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Regression Analysis

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How much does advertising impact market penetration? To assess the impact of advertising in the tobacco industry, a study looked at the amount of money spend on advertising a particular brand of cigarettes and brand preference among adolescents and adults. The data are shown below:(PLEASE SEE TABLE ATTACHED)

a). Look at the data for brand preference for adolescents and amount spent on advertising. Which variable is the dependent variable? Which is the independent variable?

b). Create a scatter plot (using excel) of advertising and adolescent brand preference. Do you think that there is a linear relationship between the two variables? Why or why not?

c). Now create another scatter plot (using excel) using adult brand preference instead. How does this plot compare to the one for adolescent brand preference? From the plots, do you think that adolescent or adult brand preference is more strongly related to advertising expenditures? Why?

d). Find the least-squares line for adolescent brand and advertising expenditures.

e). Interpret the meaning of the slope and intercept for the model. Do they make sense?

f). Use the model to predict adolescent brand preference for each brand studied. How well do the predicted values agree with the actual data?

g). Using alpha = 0.05, is the model significant?

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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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