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1978－1997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Y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X51978220834792566668.7232641101191979249736732820699.3640381118931980271638023006746.945181112791981267034173093638.2148621076731982292035513277805.952951134951983307237383514885.26593511878419843372400137701052.43717112407419853693438441071523.51896413070919864058506444951795.321020213563519874386550349732101.691196314065319884689570454522554.861492814494819894859582058482340.5216909151489199051536238621225341854815068119915638676567753139.032161815289319926697758975394473.762663815762719937716895683956811.353463416266319948428974192819355.354675916309319958980105291007010702.975847816585519969338107231081312185.796788516880319979979115111135613838.9674463169734一、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View'Correlations,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。2■Group:TmTITLEDlockfile:THITITLED:iHntitled\_□X|Wiew][Pro匚][objecl:][Print][hJame][Freewe]bample[Rheel:]凤疋？]CorrelationX1X2X3X4X5X11.0000000.9951830.9696450.9^31040.930383AX20.9951831.0000000.9596160.9090370.945442X30.9696450.9596161.0000000.S961010.827543X40.9731040.9696370.9961011.0000000.347048=X50.9303830.9454420.8276430.8470481.0000007j>图6-1解释变量间的相关系数矩阵2.综合统计检验法将Y对所有的解释变量回归，即LSYCX1X2X3X4X5,得到图6-2所示的结果：■Equation:UKTITLEDlorkfile:UNTITLED::..■□回区[“iew][Pr•□匚][obje止][print][Name][Fr已皂ZEI[Estimate)(FF][Stats][Resids]DependentVariable:YMethod:LeastSquaresDate:04/30/12Time:10:52Sample:19781997Includedobservations:20CoefficientStd.Errort-StatisticProb.C354.5884436.69680.8138420.4294X10.0260410.1200640.216S920.S314X20.9945360.1364747.2373800.0000X30.3926760.0064634.5412710.0005妊4-0.0854360.016472-5.186643o.ooo-iX5-0.0059980.006034-0.9940190.3371R-squared0.999098Meandependentvar5153.450AdjustedR-squared0.998776S.D.dependentvar2512.131S.E.ofregression07.0796Akaikeinfocriterion12.03314Sumsquaredresid108119.8Schwarzcriterion12.33106Loglikelihood-114.3314Hannan-Quinncriter.12.09145F-statistic3102.411Durbin-Watsonstat1.919746Prob(F-statistiO0.000000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：LSX1CX2X3X4X5LSX2CX1X3X4X5LSX3CX1X2X4X5LSX4CX1X2X3X5LSX5CX1X2X3X43对应的回归结果如图2—6所示。■Equation:UNTITLEDVorkfile:UNTITLED：-.-[T]回xView](Proc][object][print][Narrie[Freeze|(Estirridte][FLirE匚吕或](5tats](Resids_|Dependent'/ariable:X1Method:Leas!SquaresDate:04/30；12Time:11:00Sample:197S1997Includedobservations:20CoefficientStd.Errort-StatisticProb.c309.6478933.55410.3316S70.7447g07837950.2125553.6074870.0022X30.5...
