多重共线性问题的检验和处理

山西大学实验报告实验报告题目：多重共线性问题的检验和处理学院：专业：课程名称：计量经济学学号：学生姓名：教师名称：崔海燕上课时间：一、实验目的：熟悉和掌握Eviews在多重共线性模型中的应用，掌握多重共线性问题的检验和处理。二、实验原理：1、综合统计检验法；2、相关系数矩阵判断；3、逐步回归法；三、实验步骤：（一）新建工作文件并保存打开Eviews软件，在主菜单栏点击File\new\workfile，输入startdate1978和enddate2006并点击确认，点击save键，输入文件名进行保存。（二）输入并编辑数据在主菜单栏点击Quick键，选择empty\group新建空数据栏，根据理论和经验分析，影响粮食生产（Y）的主要因素有农业化肥施用量（X1）、粮食播种面积（X2）、成灾面积（X3）、农业机械总动力（X4）和农业劳动力（X5），其中成灾面积的符号为负，其余均应为正。下表给出了1983——2000中国粮食生产的相关数据。点击name键进行命名，选择默认名称Group01,保存文件。YX1X2X3X4X5198338728166011404716209180223115119844073117401128841526419497308681985379111776108845227052091331130198639151193111093323656229503125419874020819991112682039324836316631988394082142110123239452657532249198940755235711220524449280673322519904462425901134661781928708389141991435292806112314278142938939098199244264293011056025895303083866919934564931521105092313331817376801994445103318109544313833380236628199546662359411006022267361183553019965045438281125482123338547348201997494173981112912303094201634840199851230408411378725181452083517719995083941241131612673148996357682000462184146108463343745257436043200145264425410608031793551723651320024570643391038912731957930368702003430704412994103251660387365462004469474637101606162976402835269200548402476610427819966683983397020064980449281049582463272522325612007501605108105638250647659031444（三）用普通最小二乘法估计模型参数用最小二乘法估计模型参数。分别对y、x1、x2、x3、x4、x5取对数，克服序列相关性以及成为线性关系，建立y对所有解释变量的回归模型：lny=β0+β1*lnx1+β2*lnx2+β3*lnx3+β4*lnx4+β5*lnx5+υ在主菜单栏点击Quick\EstimateEquation，出现对话框，输入“lnyClnx1lnx1lnx2lnx3lnx4lnx5”，默认使用最小二乘法进行回归分析,得到多元线性方程模型参数:DependentVariable:LNYMethod:LeastSquaresDate:12/19/13Time:08:49Sample:19832007Includedobservations:25VariableCoefficientStd.Errort-StatisticProb.C-4.1697571.923113-2.1682330.0430LNX10.3812470.0502277.5904970.0000LNX21.2222100.1351329.0445850.0000LNX3-0.0811010.015299-5.3010320.0000LNX4-0.0473020.044750-1.0570210.3038LNX5-0.1014270.057713-1.7574470.0949R-squared0.981607Meandependentvar10.70905AdjustedR-squared0.976767S.D.dependentvar0.093396S.E.ofregression0.014236Akaikeinfocriterion-5.460540Sumsquaredresid0.003851Schwarzcriterion-5.168010Loglikelihood74.25675F-statistic202.8006Durbin-Watsonstat1.792233Prob(F-statistic)0.000000Lny^=-4.16+0.382lnx1+1.222lnx2-0.081lnx3-0.048lnx4-0.102lnx5从计算结果看，R2=0.981607，较大并接近于1，F=202.8006F0.05(5,19)=2.74，故认为粮食生产量与上述所有解释变量间总体线性相关显著。一般的，t的绝对值大于2，则解释变量对被解释变量关系显著，但是，X4、X5前参数未通过t检验，而且符号的经济意义也不合理，故认为解释变量间存在多重共线性。为了进一步检验多重共线性，进行下面操作。（四）多重共线性检验计算解释变量间的两两相关系数，得到简单相关系数矩阵如下：Lnx1Lnx2Lnx3Lnx4Lnx5Lnx11-0.5687441337920.4517002443380.9643565841160.440575584742lnx2-0.5687441337921-0.214097210616-0.69762500446-0.0734480641922Lnx30.451700244338-0.21409721061610.3987801074340.411377048274Lnx40.964356584116-0.697625004460.39878010743410.279917581652Lnx50.440575584742-0.07344806419220.4113770482740.2799175816521从相关分析结果来看，部分解释变量间确实存在相关，尤其X1与X4之间相关性达0.964356584116，高度相关。为了处理多重共线性，正确选择解释变量，进行逐步回归，首先选择最优的基本方程。（五）多重共线性检验1、找出最简单的回归形式，分别做粮食生产量对各个解释变量的回归，得A．Y对X1回归结果：DependentVariable:LNYMethod:LeastSquaresDate:12/19/13Time:09:15Sample:19832007Includedobservations:25VariableCoefficientStd.Errort-StatisticProb.C8.9020080.20603443.206570.0000LNX10.2240050.0255158.7792930.0000R-squared0.770175Meandependentvar10.70905AdjustedR-squared0.760182S.D.dependentvar0.093396S.E.ofregression0.045737Akaikeinfocriterion-3.255189Sumsquaredresid0.048114Schwarzcriterion-3.157679Loglikelihood42.68986F-statistic77.07599Durbin-Watsonstat0.939435Prob(F-statistic)0.000000B．Y对X2回归结果：DependentVariable:LNYMethod:LeastSquaresDate:12/19/13Time:09:15Sample:19832007Includedobservations:25VariableCoefficientStd.Errort-StatisticProb.C15.157485.9129712.5634290.0174LNX2-0.3834340.509669-0.7523210.4595R-squared0.024017Meandependentvar10.70905AdjustedR-squared-0.018417S.D.dependentvar0.093396S.E.ofregression0.094252Akaikeinfocriterion-1.809063Sumsquaredresid0.204321Schwarzcriterion-1.711553Loglikelihood24.61329F-statistic0.565986Durbin-Watsonstat0.335219Prob(F-statistic)0.459489c.Y对X3回归结果：DependentVariable:LNYMethod:LeastSquaresDate:12/19/13Time:09:16Sample:19832007Includedobservations:25VariableCoefficientStd.Errort-StatisticProb.C9.6197220.85974411.189050.0000LNX30.1080670.0852711.2673350.2177R-squared0.065274Meandependentvar10.70905AdjustedR-squared0.024634S.D.dependentvar0.093396S.E.ofregression0.092239Akaikeinfocriterion-1.852255Sumsquaredresid0.195684Schwarzcriterion-1.754745Loglikelihood25.15319F-statistic1.606139Durbin-Watsonstat0.597749Prob(F-statistic)0.217717d.Y对X4回归结果：DependentVariable:LNYMethod:LeastSquaresDate:12/19/13Time:09:17Sample:19832007Includedobservations:25VariableCoefficientStd.Errort-StatisticProb.C8.9490900.29825530.004790.0000LNX40.1669760.0282745.9056700.0000R-squared0.602605Meandependentvar10.70905AdjustedR-squared0.585327S.D.dependentvar0.093396S.E.ofregression0.060143Akaikeinfocriterion-2.707578Sumsquaredresid0.083194Schwarzcriterion-2.610068Loglikelihood35.84472F-statistic34.87693Durbin-Watsonstat0.625528Prob(F-statistic)0.000005e.Y对X5回归结果：DependentVariable:LNYMethod:LeastSquaresDate:12/19/13Ti