多重共线性试验报告

《计量经济学》上机实验报告三题目：多重共线性实验日期和时间：班级：学号：实验环境：WindowsXP;EViews3.1姓名：实验室：实验目的：掌握多重共线性检验及修正方法，熟悉EViews软件的相关应用实验内容：利用实例数据和EViews软件，采用有关方法对建立的回归模型进行多重共线性的检验及处理。习题4.3;4.4;4.6实验步骤：一、建立工作文件菜单方式命令方式：CREATEA起始期终止期二、输入数据datayx1x2x3x4x5x6x7三、检验多重共线性相关系数检验命令方式：cor变量名1变量名2。。。。。Coryx1x2x3x4x5x6x7辅助回归方程检验命令方式：LS解释变量名1C其他解释变量名2解释变量名3oooooLsx1cx2x3x4x5x6x7Lsx2cx1x3x4x5x6x7Lsx3cx1x2x4x5x6x7Lsx4cx1x2x3x5x6x7Lsx5cx1x2x3x4x6x7Lsx6cx1x2x3x4x5x6Lsx7cx1x2x3x4x5x6用F检验，得到判定系数R2方差膨胀因子检验Genrvif1=1/(1-R2)Genrvif1=1/(1-0.)Genrvif2=1/(1-0.)Genrvif3=1/(1-0.)Genrvif4=1/(1-0.)Genrvif5=1/(1-0.)Genrvif6=1/(1-0.)Genrvif7=1/(1-0.)四、利用逐步回归方法处理多重共线性建立基本的一元回归方程建立的多元回归模型试验结果:3.17表6是1978到1997年我国钢材产量Y(万吨)，生铁产量x］，发电量七(亿千瓦时)，固定资产投资x，国内生产总值x(亿元)，铁路运输x(万吨)的统计材料.345表格6钢材产量生铁产量固定资产国内生产铁路运输年份YX1发电量X2投资X3总值X4量X51978220834792566668.723264110119.001979249736732820699.364038111893.001980271638023006746.904518111279.001981267034173093638.214862107673.001982292035513277805.905295113495.001983307237383514885.265935118784.0019843372400137701052.437171124074.0019853693438441071523.518964130709.0019864058506444951795.3210202135635.0019874386550349732101.6911963140653.0019884689570454522554.8614928144948.0019894859582058482340.5216909151489.0019905153623862122534.0018548150681.0019915638676567753139.0321618152893.0019926697758975394473.7626638157627.0019937716895683956811.3534634162663.0019948428974192819355.3546759163093.0019958980105291007010702.9758478165855.0019969338107231081312185.7967885168803.0019979979115111135613838.9674463169734.00(1)计算各个变量之间的相关系数，分析多重共线性的可能类型;(2)根据逐步回归原理，建立我国钢材产量预测模型.参考答案(1)多重共线性检验①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：CORyX1X2X3X4X5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1所示。操作命令：Coryx1x2x3x4x5EViews-[Group:UNTITLEDlorkfile:UNTITLEDXUntitled]IIFileEditObjectViewProcQuickOjitionsWindowHelpVieg|Pnx|c>bjett]Print]P己me|Freeze|Temple115pe匚|YX1X2X3X4X6Y1.0000000.9975420.9975580.9652570.9693580.933985X10.9975421.0000000.9955260.9692010.9722980.928638X20.9975580.9955261.0000000.9604740.9700360.942032X30.9652570.9692010.9604741.0000000.9960420.324076X40.9693580.9722980.9700360.9960421.0000000.842854X50.9339850.9286380.9420320.8240760.8428541.000000由上表可以看出，解释变量之间相关系数至少为0.824076大于0.8，表明模型存在严重的多重共线性。②辅助回归模型检验及方差膨胀因子检验:当解释变量多余两个且变量之间呈现出较复杂的相关关系时，可以通过建立解释变量之间的辅助回归模型来检验多重共线性。本例中，在Eviews软件命令窗口中分别键入下列操作步骤，结果如下：操作命令：lsx1cx2x3x4x5GenrVIF1=1/(1-0.996i85)Genrtoli=i/vifiXi=309.7492556+0.7837793882*X2+0.5336865403*X3-0.08519190217*X4+0.007883293867*X5R2=0.996185，F=979.192，prob(F)=0.000000VIF1=1/(1-R2)=1/(1-0.996185)=262.1232,TOL1=1/VIF1操作命令：lsx2cx1x3x4x5GenrVIF2=1/(1-0.997437)X2=-2178.738401+0.6065795755*X1-0.2810604053*X3+0.08296811926*X4+0.02531311407*X5R2=0.997284，F=1377.086，prob(F)=0.000000VIF2=1/(1-R2)=1/(1-0.997284)=368.18851,TOL2=1/VIF2操作命令：lsx3cx1x2x4x5GenrVIF3=1/(1-0.997029)X3=550.3404638+1.028924602*X1-0.7001692369*X2+0.1686903967*X4-0.01904547075*X5R2=0.996964,F=1231.482，prob(F)=0.000000VIF3=1/(1-R2)=1/(1-0.996964)=329.38076,TOL3=1/VIF3操作命令：isx4cx1x2x3x5GenrVIF4=i/(i-o.99709i)X4=5984.404305-4.525903944*X1+5.695401142*X2+4.648363422*X3-0.05211728108*X5R2=0.997006,F=1248.772，prob(F)=0.000000VIF4=1/(1-R2)=1/(1-0.997006)=334.00134,TOL4=1/VIF4操作命令：isx5cx1x2x3x4GenrVIF5=1/(1-o.974837)X5=68338.5606+3.121084841*X1+12.94939533*X2-3.911040093*X3-0.3883940712*X4R2=0.977037,F=159.5556，prob(F)=0.000000VIF5=1/(1-R2)=1/(1-0.977037)=43.548317,TOL5=1/VIF5模型R2F统计量F的伴随概率方差膨胀因子VIF容许度TOLX1=f(X2,x3,x4,x5)0.996185979.1920.00000262.12320.003815X2=f(X1,x3,x4,x5)0.9972841377.0860.00000368.18850.002716X3=f(X1,x2,x4,x5)0.9969641231.4820.00000329.38080.003036X4=f(X1,x2,x3,x5)0.9970061248.7720.00000334.00130.002994X5=f(X1,x2,x3,x4)0.977037159.55560.0000043.548320.022963上述辅助回归模型的F统计量，其伴随概率均接近于零或小于显著性水平0.05,表明模型存在严重多重共线性，这一结论也可通过各方差膨胀因子（VIF）均大于10和容许度均小于0.1中得到。（2）逐步回归法由相关系数图表可知，Y与X2相关系数最大，故先建立Y与X2的一元基本线性回归模型：Lsycx2估计结果如下：HVievsE—ion-WoxtIeztEiXe：-3—17Xllirtitled：I】FileH_ditQ_bJct.兰i己wE.i_oaRu立ukOE-tiort=ndowT£elpIPr口仁1Olzdw匚町Imnt1FJmmwl户nwtlmF户口IRmmtclr■DependentVariabIe:YNl^thod:l_e寻等，SquaresDale:12/^2/1□Time:02:15Sample;1S76155了Included<□bmbi-vations:20wQf口曰wQf口曰-XJ=2口sknL=HiqLJ:.F—-bnJJluJrQJr-kd.unurassldId或曰rd曰IaII口.5SS-4II

