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Unformatted text preview: Multiple Regression Statistics for Management and Economics Chapter 18 Multiple Regression Model Now assume k independent variables (x k ) are related to the independent variable y. The model is now represented by the equation: y = + 1 x 1 + 2 x 2 + + k x k + Retaining the error variable because there will still be some deviations between predicted yhat and actual y values. Has the same required conditions with respect to the error variable as we saw for simple linear regression. Steps To Perform a Multiple Regression Analysis 1. Use a computer and software to generate the coefficients and the statistics used to assess the model. 2. Diagnose violations of required conditions. If there are problems, attempt to remedy them. 3. Assess the models fit. Three statistics that perform this function are the standard error of the estimate, the R 2 , and the F test of the analysis of variance. 4. If we are satisfied with the models fit and that the required conditions are met, we can interpret the coefficients and test them as we learned with simple linear regression. We use the model to predict or estimate the expected value of the dependent variable. Example: How Can You Predict the Selling Price of a House? Scenario: You are saving money to buy a house or condo and you wonder how much it will cost. Depending on what you want and its location, the price will vary dramatically. Data was collected on 100 home sales in Gainesville, Florida, in November 2003. Variables collected are: selling price in dollars, house size (square feet), number of bedrooms, number of bathrooms, the lot size (sq ft), the annual real estate tax ($), and whether the house is in the northwest (NW) quadrant of town, a desirable location (Y or N). Example: House Sales In your community, if you know values of such variables: How can you predict a homes selling price? How can you describe the association between selling price and the other variables? How can you make inferences about the population based on the sample data? You can find a regression equation to predict selling price by treating one of the other variables as the explanatory variable. But, since there are several explanatory variables, we may make better predictions by using all of them at once. This is the idea behind multiple regression . Example: Predicting Selling Price Using House and Lot Sizes Regression Statistics Multiple R 0.843424448 R Square 0.7113648 Adjusted R Square 0.705413559 Standard Error 30588.10044 Observations 100 ANOVA df SS MS F Significance F Regression 2 2.23676E+11 1.12E+11 119.5322 6.71337E27 Residual 97 90756293211 9.36E+08 Total 99 3.14433E+11 Coefficients Standard Error t Stat Pvalue Lower 95% Upper 95%Lower 95.0%Upper 95%Lower 95....
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This note was uploaded on 06/25/2008 for the course BUSSPP MCE taught by Professor Atkins during the Spring '08 term at Pittsburgh.
 Spring '08
 Atkins

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