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（XI、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GroupOl,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=Bo+Bi*lnx1+B2*1nx2+B3*1nx3+B4*lnx4+B5*1nx5+u在主菜单栏点击Quick'EstimateEquation,出现对话框，输入“InyCInx1Inx1Inx2Inx3Inx4Inx5”，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心-4.16+0.3821nx1+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=202.8006>F0.05（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：Lnx1Lnx2Lnx3Lnx4Lnx5Lnx11-0.5687441330.4517002440.9643565840.440575584792338116742lnx2-0.568744131-0.214097210-0.697625004-0.0734480643792616461922Lnx30.451700244-0.21409721010.3987801070.411377048338616434274Lnx40.964356584-0.6976250040.39878010710.27991758111646434652Lnx50.440575584-0.0734480640.4113770480.27991758117421922274652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aY对X1回归结果：DependentVariable:LNYMethod:LeastSquaresDate:12/19/13Time:09:15Sample:19832007Includedobservations:25VariableCoefficientStd.Error t-StatisticProb.C8.9020080.206034 43.206570.0000LNX10.2240050.025515 8.7792930.0000R-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:25Variable Coefficient Std.Errort-StatisticProb.

C15.157485.912971 2.5634290.0174LNX2-0.3834340.509669 -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)0.459489Y对X3回归结果：DependentVariable:LNYMethod:LeastSquaresDate:12/19/13Time:09:16Sample:19832007Includedobservations:25VariableCoefficientStd.Error t-StatisticProb.C9.6197220.859744 11.189050.0000LNX30.1080670.085271 1.2673350.2177R-squared0.065274Meandependentvar10.70905AdjustedR-squared0.024634S.D.dependentvar0.093396S.E.ofregression0.092239Akaikeinfocriterion-1.852255Sumsquaredresid0.195684Schwarzcriterion-1.754745Loglikelihood25.15319F-statistic1.606139Durbin-Watsonstat0.597749Prob(F-statistic)0.217717———Y对X4回归结果：DependentVariable:LNYMethod:LeastSquaresDate:12/19/13Time:09:17Sample:19832007Includedobservations:25VariableCoefficientStd.Error t-StatisticProb.C8.9490900.298255 30.004790.0000LNX40.1669760.028274 5.9056700.0000R-squared0.602605Meandependentvar10.70905AdjustedR-squared0.585327S.D.dependentvar0.093396S.E.ofregression0.060143Akaikeinfocriterion-2.707578Sumsquaredresid0.083194Schwarzcriterion-2.610068Loglikelihood35.84472F-statistic34.87693Durbin-Watsonstat0.625528Prob(F-statistic)0.000005===Y对X5回归结果:DependentVariable:LNYMethod:LeastSquaresDate:12/19/13Time:09:18Sample:19832007Ineludedobservations:25VariableCoeffieientStd.Error t-StatistieProb.C5.5937852.453373 2.2800390.0322LNX50.4893980.234718 2.0850480.0484R-squared0.158970Meandependentvar10.70905AdjustedR-squared0.122404S.D.dependentvar0.093396S.E.ofregression0.087494Akaikeinfoeriterion-1.957881Sumsquaredresid0.176068Sehwarzeriterion-1.860371Loglikelihood26.47352F-statistie4.347423Durbin-Watsonstat0.328025Prob(F-statistie)0.048355———可见，x1与y的RA2=0.770175,粮食生产受农业化肥施用量的影响最大， 与经验相符合，因此选a为初始的回归模型。2、逐步回归y对x1、x2的回归结果：DependentVariable:LNYMethod:LeastSquaresDate:12/19/13Time:09:19Sample:19832007Ineludedobservations:25VariableCoeffieientStd.Errort-StatistieProb.C-6.2956821.814941-3.4688090.0022LNX10.2978540.01548219.239290.0000LNX21.2586220.1500668.3871270.0000R-squared0.945246Meandependentvar10.70905AdjustedR-squared0.940269S.D.dependentvar0.093396S.E.ofregression0.022826Akaikeinfoeriterion-4.609666Sumsquaredresid0.011463Sehwarzeriterion-4.463401Loglikelihood60.62083F-statistie189.9002RA2=0.94524变化显著，t的绝对值大于2,所以可作为独立解释变量保留在模型中y对x1、x2、x3的回归结果：DependentVariable:LNYMethod:LeastSquaresDate:12/19/13Time:09:21Sample:19832007Ineludedobservations:25Variable CoeffieientStd.Errort-StatistieProb.

C-5.9996381.162078-5.1628520.0000LNX10.3233850.01086129.775520.0000LNX21.2907290.09615313.423650.0000LNX3-0.0867540.015155-5.7244840.0000R-squared0.978616Meandependentvar10.70905AdjustedR-squared0.975561S.D.dependentvar0.093396S.E.ofregression0.014601Akaikeinfocriterion-5.469854Sumsquaredresid0.004477Schwarzcriterion-5.274834Loglikelihood72.37318F-statistic320.3438Durbin-Watsonstat1.412883Prob(F-statistic)0.000000===RA2=0.97861变化显著，t的绝对值大于2,所以可作为独立解释变量保留在模型中y对x1、x2、x3、x4的回归结果：DependentVariable:LNYMethod:LeastSquaresDate:12/19/13Time:09:23Sample:19832007Includedobservations:25VariableCoefficientStd.Errort-StatisticProb.C-6.0415541.682783-3.5902150.0018LNX10.3220610.0391618.2239570.0000LNX21.2940010.1353689.5591170.0000LNX3-0.0866650.015730-5.5095090.0000LNX40.0013030.0369720.0352510.9722R-squared0.978617Meandependentvar10.70905AdjustedR-squared0.974341S.D.dependentvar0.093396S.E.ofregression0.014961Akaikeinfocriterion-5.389916Sumsquaredresid0.004476Schwarzcriterion-5.146141Loglikelihood72.37395F-statistic228.8316Durbin-Watsonstat1.413284Prob(F-statistic)0.000000RT=0.978617变化不太显著，t的绝对值小于2，Prob=0.9722所以不可作为独立解释变量保留在模型中。y对x1、x2、x3、x5的回归结果：Dependent