口J日与1=5E

T7J.BZ3BH

550255.5

-13O.6C25

口.日=2耳了了4『5candepEncdentvarS.O.cdqpqncdqnl,■.■arJXkaikqirifizicritqri□nSchwarzcrilsrionF-stmtisticPro：a1a!i91in)515Z34三匚I3512i3-1■I13_359O23日口4一493ojjnnrioo、^寻ri寻l:・lmOo&ffici^ntStd.Errort-StatielicProb.C-Z3-4.与了11~T91.7-7-q□1-ll匚|_丁lasX2口.曰曰q1口15□.□1-II4£iE2.4曰占日q以上述一元线性回归模型为基本模型，顺次引入其他变量估计二元回归模型，结果如下:Lsycx2x1Lsycx2x3Lsycx2x4Lsycx2x5~C209.54371b5.Ei2241.127656U.27blX20.8065920.05176615.581410.0000X30.0537650.0341081.5763350.1345R-squared0.995778Meandependentvar5293.263AdjustedR-squared0.995251S.D.dependentvar2499.746S.E.ofregression172.2707Akaikeinfocriterion13.27995Sumsquaredresid474834.9Schwarzcriterion13.42907Loglikelihood-123.1595F-statistic1887.010Durbin-Watsonstat0.904462Prob(F-statistic)0.000000

