计量经济学--异方差的检验及修正

经济计量分析实验报告一、实验项目异方差的检验及修正二、实验日期2015.12.06三、实验目的对于国内旅游总花费的有关影响因素建立多元线性回归模型，对变量进行多重共线性的检验及修正后，进行异方差的检验和补救。四、实验内容建立模型，对模型进行参数估计，对样本回归函数进行统计检验，以判定估计的可靠程度，包括拟合优度检验、方程总体线性的显著性检验、变量的显著性检验，以及参数的置信区间估计。检验变量是否具有多重共线性并修正。检验是否存在异方差并补救。五、实验步骤1、建立模型。以国内旅游总花费Y作为被解释变量，以年底总人口表示人口增长水平，以旅行社数量表示旅行社的发展情况，以城市公共交通运营数表示城市公共交通运行状况，以城乡居民储蓄存款年末增加值表示城乡居民储蓄存款增长水平。2、模型设定为:ttttt443322110t其中：t—国内旅游总花费（亿元）t1—年底总人口（万人）t2—旅行社数量（个）t3—城市公共交通运营数（辆）t4—城乡居民储蓄存款年末增加值（亿元）3、对模型进行多重共线性检验。4、检验异方差是否存在。六、实验结果（一）、消除多重共线性之后的模型Sample(adjusted):19942008Includedobservations:15afteradjustmentsVariableCoefficientStd.Errort-StatisticProb.C81113.9926581.733.0514940.0122PEOPLE-0.7200760.230790-3.1200460.0109AGENT0.1519240.1082231.4038050.1907TRANSIT0.0533290.0138343.8549880.0032SAVE0.0007790.0205020.0380200.9704R-squared0.969693Meandependentvar3875.880AdjustedR-squared0.957571S.D.dependentvar2295.093S.E.ofregression472.7528Akaikeinfocriterion15.41622Sumsquaredresid2234952.Schwarzcriterion15.65224Loglikelihood-110.6217Hannan-Quinncriter.15.41371F-statistic79.98987Durbin-Watsonstat2.028677Prob(F-statistic)0.000000多元线性回归模型估计结果如下：4321000779.0053329.0151924.0720076.0-99.81113ˆiSE=(26581.73)(0.230790)(0.108223)(0.013834)(0.020502)t=(3.051494)(-3.120046)(1.403805)(3.854988)(0.038020)R2=0.969693R2=0.957571F=79.98987(1)拟合优度检验：可决系数R2=0.969693较高，修正的可决系数R2=0.957571也较高，表明模型拟合较好。(2)方程总体线性的显著性检验(F)：针对043210：，取=0.05，查自由度为k=4和n-k-1=10的临界值F(4,10)。由于F=79.98987F(4,10)=3.48，p值0.05，应拒绝0，说明回归方程整体显著。(3)变量的显著性检验(t检验)：给定=0.05，自由度为n-k-1=10，临界值为t025.0(10)=2.228。虽然1，3的参数对应的t统计量均大于2.228,且p值小于0.05。但2，4的参数对应的t统计量均小于2.228,且p值大于0.05，说明参数估计值不能通过显著性检验。(4)1ˆ=—0.720076所估计的参数的符号与经济理论分析不一致。（5）多重共线性的检验及修正经检验变量具有多重共线性，所以对模型进行修正。Sample(adjusted):19942008Includedobservations:15afteradjustmentsVariableCoefficientStd.Errort-StatisticProb.C-301.8388394.3549-0.7653990.4577AGENT0.3829630.03223111.881750.0000R-squared0.915681Meandependentvar3875.880AdjustedR-squared0.909195S.D.dependentvar2295.093S.E.ofregression691.6017Akaikeinfocriterion16.03946Sumsquaredresid6218068.Schwarzcriterion16.13387Loglikelihood-118.2960Hannan-Quinncriter.16.03846F-statistic141.1760Durbin-Watsonstat0.641734Prob(F-statistic)0.000000修正后的回归模型为2382963.08388.301ˆXY，说明旅行社数量每增加1个，平均说来国内旅游总花费将增加3829.63万元。（二）异方差的检验①图示法（1）作散点图1.Y-X02,0004,0006,0008,00010,00012,00014,00004,0008,00012,00016,00020,00024,000AGENTCOST从图中看不出明显信息。2.2ie-X0400,000800,0001,200,0001,600,0002,000,00004,0008,00012,00016,00020,00024,000AGENTE2残差平方和对解释变量agent的散点图主要分布在图形中的下三角部分，大致看出残差平方和随agent的变动呈增大的趋势。