試驗(yàn)五多重共線性檢驗(yàn)參考案例

1、實(shí)驗(yàn)五多重共線性檢驗(yàn)實(shí)驗(yàn)時(shí)間：姓名：學(xué)號(hào)：成績(jī)：【實(shí)驗(yàn)?zāi)康摹?、掌握多元線性回歸模型的估計(jì)、檢驗(yàn)和預(yù)測(cè)；2、掌握多重共線性問題的檢驗(yàn)方法3、掌握多重共線性問題的修正方法【實(shí)驗(yàn)內(nèi)容】1、數(shù)據(jù)的讀取和編輯；2、多元回歸模型的估計(jì)、檢驗(yàn)、預(yù)測(cè)；3、多重共線性問題的檢驗(yàn)4、多重共線性問題的修正【實(shí)驗(yàn)背景】為了評(píng)價(jià)報(bào)賬最低工資（負(fù)收入稅）政策的可行性，蘭德公司進(jìn)行了一項(xiàng)研究，以評(píng)價(jià)勞動(dòng)供給（平均工作小時(shí)數(shù)）對(duì)小時(shí)工資提高的反應(yīng)，詞研究中的數(shù)據(jù)取自6000戶男戶主收入低于15000美元的一個(gè)國(guó)民樣本，這些數(shù)據(jù)分成39個(gè)人口組，并放在表1中，由于4個(gè)人口組中的某些變量確實(shí)，所以只給出了35個(gè)組的數(shù)據(jù)，用于分

2、析的各個(gè)變量的定義如下：Y表示該年度平均工作小時(shí)數(shù)；X1表示平均小時(shí)工資（美元）；X2表示配偶平均收入（美元）；X3表示其他家庭成員的平均收入（美元）；X4表示年均非勞動(dòng)收入（美元）；X5表示平均家庭資產(chǎn)擁有量；X6表示被調(diào)查者的平均年齡；X7表示平均贍養(yǎng)人數(shù)；X8表示平均受教育年限。N為隨機(jī)干擾項(xiàng)，考慮一下回歸模型：Y=01X12X2-3X34X45X56X67X7-8X8（1）將該年度平均工作小時(shí)數(shù)Y對(duì)X進(jìn)行回歸，并對(duì)模型進(jìn)行簡(jiǎn)單分析；（2）計(jì)算各變量之間的相關(guān)系數(shù)矩陣，利用相關(guān)系數(shù)法分析變量間是否具有多重共線性；（3）利用逐步回歸方法檢驗(yàn)并修正回歸模型，最后再對(duì)模型進(jìn)行經(jīng)濟(jì)意義檢驗(yàn)、統(tǒng)計(jì)

3、檢驗(yàn)表5觀測(cè)組YX1X2X3X4X5X6X7X8121572.9051121291380725038.52.3410.5221742.971128301398774439.32.33510.5320622.351214326185306840.12.8518.9421112.511120349117163222.41.15911.5521342.79110135947301271057.71.2298.8621853.04113528738277638.62.60210.7722103.22211002954749338392.187112821052.4951180310255473039.

4、92.6169.3922672.8381298252431831738.92.02411.11022052.356885264373648938.82.6629.51121212.9221251328312590739.82.28710.31221092.4991207347271506939.73.1938.91321082.796103630025946141420472.4531213397139198740.32.5459.11521743.582114141449810239402.06411.71620672.9091805290239443939.12.301

5、10.51721592.5111075289308562139.32.4869.51822572.5161093176392729337.92.04210.11919851.423553381146186640.63.8336.62021843.63610912915601124039.12.32811.62120842.9831327331296565339.82.20810.22220512.57311972791722806402.3629.12321273.2631226314408804239.52.25910.82421023.2341188414352755739.82.0191

6、0.72520982.28973364272440040.62.6618.42620422.3041085328140173941.82.4448.22721812.91210723043839340392.33710.22821863.015112230352729237.22.04610.92921883.01990366374732538.42.84710.63020771.90135020995137037.44.1588.23121963.009947294342688837.53.04710.63220931.899342311120142537.54.5128.13321732.