Dpcride«ntWriat>le«:"VHiti■1=1:l_iaaa1：l-lHIHi3Oata:IME3/l口Tlr-ria:anm户|g：1SZB1SS7-1no1ud«■clob*■=■rwmt1on*:■□3：i~r2CiVniriablee二owffiui日ntStd.Errinrt-Stntistic：Rrob.oxm.□31曰卫1S3.：S曰曰-1□.31口,曰与曰1口曰nnn33BB口.口mmim口口口.口口口口5<-4nnn^sonn4WZ3口m曰n.曰日曰：2FS-«3qure®dMi=»日mde»pi=»ndasnl戚e「«51«5：5-460>k.i4jiiebIbHR-bh1nsasaaggs名.D.HispiHi-iidentr2©i31:BiS.E.orFgg广曲巨dli=i*"i17e.33-1gAh:邑Ikq1nTcic：FltoiJi=iriim=34曰二耳Suh-r-imquiarucJkaa1cJ1.\Sc：h'vvsrzc=Kitarloni3.斗三才曰口1_口口11Ra11|-ioad1Z3口点曰三土F-Btatlet1匚1曰曰曰=1S3Eiijrbin-W«tsonat□-e«56S37F'rob(F-stiu)0.000000EViews-[Equation:EQ09¥orkfile:3-lT\Untitled]IIFileEditObjectViewProcQuickO^tionsWindowHelpPrint|N血日|Fr如矣|EstimmE|Fur口匚技|5t击|R洞山|DependentVariable:YMethod:LeastSquaresDate:12Z22/10Time:02:17Sample:19781997Includedobservations:20经比较可知，新加入X5的回归模型tYfx2，x5)，湖回归系数为负，不符合实际的经济意义且T检验不通过；新加入X3的回归模型丫=峪2?3)及新加入X4的回归模型Y=f(x2,x4)虽经济意义合…，一-一、〃，,538.3551_544,11210.989310-.^3364十一一理，但X3和X4回归系数的T检验不通过；新加入X2的回归模型Y=f(x2,xi)不仅经济意义合理、回归系数T检验诵过，而且胡比一元回归模型丫=捋"的号2提高地此，Y=f(x2,x1)估计的结果为最优的二元回归模型，以此为翱Ls.yc成2项海ion174.1597TSumsquaredresid为最优的二元回归模型，以此为翱Ls.yc成2项海ion174.1597TSumsquaredresid515637.4L?oyc螺.补制-129.9530LS明如rx2xisx5stat0.908494螺三元血：瓷客Akaikeinfocriterion13.29530Schwarzcriterion13.44466F-statistic1968.073Prob(F-statistic)0.000000IIFileEdit0bjectViewFrucy.uick0IlS艮让血胃HelpWiEwIPrciclobjEiztl珂1~1亦的£旧配如|Estimmte|Fnr口匚a】t|5tat$|Ranicls|DependentVariable:YMethod:LeastSquaresDate:12Z22/10Time:02:22Sample:19781997Includedobservations:19VariableCoefficientStd.Errort-StatisticProb.-e,idIM1IIITAjl\□.□Or4-1.1笑554Cl.WGFIX20.4498880.1272093.5365990.0030X10.4421820.1486742.9741680.0095X30.0064080.0321580.1992800.8447R-squared0.997344Meandependentvar5293.263AdjustedR-squared0.996813S.D.dependentvar2499.746S.E.ofregression141.1128Akaikeinfocriterion12.92166Sumsquaredresid298692.4Schwarzcriterion13.12049Loglikelihood-118.7558F-statistic1077.825Durbin-Watsonstat0.716038ProbfF-statistic)0.000000

