计量经济学庞皓第二版第五章答案.doc

5.2 (1) 对原模型OLS回归分析结果：Dependent Variable: YMethod: Least SquaresDate: 04/01/09 Time: 15:44Sample: 1 60Included observations: 60VariableCoefficientStd. Errort-StatisticProb. C9.3475223.6384372.5691040.0128X0.6370690.01990332.008810.0000R-squared0.946423 Mean dependent var119.6667Adjusted R-squared0.945500 S.D. dependent var38.68984S.E. of regression9.032255 Akaike info criterion7.272246Sum squared resid4731.735 Schwarz criterion7.342058Log likelihood-216.1674 F-statistic1024.564Durbin-Watson stat1.790431 Prob(F-statistic)0.000000(2) White检验结果：White Heteroskedasticity Test:F-statistic6.301373 Probability0.003370Obs*R-squared10.86401 Probability0.004374Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 04/01/09 Time: 15:45Sample: 1 60Included observations: 60VariableCoefficientStd. Errort-StatisticProb. C-10.03614131.1424-0.0765290.9393X0.1659771.6198560.1024640.9187X20.0018000.0045870.3924690.6962R-squared0.181067 Mean dependent var78.86225Adjusted R-squared0.152332 S.D. dependent var111.1375S.E. of regression102.3231 Akaike info criterion12.14285Sum squared resid596790.5 Schwarz criterion12.24757Log likelihood-361.2856 F-statistic6.301373Durbin-Watson stat1.442328 Prob(F-statistic)0.003370nR2=10.86401, 查表得0.05(2)=5.99147，nR25.99147,所以拒绝原假设，表明模型中随机误差项存在异方差。Goldfeld-Quandt检验：Dependent Variable: YMethod: Least SquaresDate: 04/01/09 Time: 16:16Sample: 1 22Included observations: 22VariableCoefficientStd. Errort-StatisticProb. C12.536957.0695781.7733650.0914X0.6059110.0639109.4807300.0000R-squared0.817990 Mean dependent var78.63636Adjusted R-squared0.808890 S.D. dependent var12.56050S.E. of regression5.490969 Akaike info criterion6.330594Sum squared resid603.0148 Schwarz criterion6.429780Log likelihood-67.63654 F-statistic89.88424Durbin-Watson stat1.136382 Prob(F-statistic)0.000000Dependent Variable: YMethod: Least SquaresDate: 04/01/09 Time: 16:17Sample: 39 60Included observations: 22VariableCoefficientStd. Errort-StatisticProb. C-39.5439327.08272-1.4601160.1598X0.8412150.1132667.4269270.0000R-squared0.733898 Mean dependent var160.8182Adjusted R-squared0.720593 S.D. dependent var21.13367S.E. of regression11.17103 Akaike info criterion7.751033Sum squared resid2495.840 Schwarz criterion7.850219Log likelihood-83.26137 F-statistic55.15924Durbin-Watson stat0.610587 Prob(F-statistic)0.000000F=2495.840/603.0148=4.139, 查得F0.05(20，20)=2.12，4.1392.12，则拒绝原假设，表明模型中随机误差项存在异方差。(3) 加权最小二乘法修正异方差W1=1/XDependent Variable: YMethod: Least SquaresDate: 04/01/09 Time: 15:53Sample: 1 60Included observations: 60Weighting series: W1VariableCoefficientStd. Errort-StatisticProb. C10.370512.6297163.9435870.0002X0.6309500.01853234.046670.0000Weighted StatisticsR-squared0.211441 Mean dependent var106.2101Adjusted R-squared0.197845 S.D. dependent var8.685376S.E. of regression7.778892 Akaike info criterion6.973470Sum squared resid3509.647 Schwarz criterion7.043281Log likelihood-207.2041 F-statistic15.55188Durbin-Watson stat1.969805 Prob(F-statistic)0.000219Unweighted StatisticsR-squared0.946335 Mean dependent var119.6667Adjusted R-squared0.945410 S.D. dependent var38.68984S.E. of regression9.039689 Sum squared resid4739.526Durbin-Watson stat1.796748White Heteroskedasticity Test:F-statistic3.138491 Probability0.050925Obs*R-squared5.951910 Probability0.050999Test Equation:Dependent Variable: STD_RESID2Method: Least SquaresDate: 04/01/09 Time: 15:54Sample: 1 60Included observations: 60VariableCoefficientStd. Errort-StatisticProb. C238.836373.631913.2436520.0020X-2.1395840.909493-2.3525020.0221X20.0056900.0025752.2096420.0312R-squared0.099198 Mean dependent var58.49412Adjusted R-squared0.067591 S.D. dependent var59.49678S.E. of regression57.45087 Akaike info criterion10.98844Sum squared resid188134.3 Schwarz criterion11.09316Log likelihood-326.6533 F-statistic3.138491Durbin-Watson stat1.606243 Prob(F-statistic)0.050925虽然White检验结果nR2=5.951910.05(2)=5.99147，显示异方差仍存在，不是理想的结果。