7、9591116296387762539.22.34210.53421792.9591116296387762539.22.34210.53522002.981126204393788539.22.34110.6【實(shí)驗(yàn)過程】-、利用Eviews軟件建立年度平均工作小時(shí)數(shù)y的回歸模型。（一）首先創(chuàng)建Workfile（命令窗口輸入CreateU,再輸入35個(gè)樣本觀測(cè)值），其次輸入數(shù)據(jù)Y,X1,X2,X3,X4,X5,X6,X7,X8(命令窗口DataYX1X2X3X4X5nX6X7X8）將上述表格中的數(shù)據(jù)復(fù)制粘貼到數(shù)據(jù)窗口中匚叵區(qū)IView|ProcObjMtlRW15ave|Detafe+/-|S

8、how|Fetch|5tore|)etetBi|Gsflr|5ampla|WorWilestructuretypeunsfructuredIUndatedlDatarangeObservations;卜5/庶angu:135-33口bwSamp厄:1箝-一5口必必residDi&playFilter*IrregularDatedandPan國(guó)workFlesnnaybemadefromUnstructuredbylaterEpeofdataaix|/arodiBridentifierseries.Names(optionaOWF：LCancelPage;<:'umnije

9、u£new戶wga/口e二MffTITLED:Tintit1ed1;叵岡Vte掰Proc|Qbjed:用閨（婦對(duì)舊Freeze|Default5art|Transpose|Edt+/-|5mph-J-|na2157口MS丫KIK?鞏KW|iifewPr«|otOiMtFtinftr-tarre-Rteze|H刁Sort1215.0叫2.9Q50Q01121000291.0000390.0(422174.0002.97000011211DOO301.0000390.QII32062.0002.50000121<ooo326.0000IBS.OtubsJ1WMAc2111

10、.0002.51100J1203.DD049.00000117.0(3NANX52134.00027910001(113m594.0000730.0(3NA它2163,0003.04100001保血白297.00003S2.0(HANA72210.0003.222000_10CJDD295.0000m5nAM.fiNAMA.92105.0002.49500011S0DOO310.0000255。7NAg2267.QQO2.838Q001-ODO252.000Q431.01eNAMAia2205.0002.3560008陋DODO264.0000373.01!jNAF-4Aii212100029

11、220001251UM3290000313UC10N居NA122109.0002.49900012C7ODO34J.Q000271.0«itNANA12hiA1321oe.ooo2.7960001O30JDDD300.i：ii：ii：ii：i259.0(13NANAUla.ooo24530001211000397QOOQ139QCNANA152174.0003.5320001U1000414.0000498.0(15NANA1621Kzmcl2.9090(101905DOO290.0000239.0(HAP4A.172159.ann3.5110001075aaa299,0000309

12、.0117NANA1BNJMb19”仃nnn7#;iRntfininoqmnni7ftnnnnqQ7nr*1ac>.hi.（二）進(jìn)行OLS回歸命令窗口輸入命令LSYCX1X2X3X4X5X6X7X8CimTTTTFDWnrkfilR：njnTTJ.ED:llnti11edk|L|C|Xj如.|FiulCbR|FrHjhlanu|F,ee£e巴寸1趾七|Furu-E.|Slat*FjesiciDppcnd«irVadabl»:YMethod.LesisquaresDate;DBfi7/i3Uma7,口？Sample135InrluriprlobsPlatini

13、s-P.VariableCoeflcieritStjErrortStatisticPmbC2204.5611272e01955695O.OCOOXI-24TOSIg2£33K4-0.93611D0.3560X2OJO3O7331,039043U.7SM7DJ.4JtJ心-0576150.C95S2O2.6S573D00124Xi0JSB5T990.1307754.4fS42?o.aooi乂60.00027：0.00677.0,06S25?0.3640K&5.4TD3門2,59222205124U.0498X7ae.aoaEi16,167201.8B3E7T0.0737X60.

14、0J92590.3423220.IHT130.9090frsquared797133Meanjepndentr2i37.caeArfjiltPciR-squarAd7M7I2SDrl?ppndlpnlvarGd11547SE.Qfregie&siun33.02355Alk'ikEinftiicrrteriur104934SumiiuarlrpsicJ26354峭SchfWHt?rritpricn1044929Logllkeliihood-166.6535Hann&n-Ciuinncriter.1DL1O74OF聞洲stk1277033Durbir-atscnsial1.

15、67S491PobiF-sladgiic)OjOOOOIO從表中可以看到，模型可能存在多重共線性。因?yàn)閿M合優(yōu)度較高，F(xiàn)統(tǒng)計(jì)量對(duì)應(yīng)的P值小于1%,說明回歸方程是顯著地，回歸系數(shù)X3,X4,X6,X7在10%的水平下顯著，其他回歸系數(shù)的t統(tǒng)計(jì)量對(duì)應(yīng)的P值大于0.1,是不顯著變量，說明解釋變量可能存在多重共線性。二、多重共線性的檢驗(yàn)1、簡(jiǎn)單相關(guān)系數(shù)法這種方法只適用于只有兩個(gè)解釋變量的情況。當(dāng)這兩個(gè)解釋變量相關(guān)系數(shù)的絕對(duì)值很大時(shí)，認(rèn)為這兩個(gè)解釋變量存在共線性。操作：QuickfGroupstatisticsCorrelations7對(duì)話框x1x2x3x4x5x6x7x8fok,得到關(guān)于上述8個(gè)變量之間

