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start date1978和end date 2006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。
Y X1X2X3X4X5 1983387281660114047162091802231151 1984407311740112884152641949730868 1985379111776108845227052091331130 1986391511931110933236562295031254 1987402081999111268203932483631663 1988394082142110123239452657532249 1989407552357112205244492806733225 1990446242590113466178192870838914 1991435292806112314278142938939098 1992442642930110560258953030838669 1993456493152110509231333181737680 1994445103318109544313833380236628 1995466623594110060222673611835530 1996504543828112548212333854734820 1997494173981112912303094201634840 1998512304084113787251814520835177 1999508394124113161267314899635768 2000462184146108463343745257436043 2001452644254106080317935517236513 2002457064339103891273195793036870 2003430704412994103251660387365462004469474637101606162976402835269 2005484024766104278199666839833970 2006498044928104958246327252232561 2007501605108105638250647659031444（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\Estimate Equation，出现对话框，输入“lny Clnx1 lnx1 lnx2 lnx3 lnx4 lnx5”，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:Dependent Variable: LNYMethod: Least SquaresDate: 12/19/13 Time: 08:49Sample: 1983 2007Included observations: 25Variable Coefficient Std. Error t-Statistic Prob.C-4.169757 1.923113-2.1682330.0430LNX10.3812470.0502277.5904970.0000LNX2 1.2222100.1351329.0445850.0000LNX3-0.0811010.015299-5.3010320.0000LNX4-0.0473020.044750-1.0570210.3038LNX5-0.1014270.057713-1.7574470.0949R-squared0.981607Mean dependent var10.70905Adjusted R-squared0.976767S.D. dependent var0.093396S.E. of regression0.014236Akaike info criterion-5.460540Sum squared resid0.003851Schwarz criterion-5.168010Log likelihood74.25675F-statistic202.8006Durbin-Watson stat 1.792233Prob(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=202.8006>F0.05(5,19)一般的，t的绝对=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。
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：Dependent Variable: LNYMethod: Least SquaresDate: 12/19/13 Time: 09:15Sample: 1983 2007Included observations: 25Variable Coefficient Std. Error t-Statistic Prob.C8.9020080.20603443.206570.0000LNX10.2240050.0255158.7792930.0000R-squared0.770175Mean dependent var10.70905Adjusted R-squared0.760182S.D. dependent var0.093396S.E. of regression0.045737Akaike info criterion-3.255189Sum squared resid0.048114Schwarz criterion-3.157679Log likelihood42.68986F-statistic77.07599Durbin-Watson stat0.939435Prob(F-statistic)0.000000B． Y对X2回归结果：Dependent Variable: LNYMethod: Least SquaresDate: 12/19/13 Time: 09:15Sample: 1983 2007Included observations: 25Variable Coefficient Std. Error t-Statistic Prob.C15.15748 5.912971 2.5634290.0174LNX2-0.3834340.509669-0.7523210.4595 R-squared0.024017Mean dependent var10.70905 Adjusted R-squared-0.018417S.D. dependent var0.093396 S.E. of regression0.094252Akaike info criterion-1.809063 Sum squared resid0.204321Schwarz criterion-1.711553 Log likelihood24.61329F-statistic0.565986 Durbin-Watson stat0.335219Prob(F-statistic)0.459489c.Y对X3回归结果：Dependent Variable: LNYMethod: Least SquaresDate: 12/19/13 Time: 09:16Sample: 1983 2007Included observations: 25Variable Coefficient Std. Error t-Statistic Prob.C9.6197220.85974411.189050.0000LNX30.1080670.085271 1.2673350.2177 R-squared0.065274Mean dependent var10.70905 Adjusted R-squared0.024634S.D. dependent var0.093396 S.E. of regression0.092239Akaike info criterion-1.852255 Sum squared resid0.195684Schwarz criterion-1.754745 Log likelihood25.15319F-statistic 1.606139 Durbin-Watson stat0.597749Prob(F-statistic)0.217717d.Y对X4回归结果：Dependent Variable: LNYMethod: Least SquaresDate: 12/19/13 Time: 09:17Sample: 1983 2007Included observations: 25Variable Coefficient Std. Error t-Statistic Prob.C8.9490900.29825530.004790.0000LNX40.1669760.028274 5.9056700.0000 R-squared0.602605Mean dependent var10.70905 Adjusted R-squared0.585327S.D. dependent var0.093396 S.E. of regression0.060143Akaike info criterion-2.707578 Sum squared resid0.083194Schwarz criterion-2.610068Log likelihood35.84472F-statistic34.87693Durbin-Watson stat0.625528Prob(F-statistic)0.000005e.Y对X5回归结果：Dependent Variable: LNYMethod: Least SquaresDate: 12/19/13 Time: 09:18Sample: 1983 2007Included observations: 25Variable Coefficient Std. Error t-Statistic Prob.C 5.593785 2.453373 2.2800390.0322LNX50.4893980.234718 2.0850480.0484R-squared0.158970Mean dependent var10.70905Adjusted R-squared0.122404S.D. dependent var0.093396S.E. of regression0.087494Akaike info criterion-1.957881Sum squared resid0.176068Schwarz criterion-1.860371Log likelihood26.47352F-statistic 4.347423Durbin-Watson stat0.328025Prob(F-statistic)0.048355可见，x1与y的R^2=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。