多重共线性问题

1、多重共线性【实验目的】掌握多重共线性的检验及处理方法【实验内容】建立并检验我国钢材产量预测模型【实验步骤】【例1】表1是19781997年我国钢材产量（万吨）、生铁产量（万吨）、发电量（亿千瓦时）、固定资产投资（亿元）、国内生产总值（亿元）、铁路运输量（万吨）的统计资料。表1我国钢材产量及其它相关经济变量统计资料年份钢材产量丫生铁产量X1发电量X2固定资产投资X3国内生产总值X4铁路运输量X51978220834792566668.7232641101191979249736732820699.3640381118931980271638023006746.945181112791981267

2、034173093638.2148621076731982292035513277805.952951134951983307237383514885.26593511878419843372400137701052.43717112407419853693438441071523.51896413070919864058506444951795.321020213563519874386550349732101.691196314065319884689570454522554.861492814494819894859582058482340.52169091514891990515362

3、38621225341854815068119915638676567753139.032161815289319926697758975394473.762663815762719937716895683956811.353463416266319948428974192819355.354675916309319958980105291007010702.975847816585519969338107231081312185.796788516880319979979115111135613838.9674463169734一、检验多重共线性1.相关系数矩阵检验法利用相关系数可以分析解释

4、变量之间的两两相关情况。在Eviews软件中可以直接计算相关系数矩阵。本例中，在Eviews软件命令窗口中键入：CORX1X2X3X4X5或在包含所有解释变量的数组窗口中点击ViewCorrelations,其结果如图6-1所示。由相关系数矩阵可以看出，解释变量之间的相关系数均为0.8以上，大部分更在0.9以上，即解释变量之间是高度相关的。Group:UHTIILEDVorkfile:UNTITLED:Untitled匚反明已囤PrcK)obgH)回ntN目词Free5ampl曰陆求$5prcCorrelationX1X2X3X4X5X11.DDDD0DD.SS51630969645D.973

5、104口930383八X20.9951831.0000000.95961S0.9696370.945442X30.9696450,95961610000000.9961010.827643X40.973104D.96S63709961011.0000000.847043X50.93039309454420.8276430.6470461.000000V图6-1解释变量间的相关系数矩阵2 .综合统计检验法将丫对所有的解释变量回归，即LSYCX1X2X3X4X5,得到图6-2所示的结果：Equation:UHTITLEDlorkfile;UBTITLED:二.幻叵区Hie/pt口匚Cbjed:伺向

6、七帆淅/rsweEstimetr口后工己51氏atsRe5idiDependentVariable:YMethod:LeastSquaresDte:04/30/12Time:10:52Sample:19761997Includedobservations:20CoefficientStd.Errorl-StatlsticProbC3545394436.69630.813S420.4294X10.0260410.1200640.2169920.S314X2099453601354747.2873800.0000X30.3926760.0854684,5412710,0005X4-00B54360

7、.0.D001X5*0,0059980.00S034*09940190.3371R-sqjared0999098IVI踹ndeperdentvar5153450AdjustedR-squared0.998776B.D.dependentwar2512131S.E,ofregression97,87959Akaikeinfocriterion12,03314Sumsquaredresid108119.8Schwarzcritsrion12.3318GLoglikelihood-1143314Haman-Quinnenter.12.0S145F-statistic3102

8、.411Durbin-Walsonstat1.91S746Prob(F-statistic)0.000000图6-2多元线性回归结果图6-2的结果中，R2和F的值都很大，但T的绝对值都比较小，同时，X4和X5的系数估计值不合理，所以此模型存在多重共线性。3 .辅助回归方程检验当解释变量多于两个且变量之间呈现出较复杂的相关关系时，可以通过建立辅助回归模型来检验多重共线性。本例中，在Eviews软件命令窗口中键入：LSX1CX2X3X4X5LSX2CX1X3X4X5LSX3CX1X2X4X5LSX4CX1X2X3X5LSX5CX1X2X3X4对应的回归Z果如图26所示。Equation:UVTIT

9、LEDTorkfile:UTTITLED:.g回区5已囿Pg则匕出回中比汗马而已Frc«ee我ima也4口re匚占贯5t&s,Resids：DependentVariable:XiMethod:LeastSquaresDate.04/3Q.12Tims:11:00Sample:19781997Includedobservatiors:20CoefficientStd.Errort-StatisticProb.c309.6476933.55410.3310870.7447X20.7B37050.2125553,63748700022X30.5337170.124B514.274

10、81300007X40.0351S90,027765-3.0685650,0076X50.0078840.012B150.0152050.5476R-squared0J98188Meandependentvar6209.400AdjustedR-squared0.995168S.D.dependentvar2718S51S.E.ofregression189.9864Akaikeinfocriterion13,53354Sumsquaredresid535737.7Schwarzcriterion13.7B248Loglikelihood-130.3354Hariran-Quinincrite