16、的相關(guān)系數(shù)矩陣?？贖KII.correlation即X2網(wǎng)xaX7xeXI1COQQQQQ5711140C3K39O7Q231S，Q65351237EM*Q71114-.QOC0W-0.025871Q£33:2踹0.2X5BC5-CLEM54Q-07002£00.043C870班招電-0.026574l.tMMDO051O3040.23。簽40.771151i3j053455-0,M1462心D/tflJL*U3翔BUiiMU3的1OOOULtJ0.911削U0SU割上D孫mJ22占的1H50訓(xùn)1。U2期期i儂：H001191111OUOlOO040Jl)2T&ST

17、lGifl(1ZI0M7ME014155607T115T口刖日*040QF271linnooo加0511&3-0D91S33a?<6035364a7LQ3600.D53455-(15311974城5i汨30-DOSHS31OOOOIM-nnssj?X0D2370350DWORT0.031*5?00230597-0D31633-D1J252r1OOQIJOO<>從上表結(jié)果可以看出，有幾個(gè)解釋變量，如x1和x4之間，x1和x5之間,x3和x6之間簡(jiǎn)單縣官系數(shù)都在0.7以上，x4和x5的相關(guān)系數(shù)在0.9以上，說明這些變量之間都具有很強(qiáng)的相關(guān)性，存在多重共線性。二、多重共線性

18、的修正方法（一）逐步回歸法逐步回歸法的“逐步”指的是使用回歸分析方法建立模型時(shí)，一次只能引入一個(gè)解釋變量，進(jìn)行一次引入稱為“一步”，這樣逐步進(jìn)行下去，直到最后得到的模型達(dá)到“最優(yōu)”（模型中沒有不顯者的變量）。1、找出最簡(jiǎn)單的回歸形式（對(duì)每個(gè)自變量與因變量y進(jìn)行回歸）從而決定解釋變量的重要程度，為解釋變量排序，即分別作作y對(duì)x1,x2,x3,x4,x5,x6,x7,x8的一元回歸，結(jié)果如下:一?；貧w結(jié)果（被解釋變量為y）解釋變量X1X2X3X4X5X6X7X8參數(shù)估計(jì)值77.3690.031-0.1910.3190.014-1.137-33.9530.89T統(tǒng)計(jì)量3.8360.710-1.724

19、5.3114.780-0.450-2.1131.42修正R20.287-0.0150.0550.4450.391-0.0240.0940.02DependenrtVariabie:YMeihod:LeastSquaresDale:06rD7H3Time:22:24Sample.135Includedobservations:35VariableCoefficientStd.ErrorbStatisticProt,C1924.961660691734330110.0000X177.3608220166713.5354620.0005FJ-squared0306443Meandependentva

20、r2137.066AdjustedR-squared0287487S.D.dependentvarG411542SEotregressionS4.12013Akaikeinfocriterion10.87573Sumsquaredresid96656.61Schwarzcriterion1096461Leglikelihood-196.3254Hannan*Qulnncriler.10,90641F-statistic14,71844Durtoln-Watscnstat1.3393.39F*rob(F-statisiic)O.D00534DependentVariable:YMethod:Le

21、astSquaresDate:06J07H3Time:22:25Sample:135includedobservations:35VariableCoefficientStd.ErrortStatisticProbC2101B9947.9959743834910.0000X20.0306320.0431400.7100620.4827R&quared0.015049Meandependentvar2137.086AdjustedR-squared-0014798S.D.dependentvar64.11542S.E.ofregression6453G08Akaikeinfocriter

22、ion1122938Sumsquarednesid1371663.5Schwarzcriterion11.31826Loglikelihood-1945142Hannan-Quiinncriter.1126006F-statistic0.504188Durbin-Watsonstat2.158644Prob(F-statistic)0.462663根據(jù)R2的大小排序，課間解釋變量的重要性程度依次為：x4,x5,x1,x7,x3,x8,x6,x2;2、以x4為基礎(chǔ)，進(jìn)行逐步回歸，依次引入變量x5,x1,x7,x3,x8,x6,x2加入新變量的回歸結(jié)果（一）解釋變量X1X2X3X4X5X6X7X8

