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3. 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: City | Sales ($000) | Radio Advertising ($000) | Newspaper Advertising ($000) 1 | 973 | 0 | 40 2 | 1,119 | 0 | 40 3 | 875 | 25 | 25 4 | 625 | 25 | 25 5 | 910 | 30 | 30 6 | 971 | 30 | 30 7 | 931 | 35 | 35 8 | 1,177 | 35 | 35 9 | 882 | 40 | 25 10 | 982 | 40 | 25 11 | 1,628 | 45 | 45 12 | 1,577 | 45 | 45 13 | 1,044 | 50 | 0 14 | 914 | 50 | 0 15 | 1,329 | 55 | 25 16 | 1,330 | 55 | 25 17 | 1,405 | 60 | 30 18 | 1,436 | 60 | 30 19 | 1,521 | 65 | 35 20 | 1,741 | 65 | 35 21 | 1,866 | 70 | 40 22 | 1,717 | 70 | 40 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.

          3. 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:

City | Sales ($000) | Radio Advertising ($000) | Newspaper Advertising ($000)
1 | 973 | 0 | 40
2 | 1,119 | 0 | 40
3 | 875 | 25 | 25
4 | 625 | 25 | 25
5 | 910 | 30 | 30
6 | 971 | 30 | 30
7 | 931 | 35 | 35
8 | 1,177 | 35 | 35
9 | 882 | 40 | 25
10 | 982 | 40 | 25
11 | 1,628 | 45 | 45
12 | 1,577 | 45 | 45
13 | 1,044 | 50 | 0
14 | 914 | 50 | 0
15 | 1,329 | 55 | 25
16 | 1,330 | 55 | 25
17 | 1,405 | 60 | 30
18 | 1,436 | 60 | 30
19 | 1,521 | 65 | 35
20 | 1,741 | 65 | 35
21 | 1,866 | 70 | 40
22 | 1,717 | 70 | 40

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.

3. 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:

City | Sales (000) | Radio Advertising (000) | Newspaper Advertising (000)
1 | 973 | 0 | 40
2 | 1,119 | 0 | 40
3 | 875 | 25 | 25
4 | 625 | 25 | 25
5 | 910 | 30 | 30
6 | 971 | 30 | 30
7 | 931 | 35 | 35
8 | 1,177 | 35 | 35
9 | 882 | 40 | 25
10 | 982 | 40 | 25
11 | 1,628 | 45 | 45
12 | 1,577 | 45 | 45
13 | 1,044 | 50 | 0
14 | 914 | 50 | 0
15 | 1,329 | 55 | 25
16 | 1,330 | 55 | 25
17 | 1,405 | 60 | 30
18 | 1,436 | 60 | 30
19 | 1,521 | 65 | 35
20 | 1,741 | 65 | 35
21 | 1,866 | 70 | 40
22 | 1,717 | 70 | 40

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 is20,000 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.

Added by Richard H.

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