检验多重共线性

实验目的：在回归模型牵涉到多个自变量的时候，自变量之间可能会相互关联，即他们之间存在有多重共线性，本节实验的实验目的是如何用Eviews检测各个自变量之间是否存在的多重共线问题以及如何对多重共线性进行修正。我们实验的原始数据如图所示，判断钢产量y与生铁产量XI,发电量X2,固定资产投资X3，国内生产总值X4,铁路运输量X5之间的关系。钢材产量生铁产量固定资产国内生产铁路运输年份1978197919801981198219831984198519861987198819891990199119921993199419951996199722082497271626702920307233723693405843864689485951535638669777168428898093389979X134793673380234173551373840014384506455035704582062386765758989569741105291072311511发电量X2投资X3总值X4量X525662820300630933277351437704107449549735452584862126775753983959281100701081311356668.72699.36746.9638.21805.9885.261052.431523.511795.322101.692554.862340.5225343139.034473.766811.359355.3510702.9712185.7913838.96326440384518486252955935717189641020211963149281690918548216182663834634钢材产量生铁产量固定资产国内生产铁路运输年份1978197919801981198219831984198519861987198819891990199119921993199419951996199722082497271626702920307233723693405843864689485951535638669777168428898093389979X134793673380234173551373840014384506455035704582062386765758989569741105291072311511发电量X2投资X3总值X4量X525662820300630933277351437704107449549735452584862126775753983959281100701081311356668.72699.36746.9638.21805.9885.261052.431523.511795.322101.692554.862340.5225343139.034473.766811.359355.3510702.9712185.7913838.9632644038451848625295593571718964102021196314928169091854821618266383463446759584786788574463110119111893111279107673113495118784124074130709135635140653144948151489150681152893157627162663163093165855168803169734实验步骤：1：打开Eviews7.0.—File—Workfile,选择年度数据，在初始日期和结束日期分别输入“1978”和结束年份“1997”。点击“OK”确定。2：在新建工作表中，点击Proc—Import—Read，选定需要导入的Excel工作表，在“Upper-leftdatacell”中输入数据在Excel中的初始位置“B2”，在“Excel5+….”中输入“sheet1”，在“Nameforserises、”中输入“yx1x2x3x4x5”点击“OK”即可。3：在Eviews空白处输入：“lsycx1x2x3x4x5”，回车即可，结果如下。