23、x4,x50.2760.002Rt值1.7950.303x4,x121.7260.8670.2683.1640.440t值x4,x70.3241.5371.9990.1360.428t值x4,x3-0.367-5.7630.3998.8870.719t值x4,x80.3094.9770.3430.7000.436t值x4,x60.4518.516-8.168-4.9690.677t值x4,x2-0.009-0.2830.63235.1580.429t值經(jīng)過比較，新加入x3的方程其R2=0.719改進(jìn)最大，從0.445增力口至IJ0.719,而且各參數(shù)經(jīng)濟(jì)合理，t檢驗(yàn)顯著，選擇保留x3,以此x4

24、,x3兩變量為基礎(chǔ)，再進(jìn)行逐步回歸，力口入x5,x1,x7,x8,x6,x23、以x4,x3為基礎(chǔ)，加入x5,x1,x7,x8,x6,x2R0.0.0.加入新變量的回歸結(jié)果（一）解釋變量X1X2X3X4X5X6X7X8x4,x3,x5-0.368-5.6664233.756-0.001-0.228t值x4,x3,x1-6.077-0.325-0.372-2.2620.4156.258t值x4,x3,x7-0.398-6.2540.4548.64419.0821.849t值x4,x3,x8-0.364-5.6110.3958.4030.1270.3590.711t值x4,x3,x6-0.257-

25、2.7350.4338.864-3.540-1.5660.731t值x4,x3,x2-0.024-1.023-0.374-5.8440.4118.8610.719t值-經(jīng)比較，新加入x7的方程，其擬合優(yōu)度R2=0.739有所改進(jìn)，從0.719增至0.789,而且各參數(shù)經(jīng)濟(jì)意義合理，t檢驗(yàn)顯著，所以選擇保留x7.在x4,x3,x7的基礎(chǔ)上，逐步加入x5,x1,x8,x6,x2R.0.加入新變量的回歸結(jié)果（一）解釋變量X1X2X3X4X5X6X7X8x4,x3,x7,x5-0.398-6.1390.4694.201-0.007-0.14619.0061.811t值x4,x3,x7,x

26、15.8260.304-0.394-5.9990.4436.73020.2361.816t值x4,x3,x7,x8-0.395-6.0870.4508.23618.9851.8120.1090.319t值x4,x3,x7,x6-0.271-3.0560.5028.980-4.213-1.95521.8642.191t值x4,x3,x7,x20.0090.289-0.340-6.1560.4588.35021.9511.520t值經(jīng)比較，新加入x6的方程，其R2=0.761有所改進(jìn)，從0.739增至0.761,而其各參數(shù)經(jīng)濟(jì)意義合理，t檢驗(yàn)顯著，所以選擇保留x6.再依次加入變量x5,x1,x8,

27、x2進(jìn)行回歸，發(fā)現(xiàn)回歸結(jié)果R2都沒有改進(jìn)，而且各變量的t檢驗(yàn)不顯著，從而說明加入任何一個(gè)變量都無法對(duì)模型有任何改善，所以應(yīng)予以剔除。tian:IIJ1T1TLEDInrkfile:TRTITLED:Hn.j|X陸固|Proc|ebject|PrinA|Mame|Free詞E比in«MFarctestStatiResidsDependentVariable:YMelhodLestSquaresDate:06/07/13Ume:23:27Sample:135Includedobservalicms:35VariableCDemcientstd.ErrortsiatisiicProbC21

28、66482665005333.075790.0000溺0.5225860.1088694000125Q.00D0X3-0.27233501090169-3.0202900.0052X722.3343710,306112.167099003B6X6-42600a52.199739-1.93G9140.063bX5-0.0008780.004447-0.1S74040.8449R-squared0789501Meandependentvar2137.086AdjustedR-squared0753208S.D.dependentvar64.11542SE.ofregression3185138Ak

29、aikeinfocrilerion9.914944Sumsquaredresid29420.81Schwarzcriterion10.18147LoglikfillhDOd-1B7.500BHannan-Quiinncriier.lO.aOBBfiF-statistic2175353Durbin-Watsonstat1.633161Prob(F-statis1ic)0.000000一.uation:nUTITLEDWorkfilt1;:UKTITLED:na«XView|ProcObjectPrin匕.Name|Frg日zeEstimateForecastStatsResidsDep

30、andentVariable:YMethod.Lea5tSquaresDate：06/07/13Time：23:27Sample:135Includedobseratians:35VariableCoefficientStd,Errort*StatisticProb,C9.35510&259720866700.0000X40.5336300.0730146.9030910.0000X3-0,25956701.091650-2.825Q960.0034X720.3044610747351.8892530.0689X6-4,9243742439510-3.0185920.0529XI-13

