Suppose a large consumer products company wants to measure the effectiveness of different types of advertising media in the promotion of its products. Specifically, two types of advertising media are to be considered: radio and television advertising and newspaper advertising (including the cost of discount coupons). A sample of 22 cities with approximately equal populations is selected for study during a test period of 1 month. Each is allocated a specific expenditure level for both radio and television advertising and newspaper advertising. The sales of the product (in thousands of dollars) and also the levels of media expenditure during the test month are recorded with the following results: Excel output: Regression Statistics Multiple R: 0.8993 R Square: 0.8087 Adjusted R Square: 0.7892 Standard Error: 158.9041 Observations: 22 df: 19 SS: 2028032.6896 MS: 1014016.3448 F: 80.4406 Significance F: 0.0000 Coefficients: Standard Error t Stat P-value Intercept: 156.4304 126.7579 1.2337 0.2321 RADIO&TV: 13.0807 5.7594 2.2739 0.0362 NEWSPAPER: 16.7953 2.9634 5.6661 0.0001
Added by David S.
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Compute the coefficient of multiple determination R2 and interpret its meaning. The coefficient of multiple determination, R2, is given as 0.8993. This means that 89.93% of the variation in sales can be explained by the variation in radio and television Show more…
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Suppose a large consumer products company wants to measure the effectiveness of different types of advertising media in the promotion of its products. Specifically, two types of advertising media are to be considered: radio and television advertising and newspaper advertising (including the cost of discount coupons). A sample of 22 cities with approximately equal populations is selected for study during a test period of 1 month. Each is allocated a specific expenditure level for both radio and television advertising and newspaper advertising. The sales of the product (in thousands of dollars) and also the levels of media expenditure during the test month are recorded with the following results: Excel output: Regression Statistics Multiple R: 0.8993 R Square: 0.8086 Adjusted R Square: 0.7917 Standard Error: 158.9041 Observations: 22 df: 19 SS: 2028032.6896 MS: 1014016.3448 F: 40.3036 Significance F: 0.0000 Coefficients Standard Error t Stat P-value Intercept 156.4304 126.7579 RADIO&TV 13.0807 1.7594 NEWSPAPER 16.7953 2.9634
Sri K.
A consumer products company wants to measure the effectiveness of different types of advertising media in the promotion of its products. Specifically, the company is interested in the effectiveness of radio advertising and newspaper advertising (including the cost of discount coupons). A sample of 22 cities with approximately equal populations is selected for study during a test period of one month. Each city is allocated a specific expenditure level both for radio advertising and for newspaper advertising. The sales of the products (in thousands of dollars) and also the levels of media expenditure (in thousands of dollars) during the test month are recorded with following results tabulated below: Conduct a regression analysis and (a) identify the mathematical model; (b) provide an interpretation for the slopes of the problem; (c) predict the mean sales for a city in which radio advertising is $20,000 and newspaper advertising is $20,000; (d) test the adequacy of the model using the F-statistic and determine the observed level of significance; (e) perform a global usefulness test using a 0.05 level of significance. Show all the steps involved the test of hypothesis.
Madhur L.
An advertising firm wishes to demonstrate to potential clients the effectiveness of the advertising campaigns it has conducted. The firm is presenting data from recent campaigns, with the data indicating an increase in sales for an increase in the amount of money spent on advertising. In particular, the least-squares regression equation relating the two variables, the cost of the advertising campaign (denoted by x and written in millions of dollars) and the resulting percentage increase in sales (denoted by Y), for the l campaigns is y = 6.43 + 0.1x. The standard error of the slope of this least-squares regression line is approximately 0.09. Using this information, test for a significant linear relationship between these two variables by conducting a hypothesis test regarding the population slope Β. Assume that the variable Y follows a normal distribution for each value of x and that the other regression assumptions are satisfied. Use the 0.05 level of significance and perform a two-tailed test. Then fill in the table below. The null hypothesis: The alternative hypothesis: The type of test statistic: The value of the test statistic: (Round to at least three decimal places.) The p-value: (Round to at least three decimal places.) Based on the data, we conclude (using the 0.05 level) that there is a significant linear relationship between the cost of the advertising campaign and the resulting percentage increase in sales.
Clarissa B.
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