實(shí)驗(yàn)三多重共線性【實(shí)驗(yàn)?zāi)康摹空莆斩嘀毓簿€性問(wèn)題出現(xiàn)的來(lái)源、后果、檢驗(yàn)及修正的原理，以及相關(guān)的Eviews操作方法。【實(shí)驗(yàn)內(nèi)容】以《計(jì)量經(jīng)濟(jì)學(xué)學(xué)習(xí)指南與練習(xí)》補(bǔ)充習(xí)題4-18為數(shù)據(jù)，練習(xí)檢查和克服模型的多重共線性的操作方法。【4-18】表4-3列出了被解釋變量Y及解釋變量X,X,X,X的時(shí)間序列1234觀察值。（1） 用OLS估計(jì)線性回歸模型，并采用適當(dāng)?shù)姆椒z驗(yàn)多重共線性；（2） 用逐步回歸法確定一個(gè)較好的回歸模型。表4-3YX1X2X3X46.040.15.5108636.040.34.794726.547.55.2108867.149.26.81001007.252.37.3991077.658.08.7991118.061.310.21011149.062.514.1971169.064.717.1931199.366.821.3102121實(shí)驗(yàn)步驟】1）建立線性回歸模型并檢驗(yàn)多重共線性1、建立模型利用表4-3數(shù)據(jù)分別建立Y關(guān)于X|、X、X、X的散點(diǎn)圖（SCATXY）。1234i

可以看到Y(jié)與X、X、X都呈現(xiàn)正的線性相關(guān)，與X關(guān)系不明顯。12 4 3首先建立一個(gè)多元線性回歸模型(LSYCXXXX)。12 3 4DependentVariable:YMethod:LeastSquaresDate:12/06/11Time:22:46Sample:110Includedobservaticris:10VariableCoefficientStd.Errort-StatisticProb.C3.9144511.9524402.0049020.1013X10.0602G30.04837S1.2456710.2681X20.0890300.03716S2.3969780.0619X3-0.012S980.018171-0.6933090.5190X40.0074060.0176120.42049S0.6910R-squared0.979655Meandependenivar7.570000AdjustedR-squared0.963379S.D.dependentvar1.233829S.E.ofregression0.236114Akaikeinfocriterion0.257351Sumsquaredresid0.378750Schwarzcriterion0.409144Loglikelihood3.7107^3Hannan-Quinncriter.0.051564F-statistic60.18950Durbin-Watsonstat2.213879Prob(F-statistic)0.000204輸出結(jié)果中，C、X、X、X的系數(shù)都通不過(guò)顯著性檢驗(yàn)。1 3 42、 檢驗(yàn)多重共線性進(jìn)一步選擇CovarianeeAnalysis的Correlation，得到變量之間的偏相關(guān)系數(shù)矩陣，觀察偏相關(guān)系數(shù)。CorrelationYX1X2K3X4丫1.0000000.9721690.937597-0.3887400.912166X1O.S721091.0000000.879363-0.3388760.956248X20.S375970.8793631.000000-0.3047050.760764X3-0.388740-0.338876-0.3047051.000000-0.413541X40.S121560.95624S□760764-0.412541■1.000000可以發(fā)現(xiàn)，Y與X、X、X的相關(guān)系數(shù)都在0.9以上，但輸出結(jié)果中，解1 2 4釋變量X、X的回歸系數(shù)卻無(wú)法通過(guò)顯著性檢驗(yàn)。認(rèn)為解釋變量之間存在多重1 4共線性。(2)用逐步回歸法克服多重共線性1、 找出最簡(jiǎn)單的回歸形式分別作Y與X、X、X、X間的回歸(LSYCX)。1 2 3 4 iVariableCoefficientStd.Error t-StatisticPrcb.C0.9423070.572960 1.6446300.1387X10.1221240.010405 11736720.0000R-squared0.945112Meandependentvar7.570000AdjustedR-squared0.938251S.D.dependentvar1.233839S.E.ofregression0.306599Akaikeinfocriterion0.650305Sumsquaredresid0.752024Schwarzcriterion0.710322Loglikelihood-1.251524Hanran-Quirncriter.0.503919F-statistic1377507Durbin-Watsonstat1.683709Prob(F-statistic0.000003