31、.1005620.43712-0.6410180.5206R'SCjuaredU.79216JMeanidependentvar2137.0S6AdjustedR-squared0755329S.D.dependerrtvar54.115d2S.E.ofregression31.64934Akaikeinfocriterion9.902117Sumsquaredresid29048.74Schwarzcriterion10.16S75Loglikellhnod-1C7,5G70Hanmari-QLinncriter,9.95415GF蜀葡Stic22,10644Ourbin-WatsQ

32、nstat1670657Prob(Ffistic)TQQQQMViewPro。ObjectPrintNmeFreezeEstimateIForecast50t$Re5idsDependentVariable:YMethod:LeastSquaresDate:06/07/13Time:23:26Sample:135Includedobservations:35VariableCoefficientStd.Errort-StatisticProbC2164.69765.9770332,809860,0000X40.5033560.0592653.4933130.0000X3-0.2726890.0

33、90246-3J216200.0052X722.3774710.317442.1688980.0384X641g52432.211420-1.8070730.0676XS00204710.3297130.0620390.9509R*squared0769246Meandependentvar2137.086AdjustedR-sqjared0.752909S.D.dependentvar64.11542S.E.atregression3167066Akaikeintocriterion9.916053Sumsquaredresid23456.42Schwarzcriterion10.19266

34、Loglikelihood-167.5309Hannan-Quiinncriter1000809F-statlstic21.72021Durbin-Watsonstat1.641562ProbfF-statistic)0000000ion:UNIIILED¥©rkfile:BITITLED:iE叵兇ViewProcObjectPrintbkrrteFreezeEstimateForecast5白匕口魔引叫DepandentVariable:YMethodLeastSquaresDate:06/07/13Time.23:23SaiYiple:135Includedcbsery

35、ations:35Vri3bleCoefficientStd,Errort-StatisticPrab.C2146.21090.0040523.645700.0000乂40.5092250.069£530.G654320.0000X3-0,2754270.090552-3J4130700050X725.4754414.331371.77753700660XS-4.1954332.186447-1.91929400648X20.0094800.030836130744707607R-squared0.789903r/ieanidependentvar2137086AdjustedR-s

36、quared753679S.D.dependerrtvar94.11542SE.ofregression31.62096Akaikeinfocriterion9.912932Sunnsquaredresid29364.63Schwarzcriterim10.17956Loglikelihood-167,4763Harinari'Quinncriter.10.00497F-statlstlc21.60625Durbin-Watsonstai1.5296S2Prob(F-statistic)0.000000最后修正嚴(yán)重多重共線性后的回歸結(jié)果如下圖口£ViewProcObjectD

37、ependentVariMethod:LeastEDate:0B/07/13Sample:135IncludedobserPrint|Nameable:YciuaresTime:23:"ations:35FreezeE比Forecast53bResidsVariableCoefficientStd.ErrorC21652S764.17201X40.5043040.056307X3-0,2725470.08870i6X7224082110.13301X6-42147272152400t-StatiSticProb.33.742090.00008.9563210.0000-3.07245

38、90.00452.2114070.034S-195815200596R-squared0,7S9218Meandependentvar2137.086AdjustedR-sqJared0,7S1114S.Ddependentvar64.11542S.Eofregression31.33705Akaikeinfocrrterion9.369044Sumsquaredresid29460.34Schwarzcriterion10.08124Loglikelihood-167,5333Hannan-Quiinncriter9.935744F-statistic23.06175Durbin-Watso

39、nstat1638183ProbfF-statistic)0000000回歸方程為y=2.2165.2970.504*x4-0,273*x322,408*x7-4,215*x6t值33.7428.956-3.0722.211-1.958p值(0.000)(0.000)(0.005)(0.035)(0.060)R2=0.789F=28.082D.W.=1.638從回歸估計(jì)結(jié)果可以看出，x4,x3都通過了1%的顯著性檢驗(yàn)，x7通過5%的顯著性檢驗(yàn)，x6通過10%的顯著性檢驗(yàn)，說明模型參數(shù)顯著，而且擬合優(yōu)度為0.789,F統(tǒng)計(jì)量也很大，說明整體回歸線性關(guān)系顯著。經(jīng)濟(jì)意義說明：在其他條件不變的情況下，其他家庭成員的平均收入x3每上漲1美元，則年度工作時(shí)數(shù)平均減少0.27小時(shí)；年均非勞動(dòng)收入x4每上羽美元，則年均工作時(shí)數(shù)平均增加0.50小時(shí)；被調(diào)查者的平均年齡x6每增加1年，則年度工作時(shí)數(shù)平均減少4.21