CBq,UHD~bi■口t.VIoaH.u±ok口■七1oxi.kW1H.J-口Print|IM.e.I|工・Hn~i.匕■|Li=ir.u・・k]Shat■|R_.・lid・|匚ndr—*nd<=•rrtP"1壬i「♦e卜I旦■:=,t'MfiiMocl:l_aaat曰只邪Data:I2/32Z1□Tlr-rie:03:33曰鼻fima：r曰k曰■】曰曰了CBq,UHStcl.Er'i-'QrX2X1X4口.4曰112S0.4-432-53"i口口：*3：>ISS.卫曰O.114曰曰曰O.1271E=SnnOSias曰与2□3eA曰Stcl.Er'i-'QrX2X1X4口.4曰112S0.4-432-53"i口口：*3：>ISS.卫曰O.114曰曰曰O.1271E=SnnOSias曰与2□3eA曰esn14-5-dr7e3EK32-3FI--□.□SI4rijZiriOBCl003lr<5W曰F3-Euquai-aiJ^cJJijote-dR-eij^re-cdS.E.ofre»nre«i=i=ioriSi_imccju^irr»dre»"3iidl_ci日lih：QlihiomedOlji-IdI!■-■-Wataonstat.33^-433口.曰曰曰曰qCi1：3S-9^25309013.Ei=i二-4-曰mum.s^^snsrvlaat~idapancJantvarS.D.cd—■QWiCJ—■Kitvsi-Aknike>irrfccriterionSchws「工■:：ritr»rionF'-sra-claTlc：F3koti(F=Si-t1s-tIu〉S-lS3.2G12.1^112.es32913.00243二口臼4.im曰口-口口口口口口IIFileEdi+Objec+ViewProcquickOe>+ictleWirLdowHelpViEw|「rciiz|objEizt|Frint|N日me|Fr•如Estim日te|FcireEst|如ts|ResiddDependentVariable:YMethod:LeastSquaresDate:12/22/10Time:02:23Sample:19781997Includedobservations:20VariableCoefficientStd.Errort-StatisticProb._在X2、X1基础上，加入X3后的回归模型y=f(x2,x1,x3),R2有所下降，且X3的回归系数C-188.8822495.0822-0.3815170.7078T检验不显著;加入X4或搠髀归模型监护,寤4)或yfg，xl，X5)，R2有所下降，X4的回归系数T检验不显著，甚至睨评勺回归系虱不符合经济理论分析和经验判断；加入X5后回归模型yfux2,(X1,x5)与加入］X4T后的回归模型相同，tX5回归系数经济意义不合理且T检验不显著，相较而言加入饕后的回归耀黝x淞燃其回归系数经舜理，故选择y=f(x2,xl,x3)估计结果，以此为基础,r■建立四元回归模型：Schwa住critericin13.10469L吗加呼2-1250555F-泊tiMc2018.577书存晶狄新1x3盖40.698750Prob(F-statisticJ0.000000Lsycx2xlx3x5E¥ie>s-[Equation:EQ13Vorkfile:3-17\UntitledIIFileEdi+Objer+ViewFrocquickO^tionsRirLdbiVHelp、imvj|「rciiz|c)bjmizt|Print|陷昵旧此矣|Fur□匚日吐|Rm引ds|DependentVariable:YMethod:LeastSquaresDate:12/22/10Time:02:26Sample:19781997Includedobservations:19VariableCoefficientStd.Errort-StatisticProb.C-55.97141145.4915-0.384706□7062X20.9063940.1267817.1492780.0000X10.0169290.1314750.1287620.8994X30.4119190.0884584.6566710.0004X4-0.0822020.017434-4.7150300.0003R-squared0.998974Meandependentvar5293.263AdjustedR-squared0.998681S.D.dependentvar2499.746S.E.ofregression90.79646Akaikeinfocriterion12.07605Sumsquaredresid115416.0Schwarzcriterion12.32459Dcpcn«zln±u«:Dcpcn«zln±u«:*fWl=•tHCird=■〜!=■ata:1O~FIt-r-ia:£JH:N曰sisrr-ipIa：■曰immk・*-■uIljcdq坦a!□qqI■=■ri旦：1m■:■,/〔-I.,II.,;■■.1■:.■■•■■■I11■:■,/〔-I.,II.,;■■.1■:.■■•■■■I11I」■1:111I■I111111I-IBnnlls曰-1-15y昌■Mi.Mua7:;Q----I111111I■II:!;:.-I'-...■II'.'■,•:,::・■;.■■,1-■-■■II11I---F?-i=ciljr=«dq^cd_|i_iqclF5一勺只i_i亘ra匚J曰_U.nrrapir~wsIor~i曰i_itv-isi_iaracdka=■IcdI—口QIlb^CliriCaCZidO■=!rt>in-77eto口liEto-mmwwmmiasi□nmkBW曰.3-iiD_/Nm。0.^31BOE=rvndec■dDQoriizluirn±*0r三_!=■一cl&poi-iizdet-itvia*itTro^：rltarlizi!--■曰U，~iJ■.淫日广=urltQfloL-=七由七I=七iuF^r«3!=■CF--〜曾Fti〜曾ic=)・•!:;;，一•■."■Iwu-••-II■I.::，.在X2、X1、X3基础上引入X4后，R2虽有所上升，但X1的回归系数T检验不通过且X4的回归系数为负值，与经济理论分析和经验判断不符；引入X5后也与引入X4相同，R2虽有所上升，但X3与X5的回归系数T检验不通过且经济意义不合理，故引入所有的变量建立回归模型，结果如下：Lsycx2x1x3x4x5EViews一[Equation:EQ15Torkfile:3-17\Untitled；IIFileEditObjectViewProcQuickO^tionsWindowHelp仍巳叫忡|-口匚|西已吐|Prinl:|Name|Freeze|EstimaE|Fdr•已匚ast15目怆|R巳可凹DependentVariable:YMethod:LeastSquaresDate:12/22/10Time:02:31Sample:19781997Includedobservations:19经检验X4和i^5的回归系数符号为负值，.且r*与痼的狷检验不显著。逐步回归估计结果表：方程①Y=f(x2)-e-X2X23547470X^B3兀怀3451p花5