VariableCoeificientStd.Errort-StatisticProb.C5.4974550.30750417.877680.0000X20.2054060.0269337.6205150.0001R-squared0.8790S8Meandependentuar7.570000AdjustedR-squared0.863974S.D.dependerii^ar1.233829S.E.ofregression0.455057Akaikeinfocriterion1.440070Sumsquaredresid1.656618Schwarzcriterion1.500587Loglikelihood-5.200350Hannan-Quinncriier.1.373083F-statistic58.16373Durbin-Watsonstat0.612996Prob(F-statistic)0.000062VariableCaefficientStd.Errort-SiatisticProb.C17.090217.9865872.1398640.0648X3-0.0951070.079695-1.1933860.2669R-squared0.151119Meandependert?ar7.570000Adjus怕dR-squared0.045009S.D.dependentvar1.233329S.E.ofregression1.205743Akaikeinfocriterion3.388925Sumsciuar已drpsid11.63052Schwarzcrit巳rion3.449442Loglikelihood-14.94462Hannan-Quinntriter.3.322538F-statistic1.424170Durbin-Watsonstat0.B47123Prob(F-statistic)0.266905VariableCoefTicientStd.Error t-StatisticProto.c2.0178070.S98099 2.2467520.0548X40.0550270.008741 6.2954320.0002R-squared0.032047Meandependentvar7.570000AdjustedR-squared0.011053S.D.deperideritvar1.233S29S.E.ofregr已ssici門0.536321Akaikeinfocrit已「inn1.760680Sumsquar已dr已引d2.301120Schwarzcriterion1.E29205Loglikelihood-6.843439Hannan-Quinncrit已匚1.702301F-statistic39.63246Durbin-Watsorstat0.596061Prob(F-statistic)0.000234即：⑴P=0.942+0.122X](1.64)(11.7) R2=0.9383 D.W.=1.6837P=5.497+0.205X2(17.9)(7.63) R2=0.8640 D.W.=0.6130P=17.090-0.095X

(4)Y=2.018+0.055X4(2.25)(6.30)R2=0.8111D.W.=0.5961(2.14)(-1.19)R2=0.0450 D.W.=0.6471可見，Y受X1的影響最大，選擇(1)式作為初始的回歸模型。2、逐步回歸將其他解釋變量分別導(dǎo)入上述初始回歸模型，尋找最佳回歸方程。為求簡(jiǎn)明先列出回歸結(jié)果如下表，過(guò)程截圖放在說(shuō)明部分。CX1X2X3X4R2D.W.Y=f(X)0.9420.1220.93831.68t值(1-64)(11.7)Y=f(X,X)122.3230.0820.0800.96822.26t值(3-71)(5.22)(2.92)Y=f(X,X,12X)34.0370.0790.080-0.0160.96842.32t值(2-25)(5.01)(2.92)(-1.02)Y=f(X,X,12X)42.6860.0490.0960.0120.96652.03t值(3.42)(1.13)(2.79)(0.81)說(shuō)明：第一步：在初始模型中引入X2，模型擬合優(yōu)度提高，參數(shù)符號(hào)合理，且變量通過(guò)了t檢驗(yàn)，D.W.檢驗(yàn)值落在上界以上，表明不存在1階序列相關(guān)性；VariableCoefficientStd.Errort-StatisticProti.02.3228970.62610237100920.0076X10.0818260.0156775.2195530.0012X20.0799190.0273402.9231620.0222R-squared0.9752S4Meandependentvar7.570000AdjustedR-squared0.9&8222S.D.dependenl恂「1.233329S.E.ofregression0.219943AkaikeinfocriterionC.C52476Sumsquaredresid0.338641Schwarzcriterion0.143252Loglikelihood2.737618Hannan-Quirincriter.-0.047104F-statistic138.1058Durbir-Watsorstat2.264141Prob(F-statistic)0.000002第二步，引入X，擬合優(yōu)度略微提高，但變量未通過(guò)t檢驗(yàn);3Variahl已Coeffici已ntStd.Errort-SiatisticProb.C4.0372851.7931542.3515000.0653X10.0793020.0158275.0105780.0024X20.0795030.0272652.9159510.0268X3-0.0157160.015410-1.0198850.3471R-squared0.978935Meandependent\rar7.570000AdjustedR-sqjar&d0.963403S.D.dependentvar1.233829SEofregression0.219320Akaikeinfocriterion0.092604Sumsquaredresid0.288607Schwarzcriterior0.213638Laglikelihood3.530979Hannan-Quinncriter.-0.040170F-siatistic92.94557Durbin-Watsonsiat2.31E923Prob(F-statisti巧0.000020第三步，去掉X，引入X，擬合優(yōu)度有所下降，且X、X都未能通過(guò)t3 4 1 4檢驗(yàn)；VariableCoefficientStd.Error1-StatisticProb.c2.6863450.7S48033.4229530.0141X10.0491400.0436201.1265440.3030X20.0958190.03429127943270.0314X40.0123830.0153630.S061300.4509R-squared0.977699Meandependentvar7.570000Adjust已dR-squar已日0.96654BS.D.Mependentvar1.233829S.E.ofregression0.2