计量经济学庞皓第二版第五章答案

5.2(1)对原模型OLS回归分析结果：DependentVariable:YMethod:LeastSquaresDate:04/01/09Time:15:44Sample:160Includedobservations:60VariableCoefficientStd.Errort-StatisticProb.C9.3475223.6384372.5691040.0128X0.6370690.01990332.008810.0000R-squared0.946423Meandependentvar119.6667AdjustedR-squared0.945500S.D.dependentvar38.68984S.E.ofregression9.032255Akaikeinfocriterion7.272246Sumsquaredresid4731.735Schwarzcriterion7.342058Loglikelihood-216.1674F-statistic1024.564Durbin-Watsonstat1.790431Prob(F-statistic)0.000000(2)White检验结果：WhiteHeteroskedasticityTest:F-statistic6.301373Probability0.003370Obs*R-squared10.86401Probability0.004374TestEquation:DependentVariable:RESID^2Method:LeastSquaresDate:04/01/09Time:15:45Sample:160Includedobservations:60VariableCoefficientStd.Errort-StatisticProb.C-10.03614131.1424-0.0765290.9393X0.1659771.6198560.1024640.9187X^20.0018000.0045870.3924690.6962R-squared0.181067Meandependentvar78.86225AdjustedR-squared0.152332S.D.dependentvar111.1375S.E.ofregression102.3231Akaikeinfocriterion12.14285Sumsquaredresid596790.5Schwarzcriterion12.24757Loglikelihood-361.2856F-statistic6.301373Durbin-Watsonstat1.442328Prob(F-statistic)0.003370nR2=10.86401,查表得2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：DependentVariable:YMethod:LeastSquaresDate:04/01/09Time:16:16Sample:122Includedobservations:22VariableCoefficientStd.Errort-StatisticProb.C12.536957.0695781.7733650.0914X0.6059110.0639109.4807300.0000R-squared0.817990Meandependentvar78.63636AdjustedR-squared0.808890S.D.dependentvar12.56050S.E.ofregression5.490969Akaikeinfocriterion6.330594Sumsquaredresid603.0148Schwarzcriterion6.429780Loglikelihood-67.63654F-statistic89.88424Durbin-Watsonstat1.136382Prob(F-statistic)0.000000DependentVariable:YMethod:LeastSquaresDate:04/01/09Time:16:17Sample:3960Includedobservations:22VariableCoefficientStd.Errort-StatisticProb.C-39.5439327.08272-1.4601160.1598X0.8412150.1132667.4269270.0000R-squared0.733898Meandependentvar160.8182AdjustedR-squared0.720593S.D.dependentvar21.13367S.E.ofregression11.17103Akaikeinfocriterion7.751033Sumsquaredresid2495.840Schwarzcriterion7.850219Loglikelihood-83.26137F-statistic55.15924Durbin-Watsonstat0.610587Prob(F-statistic)0.000000F=2122ee=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/XDependentVariable:YMethod:LeastSquaresDate:04/01/09Time:15:53Sample:160Includedobservations:60Weightingseries:W1VariableCoefficientStd.Errort-StatisticProb.C10.370512.6297163.9435870.0002X0.6309500.01853234.046670.0000WeightedStatisticsR-squared0.211441Meandependentvar106.2101AdjustedR-squared0.197845S.D.dependentvar8.685376S.E.ofregression7.778892Akaikeinfocriterion6.973470Sumsquaredresid3509.647Schwarzcriterion7.043281Loglikelihood-207.2041F-statistic15.55188Durbin-Watsonstat1.969805Prob(F-statistic)0.000219UnweightedStatisticsR-squared0.946335Meandependentvar119.6667AdjustedR-squared0.945410S.D.dependentvar38.68984S.E.ofregression9.039689Sumsquaredresid4739.526Durbin-Watsonstat1.796748WhiteHeteroskedasticityTest:F-statistic3.138491Probability0.050925Obs*R-squared5.951910Probability0.050999TestEquation:DependentVariable:STD_RESID^2Method:LeastSquaresDate:04/01/09Time:15:54Sample:160Includedobservations:60VariableCoefficientStd.Errort-StatisticProb.C238.836373.631913.2436520.0020X-2.1395840.909493-2.3525020.0221X^20.0056900.0025752.2096420.0312R-squared0.099198Meandependentvar58.49412AdjustedR-squared0.067591S.D.dependentvar59.49678S.E.ofregression57.45087Akaikeinfocriterion10.98844Sumsquaredresid188134.3Schwarzcriterion11.09316Loglikelihood-326.6533F-statistic3.138491Durbin-Watsonstat1.606243Prob(F-statistic)0.050925虽然White检验结果nR2=5.9519120.05(2)=5.99147，显示已消除异方差，但R2=0.2114,拟合优度太低，不是理想的结果。W2=1/X2DependentVariable:YMethod:LeastSquaresDate:04/01/09Time:15:55Sample:160Includedobservations:60Weightingseries:W2VariableCoefficientStd.Errort-StatisticProb.C10.123272.7557753.6734750.0005X0.6330290.02459025.743740.0000WeightedStatisticsR-squared0.961581Meandependentvar94.01206AdjustedR-squared0.960918S.D.dependentvar41.02965S.E.ofregression8.111184Akaikeinfocriterion7.057130Sumsquaredresid3815.896Schwarzcriterion7.126941Loglikelihood-209.7139F-statistic1451.660Durbin-Watsonstat2.091305Prob(F-statistic)0.000000UnweightedStatisticsR-squared0.946381Meandependentvar119.6667AdjustedR-squared0.945457S.D.dependentvar38.68984S.E.ofregression9.035795Sumsquaredresid4735.444Durbin-Watsonstat1.795043WhiteHeteroskedasticityTest:F-statistic39.31455Probability0.000000Obs*R-squared34.78417Probability0.000000TestEquation:DependentVariable:STD_RESID^2Method:LeastSquaresDate:04/01/09Time:15:56Sample:160Includedobservations:60VariableCoefficientStd.Errort-StatisticProb.C735.745289.808828.1923490.0000X-7.3807901.109309-6.6535050.0000X^20.0181320.0031415.7728210.0000R-squared0.579736Meandependentvar63.59827AdjustedR-squared0.564990S.D.dependentvar106.2429S.E.ofregression70.07281Akaikeinfocriterion11.38565Sumsquaredresid279881.3Schwarzcriterion11.49037Loglikelihood-338.