13_Multiple_Regression_Part3 - MULTIPLE REGRESSION PART 3 Topics Outline Dummy Variables Interaction Terms Nonlinear Transformations Quadratic

13_Multiple_Regression_Part3 - MULTIPLE REGRESSION PART 3...

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- 1 - MULTIPLE REGRESSION – PART 3 Topics Outline Dummy Variables Interaction Terms Nonlinear Transformations – Quadratic Transformations – Logarithmic Transformations Dummy Variables Thus far, the examples we have considered involved quantitative explanatory variables such as machine hours, production runs, price, expenditures. In many situations, however, we must work with categorical explanatory variables such as gender (male, female), method of payment (cash, credit card, check), and so on. The way to include a categorical variable in the regression model is to represent it by a dummy variable. A dummy variable(also called indicatoror 0 – 1 variable) is a variable with possible values 0 and 1. It equals 1 if a given observation is in a particular category and 0 if it is not. If a given categorical explanatory variable has only two categories, then you can define one dummy variable xdto represent the two categories as =otherwise01category in isn observatiotheifdxExample 1 Data collected from a sample of 15 houses are stored in Houses.xlsxHouse Value ($ thousands) Size (thousands of square feet) Presence of Fireplace 1 234.4 2.00 2 227.4 1.71 MMMM14 233.8 1.89 15 226.8 1.59 (a) Develop a regression model for predicting the assessed value yof houses, based on the size 1of the house and whether the house has a fireplace. To include the categorical variable for the presence of a fireplace, the dummy variable is defined as =fireplaceahavenot doeshousetheiffireplaceahashousetheif12x1. Yes No Yes No x0
To code this dummy variable in Excel, enter =IF(C2="Yes",1,0) in cell D2 and drag it down. The data become: House Value Size Fireplace 1 234.4 2.00 2 227.4 1.71 MMMM14 233.8 1.89 15 226.8 1.59 Assuming that the slope of assessed value with the size of the house is the same for houses that have and do not have a fireplace, the multiple regression model is εββα=2211xxyHere are the regression results for this model. Regression Statistics Multiple R 0.9006 R Square 0.8111 Adjusted R Square 0.7796 Standard Error 2.2626 Observations 15 ANOVA df SS MS F Significance F Regression 2 263.7039 131.8520 25.7557 0.0000 Residual 12 61.4321 5.1193 Total 14 325.1360 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 200.0905 4.3517 45.9803 0.0000 190.6090 209.5719 Size 16.1858 2.5744 6.2871 0.0000 10.5766 21.7951 Fireplace 3.8530 1.2412 3.1042 0.0091 1.1486
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6.5574 (b) Interpret the regression coefficients.
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a
Interpretation of 1b

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