[Gretl-users] Re: FGLS/WLS estimation

Yes, lets use data7-24.gdt These are the results when we use "pisua" as weight, where "pisua" is equal to 1/sqft^2 Model 1: WLS, using observations 1-224 Dependent variable: salepric Variable used as weight: pisua coefficient std. error t-ratio p-value ---------------------------------------------------------- const −285.205 37.2121 −7.664 5.70e-013 *** sqft 0.215569 0.00959143 22.48 6.74e-059 *** age −0.549288 2.28001 −0.2409 0.8098 city 110.780 15.6896 7.061 2.14e-011 *** Statistics based on the weighted data: Sum squared resid 0.150742 S.E. of regression 0.026176 R-squared 0.798817 Adjusted R-squared 0.796073 F(3, 220) 291.1769 P-value(F) 2.64e-76 Log-likelihood 500.1866 Akaike criterion −992.3732 Schwarz criterion −978.7266 Hannan-Quinn −986.8648 Statistics based on the original data: Mean dependent var 642.9294 S.D. dependent var 371.3762 Sum squared resid 4735143 S.E. of regression 146.7085 And these are the results when I build the transformed variables (variable_n=variable*sqrt(pisua)) and apply OLS in the transformed model: Model 2: OLS, using observations 1-224 Dependent variable: salepric_n coefficient std. error t-ratio p-value ---------------------------------------------------------- const_n −285.205 37.2121 −7.664 5.70e-013 *** sqft_n 0.215569 0.00959143 22.48 6.74e-059 *** age_n −0.549288 2.28001 −0.2409 0.8098 city_n 110.780 15.6896 7.061 2.14e-011 *** Mean dependent var 0.153250 S.D. dependent var 0.034928 Sum squared resid 0.150742 S.E. of regression 0.026176 R-squared 0.445905 Adjusted R-squared 0.438349 F(3, 220) 59.01455 P-value(F) 4.97e-28 Log-likelihood 500.1866 Akaike criterion −992.3732 Schwarz criterion −978.7266 Hannan-Quinn −986.8648 AS can be seen, all the statistics depending on the TSS (R-squared, Adjusted R-squared, F value and its p-value…) are different (however, the sum of the squared residuals, the S.E. of the regression, etc. are the same)