n[上初9②Y=f(x2,x1)3Y=flX1X30.8841(62.4859)0.036VB0.3882W0.133337O.OE32O61X40.4872-0.0060U-0141剖的3口伽诩1

逐步回归估计结果表：方程①Y=f(x2)-e-X2X23547470X^B3兀怀3451p花5

n[上初9②Y=f(x2,x1)3Y=flX1X30.8841(62.4859)0.036VB0.3882W0.133337O.OE32O61X40.4872-0.0060U-0141剖的3口伽诩1

0.0J7643Cl/859耳二CL44甲枷如丁」iR2nmn0.2711040.99527904.21687^0.001■□■961529__0:353-4.7890840.997?.47]O3J34(justedR-scy.E.ofregresY==f(X2iX4)SquaredLuglikElihcwdY=f(X2ixb)n-Watsci(4.3234)二0.8066惟阈14)希瞩1resid(14.5003)(3.5394)二=二0.9990^.^.05^1dependentvar1i.5?63P・

bAkai8Sch\-1勇.此98__F-stM%45?1)0.9986791.0421'107752dependevarzcntentvartenonrion0.99525^632499.7450®W81一.3?711,3951.881910Prob(F-statistG0.00590.99152)000J(21.4465)(-1.0680)⑥Y=f(x2,x1,x3)0.44990.44220.00640.9968(3.5366)(2.9742)(0.1993)⑦Y=f(x2,x1,x4)0.4911(4.2748)0.4433(3.4857)-0.0039(-0.6347)0.9969⑧Y=f(x2,x1,x5)0.5025(3.6357)0.4073(3.1797)-0.0010(-0.2042)0.9969⑨Y=f(x2,x1,x3,x4)0.9064(7.1493)0.0169(0.1288)0.4119(4.6567)-0.0822(-4.7150)0.9987⑩Y=f(x2,x1,x3,x5)0.4710(2.7820)0.4524(2.7921)-0.0051(-0.0758)-0.0020(-0.1983)0.9966(11)Y=f(x2,x1,x3,x4,x5)0.9837(6.5395)0.0362(0.2711)0.3882(4.2169)-0.0845(-4.7891)-0.0060(-0.9615)0.9987注：表中数字为估计的回归系数及其T统计量值经过反复的引入-检验-剔除，最终确定理想模型为Y=-287.6866944+0.4871854249*X2+0.4158668957*X1t(101.2341)(0.112687)(0.117497)t=(-2.841797)(4.323352)(3.539376)R2=0.997358，F=3208.727，prob(F)=0.000000DW=0.692473此模型经济意义合理，可决系数为0.997358，接近于1，表明模型对样本拟合优度高；F统计量为3208.727,其伴随概率为0.000000，接近于零，表明模型整体线性关系显著；回归系数显著，在给定显著性水平=0.05下模型虽不存在高阶自相关，但存在一阶自相关，为此运用广义差分法调整模型，估计结果如下：EViews-[Equation:UNTITLEDTorkfile:3-17\UntHIIFileEditObjectViewFrocQuickO^tionsWindowHelp日叫Print|阻mm|Fr能Esti顽Rmnid』DependentVariable:YMethod:LeastSquaresDate:12/30/10Time:05:38Sample(adjusted):19791997Includedobservations:19afteradjustmentsConvergenceachievedafter10iterationsVariableCoefficientStd.Errort-StatisticProb.WhiteHeteroskedasticitvTest:-214：1609162.8584-1.3150130.20830.5155820.1189794.333368J.0006一一一>20.3758790.1164933.2266350.0056F-statisticar.)