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Regression Analysis

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Passage of the 1983 Dairy Product Stabilization Act authorized establishing a national program for dairy products designed to increase human consumption of milk dairy products and reduce the industry's reliance on government price supports. The activities of the (then) newly established organization-the National Dairy Promotion and Research Board-were funded through a mandatory 15-cent-per-hundredweight assessment on all milk produced and commercially marketed by dairy farmers (in 1997 dairy producers received approximately $13.00 per hundredweight of milk). The National Dairy Promotion and Research Board's primary advertising campaign "Got Milk?" targeted consumers between the ages of 13 and 34 by paying celebrities to endorse milk consumption. According to a February 2004 CNN.com article, dairy farmers Joseph and Brenda Cochran have challenged the legality of the funding of the "Got Milk?" campaigns. The Cochrans argue that the "Got Milk?" campaign do little to support milk from cows that are not injected with hormones and other sustainable agriculture products, and therefore violate their (and other farmers') First Amendment Rights. The 3 rd U.S. Circuit Court of Appeals agreed with the Cochrans and concluded that dairy farmers cannot be required to pay to fund the advertisement campaigns. One of the obvious backlashes to the National Dairy Promotion and Research Board is reduced funding for advertising campaigns. To assess the likely impact on milk consumption, suppose that the National Dairy Promotion and Research Board collected data on the number of gallons of milk households consumed weekly (in millions), weekly price per gallon, and weekly expenditures on milk advertising. These data, in forms to estimate both linear model and log-linear model, is contained in a file named Q20.xls in the Chapter 3 folder of the textbook. Use these data to perform two regressions: a linear regression and a log-linear regression. Compare and contrast the regression output of the two models. Comment on which model does a better job fitting the data. Suppose that the weekly price of milk is $3.10 per gallon and the National Dairy Promotion and Research Board's weekly advertising expenditures falls to $100 after the court's ruling. Use the best-fitting regression model to estimate the weekly quantity of milk consumed after the court's ruling.

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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?

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