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Regression Analysis

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The data file contains information on 76 single-family homes in Eugene, Oregon during 2005. At the time the data were collected, the data submitter was preparing to place his house on the market and it was important to come up with a reasonable asking price. Whereas realtors use experience and local knowledge to subjectively value a house based on its characteristics (size, amenities, location, etc.) and the prices of similar houses nearby, regression analysis provides an alternative that more objectively models local house prices using these same data. Please address items (a) through (c) below

a) Using price as the dependent variable (Y) use regression to determine the fitted regression equation using size, bath, bed, and garage. (Use Data Analysis in Excel or MegaStat)
b) What does the R-squared value tell you?
c) Using an alpha value of 0.05, which variables are significant (size, bath, bed, garage)?
d) The variable "bed" has a negative coefficients. What does this mean. (i.e. what happens to the selling price when the number of bedrooms increases)

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The solution provides detailed Regression Analysis performed on the given data.

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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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