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Regression analysis problem

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Use the Cartesian coordinate system to find the distance between two points; illustrate linear functions and their relationship to business, economics, social science, etc., and find the intersection of two lines.

Great news! ABC Advertising has called you in for an interview to join their advertising team. During the interview process, you are expected to solve a linear regression problem. Consider the following data in the table below that show U.S. advertising expenditures in millions of the current U.S. dollars.

Based on these data, please supply the following:
1. Provide graphs of Grand Total versus Year, Newspapers versus Year, and Internet versus Year.
2. Which advertising expenditure from #1 has the best linear graph for predicting? Explain.
3. Based on your answer for #2, provide a regression equation for the advertising method and explain how well the equation predicts known expenditure values.
4. How quickly are expenditures for the advertising method chosen in #2, growing per year? Would you expect this rate to continue? Explain why or why not.
5. Complete a 5-year prediction for advertising expenditures for the particular advertising method chosen in #2. Next, complete a 20-year prediction. Explain the validity in these predictions.
6. Based on the method chosen in #2, in what year would you expect the Internet expenditures to reach 20,000 (in millions)? Explain the validity of this prediction

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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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