。.90054匏2翱词岫的063133.12^548y/63,0069Obs*R-squared3888230Probability0421344R-squared0.998626Meandependentvar5308.474AdjustedR-squared0.998351S.D.dependentvar2480.737S.E.ofregression100.7230Akaikeinfocriterion12.24729Sumsquaredresid152176.9Schwarzcriterion12.44612Loglikelihood-112.3492F-statistic3634.613Durbin-Watsonstat1.589374Pmb(F-statistic)0.000000Y=-214.1608725+0.5155815658*X1+0.3758793163*X2+[AR(1)=0.5825343132](162.8584)(0.118979)(0.116493)(0.186313)T=(-1.315013)(4.333368)(3.226635)(3.126638)R2=0.998626，R2=0.998351F=3634.613，prob(F)=0.000000DW=1.589374调整后模型经济意义合理，调整的可决系数R2有所改善，达0.9984,接近于1,表明模型对样本数据拟合较好；F统计量为3634.613，其伴随概率为0.000000，接近于零，表明X1和X2共同对被解释变量有显著影响，模型总体线性关系显著；解释变量各自的回归系数均显著，且AR(1)项回归系数也显著，表明回归模型确实存在一阶自相关；调整后模型经再检验已不存在一阶自相关。利用White检验，得辅助回归模型的nR2=3.888230，prob(nR2)=0.421344小于给定的显著性水平=0.05，表明调整后模型也不存在异方差。模型估计结果说明，钢材产量Y主要取决于生铁产量七和发电量气，在其他因素不变的情况下，生铁产量七每增加1万吨，钢材产量Y增加0.5156万吨；在其他因素不变的情况下，发电量气每增加一亿千瓦时，钢材产量Y增加0.3759万吨。例5.服装需求函数。根据理论和经验分析，影响居民服装需求Y的主要因素有:可支配收入X、流动资产拥有量K、服装类价格指数P1和总物价指数P0，统计资料如下。设服装需求函数为：Y=a+b1x+b2P1+b3P0+b4K+e服装需求可支配收入流动资产拥有量服装类价格指数总物价指数YXKP1P019798.482.917.1929419809.68821.39396198110.499.925.19697198211.4105.3299497198312.2117.734100100198414.213140101101198515.814844105104198617.9161.849112109198719.3174.251112111198820.8184.753112111要求:(1)多重共线性检验运用①相关系数、②辅助回归模型以及③方差膨胀因子检验服装需求回归模型的多重共线性的可能类型；(2)逐步回归法根据相关分析，建立服装需求一元基本回归模型根据逐步回归原理，建立服装需求模型答案：⑴多重共线性检验①相关系数检验键入：CORYXKP1P0输出的相关系数矩阵为：EViews-[Group:GROUP02Torkfile:UNTITLED]IIFileEditObjectsViewProcsck0p.+iotleWiruluwHelpView^|Procs^lCTbj§cts■Bint]Earne[Fr巽ze|SampleISheetIStatsISpec|YXKP1P0Y1.0000000.9977910.9833590.9754800.988705X0.9977911.0000000.9882640.9804160.987785K0.9S33590.9S82641.0000000.9699620.969477P10.9754800.9804160.9699621.0000000.991796P00.9887050.9877850.9694770.9917961.000000由上表可以看出，解释变量之间相关系数至少为0.969477大于0.8,表明模型存在严重的多重共线性，且解释变量都与服装需求Y高度相关。②辅助回归模型检验③方差膨胀因子检验:操作命令：建立可支配收入X对其他解释变量的辅助回归模型LsxcKP1P0X=-221.5036+1.5264K-1.0540P1+3.9467P0R2=0.992164，F=253.2420，prob(F)=0.000001F统计量其伴随概率为0.000001小于a=0.05，表明模型存在严重多重共线性方差膨胀因子检验GenrVIF1=i/(i-0.992164)VIF1=1/(1-R2)=1/(1-0.0.992164)=127.6161,TOL1=1/VIF1方差膨胀因子(VIF)大于10,表明模型存在严重多重共线性操作命令：建立流动资产拥有量K对其他解释变量的辅助回归模型LsKcxP1P0K=52.5175+0.4434X+0.7331P1-1.4518P0R2=0.981982，F=108.9972，prob(F)=0.000013F统计量其伴随概率小于a=0.05，表明模型存在严重多重共线性方差膨胀因子检验GenrVIF2=1/(1-0.981982)VIF2=1/(1-R2)=1/(1-0.981982)=55.5000555001,TOL2=1/VIF2方差膨胀因子(VIF)大于10，表明模型存在严重多重共线性操作命令：建立服装类价格指数P1对其他解释变量的辅助回归模型LsP1cxKP0P1=-31.2521-0.0917X+0.2196K+1.3415P0