W3=1/Dependent Variable: YMethod: Least SquaresDate: 04/01/09 Time: 15:57Sample: 1 60Included observations: 60Weighting series: W3VariableCoefficientStd. Errort-StatisticProb. C10.109082.9807893.3914090.0013X0.6326710.01837934.423410.0000Weighted StatisticsR-squared0.801827 Mean dependent var112.9123Adjusted R-squared0.798411 S.D. dependent var18.33568S.E. of regression8.232480 Akaike info criterion7.086817Sum squared resid3930.877 Schwarz criterion7.156628Log likelihood-210.6045 F-statistic234.6742Durbin-Watson stat1.874009 Prob(F-statistic)0.000000Unweighted StatisticsR-squared0.946378 Mean dependent var119.6667Adjusted R-squared0.945454 S.D. dependent var38.68984S.E. of regression9.036056 Sum squared resid4735.718Durbin-Watson stat1.795491White Heteroskedasticity Test:F-statistic2.192831 Probability0.120928Obs*R-squared4.286664 Probability0.117263Test Equation:Dependent Variable: STD_RESID2Method: Least SquaresDate: 04/01/09 Time: 15:57Sample: 1 60Included observations: 60VariableCoefficientStd. Errort-StatisticProb. C86.1243993.861130.9175720.3627X-0.6472301.159362-0.5582640.5789X20.0027370.0032830.8337790.4079R-squared0.071444 Mean dependent var65.51461Adjusted R-squared0.038864 S.D. dependent var74.70055S.E. of regression73.23460 Akaike info criterion11.47392Sum squared resid305708.5 Schwarz criterion11.57864Log likelihood-341.2176 F-statistic2.192831Durbin-Watson stat1.510631 Prob(F-statistic)0.120928R2=0.8018,拟合优度很高，且各t检验也通过, Whit e检验结果nR2=4.28670.05(2)=5.99147，显示存在异方差。ARCH检验结果：P=1ARCH Test:F-statistic6.172299 Probability0.019226Obs*R-squared5.418686 Probability0.019922ARCH检验结果(n-p)R2=5.41870.05(1)=3.841，显示存在异方差。P=2ARCH Test:F-statistic2.781654 Probability0.080405Obs*R-squared5.111503 Probability0.077634ARCH检验结果(n-p)R2=5.11150.05(2)=5.991，显示不存在异方差。P=3ARCH Test:F-statistic1.594897 Probability0.216709Obs*R-squared4.654257 Probability0.198937ARCH检验结果(n-p)R2=4.65430.05(3)=7.815，显示不存在异方差。(3) 加权最小二乘法修正异方差W1=1/XDependent Variable: YMethod: Least SquaresDate: 05/25/11 Time: 15:12Sample: 1901 1931Included observations: 31Weighting series: W1VariableCoefficientStd. Errort-StatisticProb. C-722.503772.36495-9.9841660.0000X0.0881390.00437220.158220.0000Weighted StatisticsR-squared0.774641 Mean dependent var894.6561Adjusted R-squared0.766870 S.D. dependent var399.3095S.E. of regression192.8008 Akaike info criterion13.42353Sum squared resid1077992. Schwarz criterion13.51605Log likelihood-206.0648 F-statistic99.68358Durbin-Watson stat0.994618 Prob(F-statistic)0.000000Unweighted StatisticsR-squared0.910496 Mean dependent var1250.323Adjusted R-squared0.907409 S.D. dependent var820.9407S.E. of regression249.8017 Sum squared resid1809626.Durbin-Watson stat0.882555White Heteroskedasticity Test:F-statistic1.002103 Probability0.379894Obs*R-squared2.070723 Probability0.355098虽然White检验结果nR2=2.07070.05(2)=5.99147，显示异方差仍存在，不是理想的结果。W3=1/Dependent Variable: YMethod: Least SquaresDate: 05/25/11 Time: 15:15Sample: 1901 1931Included observations: 31Weighting series: W3VariableCoefficientStd. Errort-Statistic