DependentVariable:YMethod:LeastSquaresDate:04/19/13Time:11:24Sample:19781997Includedobservations:20VariableCoefficientStd.Errort-StatisticProb.C354.5884435.69680.8138420.4294X10.0260410.1200640.2168920.8314X20.9945360.1364747.2873800.0000X30.3926760.0864684.5412710.0005X4-0.0854360.016472-5.1866490.0001X5-0.0059980.006034-0.9940190.3371R-squared0.999098Meandependentvar5153.450AdjustedR-squared0.998776S.D.dependentvar2512.131S.E.ofregression87.87969Akaikeinfocriterion12.03314Sumsquaredresid108119.8Schwarzcriterion12.33186Loglikelihood-114.3314Hannan-Quinncriter.12.09145F-statistic3102.411Durbin-Watsonstat1.919746Prob(F-statistic)0.000000经查表可知，t(17)=1.345,结合上表可知，xl和x5没有通过t检验，而且F\检验较大，估计解释变量之间可能存在着多重共线性。相关性如下图所示：X1X2X3X4X5X110.9951830.9696450.9731040.930383X20.99518310.9596160.9696370.945442X30.9696450.95961610.9961010.827643X40.9731040.9696370.99610110.847048X50.9303830.9454420.8276430.8470481可知X1X2X3X4X5，之间存在着较强的多重共线我们分别用y和xi做线性回归，结果如下图所示。R-squared0.994453Meandependentvar5153.450R-squared0.995411Meandependentvar5153.450R-squared0.930148Meandependentvar5153.450R-squared0.939387Meandependentvar5153.450R-squared0.879348Meandependentvar5153.450可知拟合由强到弱的顺序依次是：X2XIX4X3X5,我们选定拟合最好的X2作为基准变量，分别导入X1X4X3X5做回归，结果如下：VariableCoefficientStd.Errort-StatisticProb.C-287.6867101.2341-2.8417970.0113X20.4871850.1126874.3233520.0005X10.4158670.1174973.5393760.0025X1的t统计量为3.539376，而tO.Ol(17)=1.333，处于拒绝区域，则拒绝零假设，保存X1变量。然后我们一X2X1为解释变量，对X3X4X5做回归，结果如下：VariableCoefficientStd.Errort-StatisticProb.C-260.7822215.8307-1.2082720.2445X20.4909760.1190954.1225440.0008X10.4050600.1428672.8352320.0119X30.0045540.0319860.1423780.8886VariableCoefficientStd.Errort-StatisticProb.C-393.0125195.3528-2.0118080.0614X20.4911280.1148884.2748390.0006X10.4432590.1271663.4856870.0031X4-0.0039320.006196-0.6346620.5346VariableCoefficientStd.Errort-StatisticProb.C-188.8822495.0822-0.3815170.7078X20.5025280.1382213.6356810.0022X10.4072670.1280823.1797340.0058X5-0.0009700.004752-0.2041460.8408—可知解释变量X3X4X5的t统计量均小于tO.Ol(17)=1.3334,接受零假设，即X3X4VariableCoefficientStd.Errort-StatisticProb.C-287.6867101.2341-2.8417970.0113X20.4871850.1126874.3233520.0005X10.415867VariableCoefficientStd.Errort-StatisticProb.C-287.6867101.2341-2.8417970.0113X20.4871850.1126874.3233520.0005X10.4158670.1174973.5393760.0025R-squared0.997358Meandependentvar5153.450X5前面的系数为零，可以删除，只保留解释变量X2X1,回归结果如下图示。0.9970472512.131AdjustedR-squaredS.E.ofregressionSumsquaredresidLoglikelihoodDurbin-Watsonstat136.5096316792.9-125.08150.692473S.D.dependentvarAkaikeinfocriterionSchwarzcriterionF-statisticProb(F-statistic)12.8081512.957513208.7270.000000回归结果：y=-287.6867+0.415867X1+0.487185X2(2.841797) (3.539376) (4.323352) -下面我们再次对修正后的模型进行序列相关检验和异方差检验.序列相关性检验此时t统计量均能通过检验，但是DW为0.692473，经查表可知，存在着序列相关性。又因为DW=2(1-p),得p=0.6538,以此我们可以用广义差分法再次回归，在这里我们用另一种方法,Cochrane-Orcutt法估计模型，回归结果如图所示。VariableCoefficientStd.Error t-StatisticProb.C-214.1697162.8751 -1.3149320.2083X10.5155900.118979 4.3334430.0006X20.3758720.116493 3.2265720.0056AR⑴0.5825210.186316 3.1265220.0069R-squared0.998626Meandependentvar5308.474AdjustedR-squared0.998351S.D.dependentvar2480.737S.E.ofregression100.7230Akaikeinfocriterion12.24729Sumsquaredresid152176.9Schwarzcriterion12.44612Loglikelihood-112.3492F-statistic3634.613Durbin-Watsonstat1.589375Prob(F-statistic)0.000000InvertedARRoots.58此时，DW=1.589375,duvDWv4—du，表明模型中不存在自相关。回归方程为：

y=—214.1697+0.515590X1+0.375872X2(—1.314932) (4.333443) (3.226572)异方差性检验我们对方程再次检验异方差性，如下图WhiteHeteroskedasticityTest:F-statistic0.900529Probability0.489771Obs*R-squared3.888180Probability0.421351TestEquation:DependentVariable:RESIDEMethod:LeastSquaresDate:04/19/13Time:23:41Sample:19791997Includedobservations:19VariableCoefficientStd.Errort-StatisticProb.C-48641.8642241.01-1.1515320.2688X124.8