LinearRegression4

10232012 p kolm 17 multiple regression analysis dummy

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Unformatted text preview: say that OLS is asymptotically efficient • Important to remember our assumptions though: If the error terms are not homoscedastic, then the asymptotic efficiency is no longer true VER. 10/23/2012. © P. KOLM 17 Multiple Regression Analysis: Dummy Variables VER. 10/23/2012. © P. KOLM 18 Example: C7.10 in Wooldridge (For you: Review the following example on your own using dummy variables. There is “nothing new here” besides the use of dummy variable. Think about other situations where you might be using dummy variables. It is a useful tool from the “econometrician’s toolbox.”) VER. 10/23/2012. © P. KOLM 19 We use the data in NBASAL.RAW for this exercise. (i) Estimate a linear regression model relating points per game to experience in the league and position (guard, forward, or center). Include experience in quadratic form and use centers as the base group. Report the results in the usual form. Solution: The estimated regression equation and output are shown below: points = 4.815 + 1.264exper − 0.07045exper 2 + 2.336guard + 1.590 forward (1.18) (0.328) (0.0240) n = 269, R2 = 0.091, VER. 10/23/2012. © P. KOLM (0.997) (0.999) R2 = 0.077 20 Ordinary Least-squares Estimates Dependent Variable = points R-squared = 0.0910 Rbar-squared = 0.0772 sigma^2 = 31.9327 Durbin-Watson = 2.2214 Nobs, Nvars = 269, 5 *************************************************************** Variable Coefficient t-statistic t-probability intercept 4.814859 4.097752 0.000056 exper 1.264197 3.859862 0.000143 expersq -0.070452 -2.935740 0.003621 guard 2.336508 2.342856 0.019880 forward 1.589599 1.590907 0.112827 VER. 10/23/2012. © P. KOLM 21 (ii) Why do you not include all three position dummy variables in part (i)? Solution: Including all three position dummy variables would be redundant, and result in the dummy variable trap. Each player falls into one of the three categories, and the overall intercept is the intercept for centers. VER. 10/23/2012. © P. KOLM 22 (iii) Holding experience fixed, does a guard score more than a center? How much more? Is the difference statistically significant? Solution: A guard is estimated to score about 2.3 points more per game, holding experience fixed. The t statistic is 2.34, with a p-value of 0.0199, so the difference is statistically different from zero at the 5% level, against a two-sided alternative. VER. 10/23/2012. © P. KOLM 23 (iv) Now, add marital status to the equation. Holding position and experience fixed, are married players more productive (based on points per game)? Solution: The estimated regression equation and output are shown below: points = 4.759 + 1.219exper − 0.0690exper 2 (1.18) (0.333) (0.0241) −2.309guard − 1.586 forward + 0.5598marr (1.00) (1.00) n = 269, R2 = 0.093, VER. 10/23/2012. © P. KOLM (0.738) R2 = 0.076 24 Ordinary Least-squares Estimates Dependent Variable = points R-squared = 0.0929 Rbar-squared = 0.0757 sigma^2 = 31.9842 Durbin-Watson = 2.2287 Nobs, Nvars = 269, 6 **********************...
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This document was uploaded on 02/17/2014 for the course COURANT G63.2751.0 at NYU.

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