多重共线性问题的检验和处理

1、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：计虽经济学学 号：学生姓名:教师名称：崔海燕上课时间：、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 Filenewworkfile ，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emptygroup新建空数

2、据栏，根据理论和经 验分析，影响粮食生产（V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）和钏劳动力（X5）,其中成灾面积的符号为 负，其余均应为正。下表给出了 19832000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。YX1X2X3X4X519833872816601140471620918022311511984407311740112884152641949730868198537911177610884522705209133113019863915119311109332365622950

3、312541987402081999111268203932483631663198839408214211012323945265753224919894075523571122052444928067332251990446242590113466178192870838914199143529280611231427814293893909819924426429301105602589530308386691993456493152110509231333181737680199444510331810954431383338023662819954666235941100602226

4、736118355301996504543828112548212333854734820199749417398111291230309420163484019985123040841137872518145208351771999508394124113161267314899635768200046218414610846334374525743604320014526442541060803179355172365132002457064339103891273195793036870200343070441299410325166038736546200446947463710160

5、6162976402835269200548402476610427819966683983397020064980449281049582463272522325612007501605108105638250647659031444（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= 6 0+6 i*lnx1 + 6 2*lnx2+ 6 3*lnx3+ 6 4*lnx4+ 6 5*lnx5+ u在主菜单栏点击 QuickEstimate Equation ,出

6、现对话框，输入“lny Clnxi lnxi 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: 25VariableCoefficientStd. Errort-StatisticProb.C-4.1697571.923113-2.1682330.0430LNX10.3812470.0502277.5904970.0000LNX

7、21.2222100.1351329.0445850.0000LNX3-0.0811010.015299-5.3010320.0000LNX4-0.0473020.044750-1.0570210.3038LNX5-0.1014270.057713-1.7574470.0949R-squared0.981607Mean dependent var10.70905Adjusted R-squared0.976767S.D.dependent var0.093396S.E. of regression0.014236Akaike info criterion-5.460540Sum squared

8、 resid0.003851Schwarz criterion-5.168010Log likelihood74.25675F-statistic202.8006Durbin-Watson stat1.792233Prob(F-statistic)0.000000LnyA=-4.16+0.382lnx1+1.222lnx2-0.081lnx3-0.048lnx4-0.102lnx5从计算结果看，R2 =0.981607 较大并接近丁 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问总体线性相关显著云般的,t的绝对值大丁2, 则解释变量对被

9、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，故认为解释变量问存在多重共线性。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问的两两相关系数，得到简单相关系数矩阵如下：Lnx1Lnx2Lnx3Lnx4Lnx5Lnx11-0.5687441330.4517002440.9643565840.440575584792338116742lnx2-0.568744131-0.214097210-0.697625004-0.0734480643792616461922Lnx30.451700244-0.21409721010.398780

10、1070.411377048338616434274Lnx40.964356584-0.6976250040.39878010710.27991758111646434652Lnx50.440575584-0.0734480640.4113770480.27991758117421922274652从相关分析结果来看，部分解释变量问确实存在相关，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

11、：Dependent Variable: LNYMethod: Least SquaresDate: 12/19/13 Time: 09:15Sample: 1983 2007Included observations: 25VariableCoefficientStd. Errort-StatisticProb.C8.9020080.20603443.206570.0000LNX10.2240050.0255158.7792930.0000R-squared0.770175Mean dependent var10.70905Adjusted R-squared0.760182S.D.depe

12、ndent 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. YMX2 回哗MDependent Variable: LNYMethod: Least SquaresDate: 12/19/13 Time: 09:15Sam

13、ple: 1983 2007Included observations: 25VariableCoefficientStd. Errort-StatisticProb.C15.157485.9129712.5634290.0174LNX2-0.3834340.509669-0.7523210.4595R-squared0.024017Mean dependent var10.70905Adjusted R-squared-0.018417S.D.dependent var0.093396S.E. of regression0.094252Akaike info criterion-1.8090

14、63Sum squared resid0.204321Schwarz criterion-1.711553Log likelihood24.61329F-statistic0.565986Durbin-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: 25VariableCoefficientStd. Errort-

