LinearRegression4

0453 durbin watson 21098 nobs nvars 88 4

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Unformatted text preview: lotsize 0.002068 3.220096 0.001823 sqrft 0.122778 9.275093 0.000000 bdrms 13.852522 1.537436 0.127945 White Heteroscedastic Consistent Estimates Dependent Variable = price R-squared = 0.6724 Rbar-squared = 0.6607 sigma^2 = 3580.0453 Durbin-Watson = 2.1098 Nobs, Nvars = 88, 4 *************************************************************** Variable Coefficient t-statistic t-probability intercept -21.770309 -0.599992 0.550127 lotsize 0.002068 1.691165 0.094513 sqrft 0.122778 7.089710 0.000000 bdrms 13.852522 1.672265 0.098193 VER. 10/23/2012. © P. KOLM 43 Remarks: • The robust standard error on lotsize is almost twice as large as the usual standard error, making lotsize much less significant (the t statistic falls from about 3.22 to 1.69) • The t statistic on sqrft also falls, but it is still very significant • The variable bdrms actually becomes somewhat more significant, but it is still barely significant • The most important change is in the significance of lotsize. VER. 10/23/2012. © P. KOLM 44 (ii) Repeat part (i) for log(price) = −1.297 + 0.1680 log(lotsize ) + 0.7002 log(sqrft ) + 0.0370bdrms Solution: For the log-log model, log(price) = −1.297 + 0.1680 log(lotsize ) + 0.7002 log(sqrft ) + 0.0370bdrms (0.65) (0.038) (0.093) (0.028) [0.76] [0.041] [0.101] [0.030] n = 88, R2 = 0.643. VER. 10/23/2012. © P. KOLM 45 Ordinary Least-squares Estimates Dependent Variable = log(price) R-squared = 0.6430 Rbar-squared = 0.6302 sigma^2 = 0.0341 Durbin-Watson = 2.0890 Nobs, Nvars = 88, 4 *************************************************************** Variable Coefficient t-statistic t-probability intercept -1.297041 -1.991514 0.049674 llotsize 0.167967 4.387717 0.000033 lsqrft 0.700232 7.540304 0.000000 bdrms 0.036958 1.342411 0.183080 White Heteroscedastic Consistent Estimates Dependent Variable = log(price) R-squared = 0.6430 Rbar-squared = 0.6302 sigma^2 = 0.0341 Durbin-Watson = 2.0890 Nobs, Nvars = 88, 4 *************************************************************** Variable Coefficient t-statistic t-probability intercept -1.297041 -1.699141 0.092993 llotsize 0.167967 4.145292 0.000081 lsqrft 0.700232 6.902811 0.000000 bdrms 0.036958 1.236165 0.219843 VER. 10/23/2012. © P. KOLM 46 Remarks: • The heteroscedasticity-robust standard error is slightly greater than the corresponding usual standard error, but the differences are relatively small. In particular, log(lotsize) and log(sqrft) still have very large t statistics, and the t statistic on bdrms is not significant at the 5% level against a one-sided alternative using either standard error VER. 10/23/2012. © P. KOLM 47 (iii) What does this example suggest about heteroscedasticity and the transformation used for the dependent variable? Solution: Using the logarithmic transformation of the dependent variable often mitigates, if not entirely eliminates, heteroscedasticity. This is certainly the case here, as no important conclusions in the model for log(price) depend on the choice of standard error. (We have also transformed two of the independent variables to make the model of the constant elasticity variety in lotsize and sqrft.) VER. 10/23/2012. © P. KOLM 48 Remarks • Estimates of...
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