1. The manager of Erehwon police department motor pool wants to develop a forecast model for annual maintenance costs on police cars, based on mileage in the past year, and age of cars. The following data have been collected for eight different cars:
Miles Driven Car Age (yr.) Maintenance Cost ($)
16,320 7 1,200
15,100 8 1,400
18,500 8 1,820
10,200 3 900
9,175 3 650
12,770 7 1,150
8,600 2 875
7,900 3 900
a. Using Excel,develop a multiple regression equation for these data.
b. What is the coefficient of determination? What does it mean?
c. Forecast the annual maintenance cost for a police car that is 5 years old and will be driven 10,000 miles in 1 year.
This solution is comprised of a detailed explanation of various aspects of Regression Analysis as it pertains to the given problem. Supplemented with EXCEL output, this step-by-step explanation of this complicated topic provides students with a clear perspective of Regression Analysis.
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