多重共线性分析

多重共线性分析第一步：建立一个时间序列文档第二步：在新文档中输入相关各个变量的数据器E¥ie>sFilegditObjectViewFrocQuick[Ipti(m£WindowHelpdatayXI}(2X3>(4)<5f■froup:UNTITLEDlorkfile:UHTITLED::Untitled\[T~||H|f：(View][proc][object][PrintNameJ[Fr已已z已Defaultv[5MtTranspose]Edit+/-J[5mpl+/-J1obsYX1X2X3X4|1994NANANANA卜1995NANANANA卜1996NANANANA卜1997NANANANA卜1990NANANANA卜1999NANANANA卜2000NANANANA卜2001NANANANA卜2002NANANANA卜2003NANANANA卜

第三步：对其进行回归分析得出的回归结果如下：IEquation:UNTITLEDTorkfile:UKTTTLED…口回区[vie凹][Prci匚][objeit]|Print]|rJ日[Estimate]向心日st][皇日ts][碣血]DependentVariable:YMethod:LeastSquaresDate:11/27/11Time:15:10Sample:19942003Includedobservations:9CoefficientStd.Errort-StatisticProb.C1371.3602224.6160.61644S0.5312X10.0301980.0225311.3402540.2726X257100601.4375863.9701040.0284X33.0430000.9922353.0676290.0547X411.142184.6956422.3728770.0982X5-970.2762547.6536-1.7716970.1746R-squared0.995686Meandependentvar2668.478AdjustedR-squaredO.90S496S.D.dependentvar950.5563S.E.ofregrEssicm101.9528Akaikeinfocriterion12.32162Sumsquared「Esid31103.13Schwarzcriterion12.45310Loglikelihood-49.44728Hannan-Quinncriter.12.03788F-statistic130.4040Durbin-Watsonstat2.0S4909Prob(F-statistic)0.000950分析其回归结果，可看出该回归方程的R-squared的值很大，Prob(F-statistic)的值很小，表明R-squared检验和F检验均可通过，但是除X2外的其余变量T检验均不能通过，表明变量间存在严重的多重共线性第四步：将各个变量单列出来进行回归分析