R2=0.986309,F=144.0798，prob(F)=0.000006F统计量其伴随概率小于a=0.05，表明模型存在严重多重共线性方差膨胀因子检验GenrVIF3=i/(i-0.986309)VIF3=1/(1-R2)=1/(1-0.986309)=73.0406836608,TOL3=1/VIF3方差膨胀因子(VIF)大于10，表明模型存在严重多重共线性操作命令：建立总物价指数P0对其他解释变量的辅助回归模型LsP0cxKP1P0=42.7011+0.1234X-0.1563K+0.4820*P1R2=0.992102,F=251.2234，prob(F)=0.000001F统计量其伴随概率小于a=0.05，表明模型存在严重多重共线性方差膨胀因子检验GenrVIF4=1/(1-0.992102)VIF4=1/(1-R2)=1/(1-0.992102)=126.614332742,TOL4=1/VIF4方差膨胀因子(VIF)大于10，表明模型存在严重多重共线性上述辅助回归模型的F统计量，其伴随概率均接近于零，表明模型存在严重多重共线性，这一结论也可通过各方差膨胀因子(VIF)均大于10中得到。(2)逐步回归法①建立服装需求一元基本回归模型由相关系数图表可知，收入与服装需求的相关性最强，所以，以Y=a+bX+e即Y与X的一元线性回归模型，作为服装需求基本回归模型，Lsycx估计结果如下:fEVievs-[Equation:EQ04lorkfile:UNTITLED]FileEditObjectsViewFrocsQuickOptionsWindowHelpViewProcsIObjsetsPrint|N：=mieFreezeEstimateForecastIStatsResidsIDependentVariable:YMethod:LeastSquaresDate:03/21/11Time:10:03Sample:197919SEIIncludedobservations:10VariableCoefficientStd.Errort-StatisticProb.C-1.2488730.371488-3.3618140.0099服装需求元基本回归模型为0.00277542.486040.000014.000004.3011630.6269560.687473掰腭黑14.000004.3011630.6269560.687473掰腭黑489曷。.117鬻墨

