EViews计量经济学实验报告-多重共线性的诊断与修正的讨论

实验题目多重共线性的诊断与修正一、实验目的与要求：要求目的：1二、实验内容根据书上第四章引子“农业的发展反而会减少财政收入，197－2007业增加值等数据，运用EV三、实验过程:（实践过程、实践所有参数与指标、理论依据说明等)（一)模型设定及其估计研究“农业的发展反而会减少财政收入”这个问题。1设定如下形式的计量经济模:Y=+ X+ X + X + X + X + X +1i 2 2 3 3 4 4 5 5 6 6 7 7 i其中，Yi

为财政收入CS/亿元；X2

为农业增加值NZ/亿元；X3

为工业增加值GZ/亿元；X4

为建筑业增加值JZZ/亿元；X 为总人口TPOP/X5

为最终消费CUM/亿元；X7

为受灾面积SZM/千公顷。图1： 1978~2007年财政收入及其影响因素数据年份 亿元

农业增工业增加加值值GZ/亿NZ/亿元元

建筑业增加值JZZ/亿元

总人口TPOP/万人

最终消费受灾面CUM/亿元千公顷19781132。31027。51607138。2962592239。15079019791146。41270。21769。7143。8975422633.73937019801159.91371.61996.5195。5987053007。94452619811175.81559.52048。4207。11000723361。53979019821212.31777。42162。3220。71016543714.833130198313671978。42375。6270.61030084126。43471019841642。92316.12789316。71043574846。33189019852004。82564。43448.7417。91058515986。344365198621222788.73967525.71075076821.84714019872199.432334585。8665.81093007804.64209019882357.23865。45777。28101110269839.55087019892664。94265.9648479411270411164。24699119902937。150626858859.411433312090。53847419913149。485342。28087。11015。111582314091.95547219923483。375866。610284.5141511717117203。35133319934348.956963。8141882266。511851721899.94882919945218。19572。719480。72964。711985029242.25504319956242.212135824950。63728.812112136748。24582119967407.9914015429447。64387。412238943919。54698919978651.1414441932921。44621。612362648140.65342919989875。9514817.634018.44985。812476151588.250145199911444.081477035861。55172.112578655636。949981200013395.2314944.7400365522。31267436151654688200116386.0415781.343580.65931。712762766878.352215200218903641653747431.36465.512845371691.2471192003217152517381754945.57490.812922777449。55450620042639647214127652108694.312998887032。937106200531649.292242076912.910133813075696918.138818200638760.22404091310。9118511131448110595.3410912007513217828095107367.2140141132129128444648992EVY、XX、X、X、XX等数据，采用这些数据对模型进行OLS回归。i 2 3 4 5 6 7(二)诊断多重共线性1EviewFile/Open/EVWorkfil—Excexls2、在EVlsycx2x3x4x5x6xEnteOLS：图2： OLS回归结果DependentVariable:YMethod：LeastSquaresDate:10/12/10 Time:Sample：19782007Includedobservations：30Variable