首先对Y、C、XI进行回归分析:结果如下：I■Equation:UNTITLEDTorkfile:UNTITLED:.□回[view][Proc][object][PrintNameFreeze][Estimate^ForecastjfstatsjfkesidsjDependentVariable:YMethod:LeastSquaresDate:11/27/11Time:15:21Sample:19942003Includedobsen/ations:10CoefficientStd.Errort-StatisticProb.c-3461.808700.0356-4.9451890.0011X10.0S42190.0097188.665S550.0000R-squared0.903727Meandependentvar2539.200AdjustedR-squared0.891693S.D.dependentvar985.0327S.E.ofregression324.1747Akaikeinfocriterion14.57730Sumsquaredresid040714.0Schwarzcriterion14.63732Loglikelihood-70.88649Hannan-Quinncriter.14.51091F-statistic75.09704Durbin-Watsonstat1.096453接下来按照同样的方法分别对其他变量进行单个的回归分析，结果如下—--■Equation:UHTITLEDTorkflie:UHTITLED::.,■-口问冈[view][Proc][object]PrintNameFreeze][Estimate][Forecast][5tats][Resids]DependentVariable:YMethod:LeastSquaresDate:11/27/11Time:15:25Sample:19942003Includedobseivations:9CoefficientStd.Errort-StatisticProb.C-3070.190509.3425-6.0434500.0005X29.2656640.81192411.411980.0000R-squared0.948992Meandependentvar2668.478AdjustedR-squared0.941705S.D.dependentvar950.5563S.E.ofregression229.5055Akaikeinfocriterion13.90286Sumsquaredresid363709.6Schwaizcriterion13.94669Loglikelihood-60.56288Hannan-Quinncriter.13.80828F-statistic130.2332Durbin-Watsonstat0.S37431Prob(F-statistic)0.000009Equation:UKTITLEDTorkfile:UNTITLED:.Equation:UKTITLEDTorkfile:UNTITLED:.□回区”ie训Prciu][obijeut][Print][bJame][FreeEe][Estimate](Fcireuast]btats][Resicls]DependentVariable:YMethod:LeastSquaresDate:11/27/11Time:15:28Sample:19942003Includedobservations:10CoefficientStd.Errort-StatisticProb.c640.3504393.07291.6036260.1464X311.667282.2451475.1966650.0008R-squared0.771463Meandependentvar2539.200AdjustedR-squared0.742896S.D.dependentvar985.0327S.E.ofregression499.4648Akaikeinfocriterion15.44181SumsquarEdresid1995720.SchwarzcritErion15.50232Loglikelihood-75.20904Hannan-QuinncritEr.15.37542F-statistic27.00533Durbin-Watsonstat0.643632■Equation:UHTITLEDTorkfile:UNTITLED::...口0区I[View][Proc][object][Print][Name][Freeze][Estimate](Forecast][5tats][Resid5]DependentVariable:YMethod:LeastSquaresDate:11/27/11Time:15:29Sample:19942003Includedobservations:10CoefficientStd.Errort-StatisticProb.C-2264.896754.5152-3.0017900.0170X434.3323S5.30S4S26.4674570.0002R-squared0.039440Meandependentvar2539.200AdjustEdR-squarEd0.819379S.D.depEndEntvar985.0327S.E.ofregression418.6346Akaikeinfocriterion15.08873SumsquarEdrmsid1402040.SchwarzcritEriun15.14925Loglikelihood-73.44365Hannan-Quinncriter.15.02234F-statistic41.02300Durbin-Watsonstat0.761911Prob(F-statistic)0.000195■Equation:UKTITLEDlorkfile:UKTITLED:.[T]回冈lView][Proc][object][Print][Name][Freeze][Estimate][Foreca5t][5tat5][Re5ids]DependentVariable:YMethod:LeastSquaresDate:11/27/11Time:15:30Sample:19942003Includedobservations:10CoefficientStd.Errort-StatisticProb.C-10897.181539.174-7.0798380.0001X52014.148230.22258.7486980.0000R-squared0.905370Meandependentvar2539.200AdjustedR-squared0.093541S.D.dependentvar935.0327S.E.ofregression321.3963Akaikeinfocriterion14.56009Sumsquaredresid326367.0Schwarzcriterion14.62060Loglikelihood-70.80043Hannan-Quinncriter.14.49370F-statistic76.53972Durbin-Watsonstat1.529665Prob(F-statistic)0.000023比较得X2的R-square值最高。第五步：利用不显著系数法检验各个变量间的共线性以X1为因变量回归分析得：口问Hie训Pro口问Hie训Pro匚]|objed:][Print][rJ日meFreeze][Estim日te][Fcire匚ast]btats][Resids]DependentVariable:X1Method:LeastSquaresDate:11/27/11Time:15:33Sample:19942003Includedobservations:9CoefficientStd.Errort-StatisticProb.c-69498.5935065.93-1.9819410.1135X2-4.460912DependentVariable:X1Method:LeastSquaresDate:11/27/11Time:15:33Sample:19942003Includedobservations:9CoefficientStd.Errort-StatisticProb.c-69498.5935065.93-1.9819410.1135X2-4.46091231.82397-0.1401750.8953X39.58457221.491240.4459760.6737X4147.233873.723101.9977980.1164X518043.730142.3542.215S980.0910R-squared0.980219AdjustedR-squared0.960433S.E.ofregression2262.475以X2为因变量回归分析篦器MeandependentvarS.D.dependentvarAkaikeinfocriterionSchwarzcriterionHannan-Quinncriter.72183.3311374.3610.5864910.6960618.35004■Equation:UNTITLEDlorkfile:UNTITLED:.□叵Hie艸][Prcijobjed:][Print][pJ日me[[Freeze]〔Estim曰te][Fcire匚日盘扳日TResids]DependentVariable:X2Method:LeastSquaresDate:11/27/11Time:15:42Sample:19942003Includedobservations:9CoefficientStd.Errort-StatisticProb.C-760.7973673.7654-1.1291720.3220X1-0.0010960.007317-0.1401750.8953X30.35S0070.2950511.2133740.2917X40.1457411.6315420.0893270.9331X5204.0376160.35261.2634760.2734R-squarEd0.937053Meandependentvar620.2111AdjustedR-squared0.874106S.D.dependentvar99.93844S.E.ofregression35.45972Akaikeinfocriterion10.27435SumsquarEdresid5029.567Schwarzcriterion10.38442Loglikelihood-41.23604Hannan-Quinncriter.10.03340F-statistic14.83636Durbin-Watsonstat2.099406Prob(F-statistic)0.011300以X3为因变量回归分析得:■Equation:UNTITLEDlorkfile:UNTITLED:.□回|Vie艸Pro匚Object,|PrinlN日meFreeze][Estim■Equation:UNTITLEDlorkfile:UNTITLED:.□回|Vie艸Pro匚Object,|PrinlN日meFreeze][Estim日te][Foret日或]|宝日T|Resids]DependentVariable:X3Method:LeastSquaresDate:11/27/11Time:15:44Sample:19942003Includedobservations:9CoefficientStd.Errort-StatisticProb.C203.26551116.3960.1320730.3644X10.0049420.0110820.4459760.6787X20.7515020.6193491.2133740.2917X4-1.4403482.253936-0.6390370.5576X5-95.01093271.7793-0.3525620.7422R-squaredAdjustedR-squaredS.E.ofregression0.722092Meandependentvar0.445705S.D.dependentvar51.37535174.000069.0105611.01637和X5的多重共线性较为显著。第六步：由于第四步检验中X2的R^quared值最高，第五步;检验中X3和X4的多重共线性Akaikeinfocriterion、X2并不显著，故先保留Y、C、X2、X3和X4。第七步：对Y、C、XI、X2、X3、X4作回归分析，结果得:[vie凹][Prci匚][objeit]|Print]|rJ日me■Equation:UHTITLED[vie凹][Prci匚][objeit]|Print]|rJ日meFreeze][Estimate]向低日丸]|皇日ts]|Resids]DependentVariable:YblEthod:LeastSquaresDate:11/27/11Time:15:53Sample:19942003Includedobservations:9CoefficientStd.Errort-StatisticProb.C-2533.346374.9091-6.7572270.0025X10.0005640.01S7020.0301710.9774X24.3547201.5039582.3955060.0443X33.3489941.2105562.7664910.0505X413.164415.6426792.3330070.0000R-squared0.991172Meandependentvar2660.473AdjustedR-squared0.9S2345S.D.dependentvar950.5563S.E.ofregression126.3034Akaikeinfocriterion12.81543Sumsquared「EEid63010.15Schwarzcriterion12.92500Loglikelihood-52.66944Hannan-Quinncriter.12.57898F-statistic112.2007Durbin-Watsonstat2.164051加入后iR-squared值有了小幅度的提高，但是却让X4变得不显著，故舍去第八步：对Y、C、X5、X2、X3、X4作回归分析，结果得：■Equation:UNTITLEDTorkfile:UKTITLE