A large consumer product 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/TV advertising and newspaper advertising (including the cost of discount coupons). The sales of product (in thousands of dollars) and also the levels of media expenditure (in thousands of dollars) during the test month (Sales in thousands of dollars, radio/TV ads in thousands of dollars and newspaper ads in thousands of dollars for 22 cities). Let X1 and X2 be the dollar amount of radio/TV ads and newspaper ads, respectively. Using EXCEL, answer the following:
Sales RadioTV 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
1. What is the intercept (regression coefficient) b0?
2. What is the slope b1 for X1?
3. What is the slope b2 for X2?
4. Determine which explanatory variable has a significant relationship with sales (Y) using the 5% significance level.
a) Radio/TV only
b) Newspaper only
c) Both Radio/TV and Newspaper
5. Set up a 95% confidence interval estimate of the population slope between sales and radio/TV ads.
a) (9.399, 16.763)
b) (10.593, 22.998)
c) (6.320, 18.005)
6. Set up a 95% confidence interval estimate for the average sales that have 10 radio/TV ads and 20 newspaper ads.
a) (464.393, 781.893)
b) (254.608, 991.678)
c) (158.750, 464.393)
Statistics Problems - Regression Analysis, Autocorrelation, Multicollinearity
1. Suppose an appliance manufacturer is doing a regression analysis, using quarterly time-series data, of the factors affecting its sales of appliances. A regression equation was estimated between appliance sales (in dollars) as the dependent variable and disposable personal income and new housing starts as the independent variables. The statistical tests of the model showed large t-values for both independent variables, along with a high r2 value. However, analysis of the residuals indicated that substantial autocorrelation was present.
a. What are some of the possible causes of this autocorrelation?
b. How does this autocorrelation affect the conclusions concerning the significance of the individual explanatory variables and the overall explanatory power of the regression model?
c. Given that a person uses the model for forecasting future appliance sales, how does this autocorrelation affect the accuracy of these forecasts?
d. What techniques might be used to remove this autocorrelation from the model?
2. Suppose the appliance manufacturer discussed in Exercise 1 also developed another model, again using time-series data, where appliance sales was the dependent variable and disposable personal income and retail sales of durable goods were the independent variables. Although the r2 statistic is high, the manufacturer also suspects that serious multicollinearity exists between the two independent variables.
a. In what ways does the presence of this multicollinearity affect the results of the regression analysis?
b. Under what conditions might the presence of multicollinearity cause problems in the use of this regression equation in designing a marketing plan for appliance sales?View Full Posting Details