15、StatisticProb.C9.6197220.85974411.189050.0000LNX30.1080670.0852711.2673350.2177R-squared0.065274Mean dependent var10.70905Adjusted R-squared0.024634S.D.dependent var0.093396S.E. of regression0.092239Akaike info criterion-1.852255Sum squared resid0.195684Schwarz criterion-1.754745Log likelihood25.153

16、19F-statistic1.606139Durbin-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: 25VariableCoefficientStd. Errort-StatisticProb.C8.9490900.29825530.004790.0000LNX40.1669760.0282745.905670

17、0.0000R-squared0.602605Mean dependent var10.70905Adjusted R-squared0.585327S.D.dependent var0.093396S.E. of regression0.060143Akaike info criterion-2.707578Sum squared resid0.083194Schwarz criterion-2.610068Log likelihood35.84472F-statistic34.87693Durbin-Watson stat0.625528Prob(F-statistic)0.000005e

18、. Y对X5回归结果:Dependent Variable: LNYMethod: Least SquaresDate: 12/19/13 Time: 09:18Sample: 1983 2007Included observations: 25VariableCoefficientStd. Errort-StatisticProb.C5.5937852.4533732.2800390.0322LNX50.4893980.2347182.0850480.0484R-squared0.158970Mean dependent var10.70905Adjusted R-squared0.1224

19、04S.D.dependent var0.093396S.E. of regression0.087494Akaike info criterion-1.957881Sum squared resid0.176068Schwarz criterion-1.860371Log likelihood26.47352F-statistic4.347423Durbin-Watson stat0.328025Prob(F-statistic)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a. y对x1、x

20、2的回归结果：Dependent Variable: LNYMethod: Least SquaresDate: 12/19/13 Time: 09:19Sample: 1983 2007Included observations: 25VariableCoefficientStd. Errort-StatisticProb.C-6.2956821.814941-3.4688090.0022LNX10.2978540.01548219.239290.0000LNX21.2586220.1500668.3871270.0000R-squared0.945246Mean dependent var

21、10.70905Adjusted R-squared0.940269S.D.dependent var0.093396S.E. of regression0.022826Akaike info criterion-4.609666Sum squared resid0.011463Schwarz criterion-4.463401Log likelihood60.62083F-statistic189.9002RA2=0.94524破化显著，t的绝对伯大丁 2,所以可作为独立解释变量保留在模型中b. y对x1、x2、x3的回归结果：Dependent Variable: LNYMethod:

22、Least SquaresDate: 12/19/13 Time: 09:21Sample: 1983 2007Included observations: 25VariableCoefficientStd. Errort-StatisticProb. :C-5.9996381.162078-5.1628520.0000LNX10.3233850.01086129.775520.0000LNX21.2907290.09615313.423650.0000LNX3-0.0867540.015155-5.7244840.0000R-squared0.978616Mean dependent var

23、10.70905Adjusted R-squared0.975561S.D.dependent var0.093396S.E. of regression0.014601Akaike info criterion-5.469854Sum squared resid0.004477Schwarz criterion-5.274834Log likelihood72.37318F-statistic320.3438Durbin-Watson stat1.412883Prob(F-statistic)0.000000甲2=0.97861破化显著，t的绝对伯大丁 2,所以可作为独立解释变量保留在模型中

24、c. y 对x1、x2、x3、x4 的回归钏I:Dependent Variable: LNYMethod: Least SquaresDate: 12/19/13 Time: 09:23Sample: 1983 2007Included observations: 25VariableCoefficientStd. Errort-StatisticProb.C-6.0415541.682783-3.5902150.0018LNX10.3220610.0391618.2239570.0000LNX21.2940010.1353689.5591170.0000LNX3-0.0866650.015

25、730-5.5095090.0000LNX40.0013030.0369720.0352510.9722R-squared0.978617Mean dependent var10.70905Adjusted R-squared0.974341S.D.dependent var0.093396S.E. of regression0.014961Akaike info criterion-5.389916Sum squared resid0.004476Schwarz criterion-5.146141Log likelihood72.37395F-statistic228.8316Durbin-Watson stat1.413284Prob(F-statistic)0.000000甲2=0.97861祭化不太显著，t的绝对值小丁2, Prob=0.9722所以不可作为独宜 解释变量保留在模型中。d. y对x1、x2、x3、x5的回归结果：Depe