实验五

第1页共5页计量经济学实验报告单姓名：张灵艳班级：090511学号：090511131实验地点：教A112试验时间报告上交日期实验名称实验五多重共线性的识别与补救实验目的与要求1.目的：掌握多重共线性的识别方法2.能针对具体问题提出解决多重共线性问题的措施要求：根据以上问题涉及试验步骤并写出实验报告。实验内容下表是某地区1995-2004年食品需求量Y，可支配收入X1,食品类价格指数X2，物价总指数X3和流动资产拥有量X4的数据资料。根据理论分析，食品需求量受四个因素的影响，建立回归方程：iiiiixxxx443322110iy食品需求函数有关统计资料（图略）针对该问题，检验模型是否存在多重共线性。若存在，给出消除多重共线性的方法并重新对模型进行估计。实验步骤一．建立模型：iiiiixxxx443322110iy二．用OLS估计法估计模型中的未知参数：在Quick菜单中选EstimateEquation项，在OLS对话框中键入yCx1x2x3x4,用鼠标点击OK，既得估计结果.三．检验：在quick菜单中groupstatistics选项中的correlation命令。在出现对话框时直接输入x1x2x3x4变量名即可出现结果。四.修正：(1).运用OLS发逐一求Y对各解释变量的回归。结合经济意义和统计检验选出拟合效最果好的一元线性回归方程。(2).逐步回归：将其余变量逐一带入拟合效最果好的一元线性回归第2页共5页方程进行回归检验。实验结果与分析OLS回归结果：DependentVariable:YMethod:LeastSquaresDate:11/08/11Time:10:15Sample:19952004Includedobservations:10VariableCoefficientStd.Errort-StatisticProb.C-135.335275.13155-1.8013100.1315X10.0969540.0264883.6602780.0146X2-1.9913430.901601-2.2086750.0782X33.4014051.4974882.2714070.0723X40.0150810.0493930.3053300.7724R-squared0.998009Meandependentvar140.0000AdjustedR-squared0.996416S.D.dependentvar43.01163S.E.ofregression2.575114Akaikeinfocriterion5.036517Sumsquaredresid33.15605Schwarzcriterion5.187810Loglikelihood-20.18259F-statistic626.4634Durbin-Watsonstat3.382618Prob(F-statistic)0.000001分析：F=626.4634F0.05(4,5)=5.19，表明模型从整体上看食品需求量与解释变量之间线性关系显著。检验：x1x2x3x4的关系如下：由表可以看出，解释变量之间存在高度线性相关，需要进一步分析和修正。运用OLS发逐一求Y对各解释变量的回归，其各回归结果如下：Y与X1：DependentVariable:YMethod:LeastSquaresDate:11/08/11Time:10:26Sample:19952004Includedobservations:10VariableCoefficientStd.Errort-StatisticProb.C-12.455543.762734-3.3102380.0107X10.1178450.00281041.937010.0000R-squared0.995472Meandependentvar140.0000AdjustedR-squared0.994906S.D.dependentvar43.01163S.E.ofregression3.069899Akaikeinfocriterion5.258023Sumsquaredresid75.39426Schwarzcriterion5.318540Loglikelihood-24.29012F-statistic1758.713Durbin-Watsonstat2.627059Prob(F-statistic)0.000000第3页共5页Y与X2：DependentVariable:YMethod:LeastSquaresDate:11/08/11Time:10:27Sample:19952004Includedobservations:10VariableCoefficientStd.Errort-StatisticProb.C-385.190442.01379-9.1681900.0000X25.1641140.41193412.536280.0000R-squared0.951562Meandependentvar140.0000AdjustedR-squared0.945507S.D.dependentvar43.01163S.E.ofregression10.04054Akaikeinfocriterion7.627994Sumsquaredresid806.4989Schwarzcriterion7.688511Loglikelihood-36.13997F-statistic157.1583Durbin-Watsonstat2.401329Prob(F-statistic)0.000002Y与X3：DependentVariable:YMethod:LeastSquaresDate:11/08/11Time:10:27Sample:19952004Includedobservations:10VariableCoefficientStd.Errort-StatisticProb.C-536.508136.32179-14.770970.0000X36.6324320.35546418.658500.0000R-squared0.977537Meandependentvar140.0000AdjustedR-squared0.974729S.D.dependentvar43.01163S.E.ofregression6.837496Akaikeinfocriterion6.859577Sumsquaredresid374.0108Schwarzcriterion6.920094Loglikelihood-32.29788F-statistic348.1394Durbin-Watsonstat2.172010Prob(F-statistic)0.000000Y与X4：DependentVariable:YMethod:LeastSquaresDate:11/08/11Time:10:28Sample:19952004Includedobservations:10VariableCoefficientStd.Errort-StatisticProb.C21.181678.1916582.5857610.0323X40.3268730.02135115.309560.0000R-squared0.966994Meandependentvar140.0000AdjustedR-squared0.962869S.D.dependentvar43.01163S.E.ofregression8.288125Akaikeinfocriterion7.244381Sumsquaredresid549.5442Schwarzcriterion7.304898Loglikelihood-34.22191F-statistic234.3827Durbin-Watsonstat0.468380Prob(F-statistic)0.000000第4页共5页对比可以看出，拟合效最果好的一元线性回归方程是Y与X1的方程，因为其R^2和F统计量最大，即：Y=-12.45554+0.117845X1(-3.310238)(41.93701)R^2=0.995472SE=3.069899F=1758.713将X2带入模型进行回归，结果为：DependentVariable:YMethod:LeastSquaresDate:11/08/11Time:10:36Sample:19952004Includedobservations:10VariableCoefficientStd.Errort-StatisticProb.C14.0470849.255430.2851880.7838X10.1257420.0149238.4259430.0001X2-0.3610550.668873-0.5397960.6061R-squared0.995653Meandependentvar140.0000AdjustedR-squared0.994411S.D.dependentvar43.01163S.E.ofregression3.215617Akaikeinfocriterion5.417240Sumsquaredresid72.38134Schwarzcriterion5.508016Loglikelihood-24.08620F-statistic801.6108Durbin-Watsonstat2.533515Prob(F-statistic)0.000000由以上可以看出R^2的值变大，拟合优度变好，符号正确，因此保留X2.Y=14.04708+0.125742X1+-0.361055X2(0.285188)(8.425943)(-0.539796)R^2=0.995653SE=3.215617F=801.6108继续引入X3，得一下回归结果DependentVariable:YMethod:LeastSquaresDate:11/08/11Time:10:39Sample:19952004Includedobservations:10VariableCoefficientStd.Errort-StatisticProb.C-127.592665.15987-1.9581470.0979X10.1036060.0138817.4639720.0003X2-1.8817850.762063-2.4693290.0485X33.1856371.2164102.6188840.0396R-squared0.997972Meandependentvar140.0000AdjustedR-squared0.996957S.D.dependentvar43.01163S.E.ofregression2.372560Akaikeinfocriterion4.854991Sumsquaredresid33.77426Schwarzcriterion4.976025Loglikelihood-20.27495F-statistic983.9580第5页共5页Durbin-Watsonstat3.524120Prob(F-statistic)0.000000得模型：Y=-127.5926+0.103606X1-1.881785X2+3.185637X3(-1.958147)(7.463972)(-2.469329)(2.618884)R^2=0.997972SE=2.372560F=983.9580由以上可以看出R^2的值变大，拟合优度变好，符号正确，因此保留X3.继续引入X4，得一下回归结果:DependentVariable:YMethod:LeastSquaresDate:11/08/11Time:10:40Sample:19952004Includedobservations:10Var