A consumer products company wants to measure the effectiveness of different types of advertising media in the promotion of its products. Specially, 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 population is selected for study during a test period of one month. Each city is allocated a specific expenditure level both for radio and television advertising and for newspaper advertising. The sales of the product (in thousands of dollars) and also the levels of media expenditure (in thousands of dollars) during the test month are recorded with the following results.
Sales | Radio | Newspaper |
973 | 0 | 40 |
1119 | 0 | 40 |
875 | 25 | 25 |
625 | 25 | 25 |
910 | 30 | 30 |
971 | 30 | 30 |
931 | 35 | 35 |
1177 | 35 | 35 |
882 | 40 | 25 |
982 | 40 | 25 |
1628 | 45 | 45 |
1577 | 45 | 45 |
1044 | 50 | 0 |
914 | 50 | 0 |
1329 | 55 | 25 |
1330 | 55 | 25 |
1405 | 60 | 30 |
1436 | 60 | 30 |
1521 | 65 | 35 |
1741 | 65 | 35 |
1866 | 70 | 40 |
1717 | 70 | 40 |
a) State the multiple regression equation.
b) Interpret the coefficient b1 and b2 and interpret bo
c) Predict the average sales for a city in which radio and television advertising is $20,000 and newspaper advertising is $20,000.
d) Interpret the coefficient of multiple determination and state how well the equation predicts based on it.
e) State whether there is a significant relationship between sales and the two explanatory variables (radio advertising and newspaper advertising) at the .05 level of significance, and state how you determined whether the relationship is significant. You do not need to do the six steps.
f) At the .05 level of significance, determine whether each variable makes a significant contribution to the regression model. State how you determined this, and based on the results, indicate the independent variables that should be included in the model.
A consumer products company wants to measure the effectiveness of different types of advertising media in...
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