11、r.13.58211F-statistic979.3627Durbin-Watsonstat1.322006ProbfF-statisticl0.000000>|图6-3Equstion：nWTITLEDTorkfile:IWT工TLED叵区Vaw|丁口二OhjettPdnh|iVane|Fr已宓句|E<jret曰式H5t曰t$Resid引DdpenderrtVariable:X2Method:LeastSquaresDate04/30/12Time:11:03Sample：107S1997IncludedobEervatiuns：20CoefficientStdErrort-St

12、atisticProb-2170407602.5757-3,61529100025OGOGESe0.1645133,6874870.0022-0.2811230.146607-1.9175213.0T440.0B29760.0226323.6663010.00230.025300000936027041020.0163R-squaradJ997S5h/leandependentvar5869100AdjustedR-squared0.396560S.Ddependentvar2834,91。S.E.ofregression166.2623Akaikeinfocriterion13,27733S

13、umsquaredresid4146J7.5Schwarzcriterion13.52626Loglikehhood-127.7733Hannan-Quinncrlier.13.32592F-statistlc1377.221Durbin-Watsonstat0.995444prob(F-statistic)o.oocooo图6-4Equation:UNTITLEDTorkfile:UNTITLED:.匚|回区卜危网JPr匚cbj已匚tj回1时帆石门0Je与匚曰st|5JRE5idfDependentVariable:X3Method:LeastSquaresDate:04/30/12Time

14、:11:C5Qarriple：19731S97Includedobservations:20CoefficientStdErrort-StatisticProbc550.303512932300.42552B0.6705X110290130.2407144,2748430.0007X2-07D02Q30.365207-1,S175210.0744X401666930.0323517JB22370.0000X5-0.0190440.017333-1.00B7560.2992R-squared0.096965Meandependentvar3942595AdjustedR*squared09961

15、55SD.dependentvar4231.973S.Eofregression262.4132Ahaikeinfocriterion1419004Sumsquaredresid1032910Schwarzcriterion14.43897Loglikelihood-135.0004Hannan-Quinncriter.14,23803F-statistic1231.E51Durbin-Watsanstat1.359304Prob(F-statistic)0.000000图6-5Equation:UNTITLEDVorkfile:UBTITLED:=匚回反陆科IPru/ObjectPrinHM

16、am已Free工cEstim/tTForced%，泉7七$I5DependentVariable:X4Method:LeastSquaresDate:04/30/12Time:11:33Sample:19781997Includedobseivations：20CoefficientStd.Errort-StatisticProb.C5983.32066524410.B9941703826X1-45264511475104-3.0685650.0079X25.5956991.553527366630100023X345484600.S2S6827,392237ODOOOX5-0.0521010

17、.093614-0.5565520.5860R-squared0997006Meandependentvar22353.60AdjustedR-squared0.998208SD.dependentvar2237003SEofregression1377.496Akaikeinfocriterion17,50624Sumsquaredresid23462523Schwaizcriterion17,7551BLoglikelihood-170.0624Hannan-Quinnenter.17,55484F-statistic1248.948Durbin-Watsonstat1.263358Pro

18、bT-statistic)0CiOOOOO图6-6KEquation:UKTITLEDTorkfile:UHTITLED：.,|-X卜iewjproc口印1：日旧rinfc版鹏,回兜如)归stimatg1F口佗匚曰研工工曰七降超弓讨不DependentVanable:X5Method:LeastSquaresDate:04/30J12Time:11:34Sample:19701997Includedobservations:20CoefficientStdErrorbStatisticProb.C68338.486024.37411.3435E0.0000X13.12175050743400.

19、6152050.5476X2129485647885272.7041020,0163X33,9113583.559905-1,09075602892X4-0.3903270.697737-05565520.5860R-squared0977037Meandependentvar139605.0AdjustedR-squared0.970913S.D.dependentvar22050.62SEofregression3760.683Akaikeinfocriterion19,51491Sumsquaredresid2.12E+D8Schwarzcriterion1976384Loglikeli

20、hood-190.1491Hannan-Guinncriter.19.56350F-statistic159,5559Durbin-Watsonsta10549742Prob(F-statistic)0.000000图6-7上述每个回归方程的R2都很大，F检验值都非常显著，方程回归系数的T检验值表明:X1与X5,X2与X3,X3与X2、X5,X4与X5,X5与X1、X3、X4的T检验值较小，这些变量之间可能不相关或相关程度较小。二、利用逐步回归方法处理多重共线性1 .建立基本的一元回归方程根据相关系数和理论分析，钢材产量与生铁产量关联程度最大。所以，设建立的一元回归方程为：Y=：X1；2 .逐步引入其它变量，确定最适合的多元回归方程（回归结果如表2所示）表2逐步回归过程模型CX1X2X3X4X5R2阶段最优Y=f(X1)-567.