2e并不近似于某一常数，初步判断，有可能存在异方差。②解析法1.ARCH检验HeteroskedasticityTest:ARCHF-statistic0.416944Prob.F(1,12)0.5306Obs*R-squared0.470101Prob.Chi-Square(1)0.4929TestEquation:DependentVariable:RESID^2Method:LeastSquaresDate:12/06/15Time:18:59Sample(adjusted):1326Includedobservations:14afteradjustmentsVariableCoefficientStd.Errort-StatisticProb.C367799.2205940.81.7859460.0994RESID^2(-1)0.2336070.3617820.6457120.5306R-squared0.033579Meandependentvar441155.8AdjustedR-squared-0.046956S.D.dependentvar628131.2S.E.ofregression642709.5Akaikeinfocriterion29.71634Sumsquaredresid4.96E+12Schwarzcriterion29.80763Loglikelihood-206.0144Hannan-Quinncriter.29.70789F-statistic0.416944Durbin-Watsonstat1.660130Prob(F-statistic)0.5306202(1)=3.84(n-p)2Rp值0.05接受原假设，即不存在异方差。2.White检验HeteroskedasticityTest:WhiteF-statistic3.066639Prob.F(2,12)0.0840Obs*R-squared5.073500Prob.Chi-Square(2)0.0791ScaledexplainedSS3.901442Prob.Chi-Square(2)0.1422TestEquation:DependentVariable:RESID^2Method:LeastSquaresDate:12/06/15Time:19:01Sample:1226Includedobservations:15VariableCoefficientStd.Errort-StatisticProb.C159495.6683418.60.2333790.8194AGENT^20.0039100.0059660.6554590.5245AGENT-30.28092140.0834-0.2161640.8325R-squared0.338233Meandependentvar414537.9AdjustedR-squared0.227939S.D.dependentvar613998.8S.E.ofregression539502.4Akaikeinfocriterion29.41154Sumsquaredresid3.49E+12Schwarzcriterion29.55315Loglikelihood-217.5865Hannan-Quinncriter.29.41003F-statistic3.066639Durbin-Watsonstat1.930390Prob(F-statistic)0.083990p值0.05）（22=5.992nR，接受原假设，表示不存在异方差。3.G-D检验DependentVariable:COSTMethod:LeastSquaresDate:12/06/15Time:18:01Sample:1217Includedobservations:6VariableCoefficientStd.Errort-StatisticProb.C-464.5026552.0770-0.8413730.4475AGENT0.4565810.1039264.3933230.0118R-squared0.828336Meandependentvar1895.567AdjustedR-squared0.785420S.D.dependentvar673.2631S.E.ofregression311.8745Akaikeinfocriterion14.58428Sumsquaredresid389062.8Schwarzcriterion14.51487Loglikelihood-41.75284Hannan-Quinncriter.14.30641F-statistic19.30128Durbin-Watsonstat3.104838Prob(F-statistic)0.011752DependentVariable:COSTMethod:LeastSquaresDate:12/06/15Time:18:03Sample:2126Includedobservations:6VariableCoefficientStd.Errort-StatisticProb.C-6878.2701141.633-6.0249400.0038AGENT0.7628110.06682911.414310.0003R-squared0.970213Meandependentvar6031.417AdjustedR-squared0.962766S.D.dependentvar1972.540S.E.ofregression380.6227Akaikeinfocriterion14.98270Sumsquaredresid579494.4Schwarzcriterion14.91328Loglikelihood-42.94809Hann