3110 210 48 2862 210 48 1042 75 30 1517 90 36 1619 90 36 1552 105 42 1962 105 42 1470 120 30 1637 120 30 2713 135 54 2629 135 54 1740 150 0 1523 150 0 2215 165 30 2217 165 30 2342 180 36 2393 180 36 1740 150 0 1523 150 0 2215 165 30 2217 165 30 2342 180 36 2393 180 36 2535 195 42 2902 195 42 3110 210 48 2862 210 48 1042 75 30 1517 90 36 1619 90 36

Explanation / Answer

a. Sales = B0 + B1*Radio + B2*Newspaper

b. Below is the estimated regression:

c. Yes the estimated coefficients are statistically significant at 5% level of significance as the p-value is less than the 0.05.

d. A unit increases in Radio advertising results in increase in sales by 8.46 units.

Likewise, a unit increases in Newspaper advertising results in increase in sales by 20.69 units.

e. Predicted Sales = 167.52 + 8.46*Radio + 20.69*Newspaper

when radio advertising is $60,000 and newspaper advertising is $60,000, predicted sales = 167.52 + 8.46*60000+ 20.69*60000 = 1,749,167.52

Regression Statistics Multiple R 0.912852017 R Square 0.833298805 Adjusted R Square 0.826205137 Standard Error 234.1951643 Observations 50

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