S.E.ofregression_0.303040S.D.dependentvar7AkaikeinfocriterionTumsquaredresid(42.48.6°)63SchwarzcriterionR2=0扇5588h口口R2=0.9950§634F=1805掴6衲cprob(F)=0.00000063Durbin-Watsunstat2.ti：zlH544Prubi'F-statistic)LI.LIUULIUU②根据逐步回归原理，建立服装需求模型以上述一元线性回归模型为基本模型，顺次引入其他变量估计二元回归模型，结果如下：LsycxKLsycxP1LsycxP0?!■EViews-[Equation:EQ05lorkfile:UHTITLED]FileEditObjec15ViewProcsQuickOptionsWindowHelpVi即|Frouw|CMctw■Frint|ITamm|Fr金二日|Ewtim「to|F『Emiewt|Strtw|REwidw|DependentVariable:YMethod:LeastSquaresDate:03/21/11Time:10:04Sample:19791988Includedobservations:10VariableCoefficientStd.Errort-StatisticProb.C-1.6013030.612419-2.6147180.0347X0.1315130.0187077.0302020.0002k-nD38786n052630-n736961□4051EVie»s-[Equation:EQ06Torkfile:UNTITLED]□FileEdi+0bjecteViewFroce^[uickOp.tioreWindowHelpView|Fr(|Ob」ects|Fsint.|Name|Frei工旦|E5t.ima±H|Fir」3a^t.|st.at..|Resi|DependentVariable:YMethod:LeastSquaresDate:03/21/11Time:10:05Sample:19791988Includedobservations:10VariableCoefficientStd.Errort-StatisticProb.C1.5262374.8567210.3142530.7625X0.1261620.0147218.5703730.0001P1-0.0378100.065959-0.5732290.5844R-squared0.995785Meandependentvar14.00000AdjustedR-squared0.994581S.D.dependentvar4.301163S.E.ofregression0.316618Akaikeinfocriterion0.781082Sumsquaredresid0.701728Schwarzcriterion0.871858Loglikelihood-0.905412F-statistic826.9501Durbin-Watsonstat2.533749Prob(F-statistic)0.000000EVicts-[Equation:EQ07Torkfile:UWTITLED]^3FileEditObjactsViewProcsQuickO^tioniWindowHelpView|Frees|Objacts|Print.|Wame|FreezeBEst.imat.a|Foraca5t|Stat5|RasidsjDependentVariable:YMethod:LeastSquaresDate:03/21/11Time:10:06Sample:19791900Includedobservations:10VariableCoefficientStd.Errort-StatisticProb.C-8.0595058.206596-0.9820760.3588X0.1029840.0181635.6700880.0008P00.0856720.1031220.8307830.4335R-sc经比较可知，新加入K的曲归模型rY=f(X»K)，K.的回归系数为负，不符合魏的经济意义且T检验不通过；新加入薄的回归模型法f"1)及新加入P0的阿卿模型Y=f(x,P0)虽鲫和P0c回归系i数的T检验均不通过，但经济意义合理，Loglikelihood-0.664594F-statistic867.9263由于Y缎X,P0*的调整判定系数煎2值略高于Y=f(x,P1)，因此，Y=f(x,P0)估计的结果为最优的二元回归模型，以此为基础，建立三元回归模型:LsycxP0KLsycxP0P1EVios-[Equation:EQ08Torkfile:UNTITLED]I:FileEditObjectsViewProcsQuickOptionsWindowHelpView|Frocw|Dbjectw.Frint|Uajne|FreeHe.Ewtimale|FQrecawt|St8tsIResids|DependentVariable:YMethod:LeastSquaresDate:03/21/11Time:10:09Sample:19791988Includedobservations:10VariableCoefficientStd.Errort-StatisticProb.C-7.0408828.917396-0.7896670.4598X0.1159270.0321533.6054900.0113P00.0695590.1137370.6115820.5633K-0.028S660.057490-0.5021140.6335R-squared0.996146Meandependentvar14.00000AdjustedR-squared0.994218S.D.dependentvar4.301163S.E.ofregression0.327049Akaikeinfocriterion0.891758Sumsquaredresid0.641765Schwarzcriterion1.012792Loglikelihood-0.458790F-statistic516.8819Durbin-Watsonstat3.301000Prob(F-statistic)0.000000EViews-[Equation:EQ09Torkfile:UWTITLED]FileEditObjectsViewFrocsQuickOptionsWindowHelp¥iew|Frocs|Objects■Frint|lTaine|Free：Ee・Estima±e|Fcirec:ast|Stats|Resids|DependentVariable:YMethod:LeastSquaresDa