Coefficient Std

t—Statistic Prob.C—6646。6946454。156—1.0298320。3138X2-0.9706880.330409—2。9378410。0074X31.0846540。2285214。7463970.0001X4-2.7639282.076994—1。3307350。1963X50。0776130.0679741。1418080。2653X6-0.0471190。081509-0。5780840.5688X70.0075800。0350390.2163290。8306R-squared0。994565Meandependentvar10049.04AdjustedR-squared0.993147S.D.dependentvar12585。51S.E.ofregression1041.849Akaikeinfocriterion16.93634Sumsquaredresid24965329Schwarzcriterion17。26329Loglikelihood-247.0452F—statistic701.4747Durbin—Watsonstat2.167410Prob(F-statistic）0.000000由此可见，该模型的可决系数为0.995,修正的可决系数为0.993，模型拟和很好,F统计量为701。47，模型拟和很好，回归方程整体上显著。但是当=005时，t (nk)=t (23)=2069,不仅X4、X5、X6、X7的系数t检验不显,而且X2、X4、X6系/2 0.025数的符号与预期相反，这表明很可能存在严重的多重共线性（即除了农业增加值X 、工业增加值X外，其他因素对2 3财政收入的影响都不显著,且农业增加值X、建筑业增加值X、最终消费X的回归系数还是负数，这说明很可能存2 4 6在严重的多重共线性.)3、计算各解释变量的相关系数：在Workfile窗口，选择X2、X3、X4、X5、X6、X7数据，点击“Quick”-GroupStatistics—Correlations-OK，出现相关系数矩阵，如图3:图3：相关系数矩阵X2X3X4X5X6X70。0。0.9729806145982660623490.92797842940.988962619722619996587X2161479789067452466724650。0。0。0.9729806145998521808390.84390020659926412367112944371033X361471318868758178462150。0。0。982660623490.99852180830.86415213599960568434415464571840X4978993188128051159643530。0.92797842940.8439002065864152135920.88884805550.3877672648X506745687588051146979087870。0。0。0.988962619799264123671996056843440.88884805551858085X6246671784159646979115820。0。0。0.22619996580.129443710315464571840387767264801858085X772465362154353878715821由相关系数矩阵可以看出，各解释变量相互之间的相关系数较高，特别是农业增加值X2

、工业增加值X3

、建筑业增加值X4

、最终消费之间X6

，相关系数都在0.8以上。这表明模型存在着多重共线性。（三）修正多重共线性1、采用逐步回归法，去检验和解决多重共线性问题。分别作Y对X2、X3、X4、X5、X6、X7的一元回归,结果如下图4:在EVlsycx2DependentVariable：Method:LeastSquaresDate:10/12/10 Time:Sample:19782007Includedobservations:30Variable

Coefficient

Std.Error t-Statistic Prob。C—4086。5441463。091—2.7930900.0093X21.4541860。11723512.403980.0000R—squared0.846034Meandependentvar10049。04AdjustedR-squared0.840536S.D。dependentvar12585.51S。E.ofregression5025.770Akaikeinfocriterion19.94689SumsquaredresidLoglikelihood07E+08—297。2033SchwarzcriterionF—statistic20.04030153.8588Durbin-Watsonstat0。166951Prob(F-statistic）0.000000依次如上推出X3、X4、X5、X6、X7的一元回归。综上所述,结果如下图4:图4。一元回归估计结果变量X2X3X4X5X6X7参数估计值1.45418604268173186851082978903303540.111530t统计量12.40398289016822.67733620602518.128950320338R20.84603409675670.94836405790410.9214940003651R20。8405360966408094652005640060.918690-0.0319322、其中，加入X的R2最大,以X为基础，顺次加入其他变量逐步回归。结果如下图5：3 3DependentVariable:YMethod：LeastSquaresDate：10/13/10 Time：01:27Sample:19782007Includedobservations：30Variable

Coefficient

Std.Error

t-Statistic

Prob。C1976。086388。24135。0898410。0000—1.10533X290。105222—10.504860.0000X30.7219890。02887925.000560。0000R-squared0.993624Meandependentvar10049.04AdjustedR-squared0.993152S。Ddependentvar12585。51S.E.ofregression1041.474Akaikeinfocriterion16。82930Sumsquaredresid29286057Schwarzcriterion16。96942Loglikelihood-249.4395F—statistic2103.946Durbin-Watsonstat1.662637Prob(F—statistic）0。000000依照上面,在顺次加入X4、X5、X6、X7，进行逐步回归。综合结果如下图5：变量X2X3变量X2X3X4X5X6X7R2-1.1053390。721989X3X20.993152X3X40.990547X3X50。98301X3,X60。985025X3X70.970053（—10.50486）（25.00056)1。65227—9。255748(11.46367）0.514796（-8.514941）-0。261997（26.29703）0.910503（-5。325453）-0。386459（11.18199）0.430639(—5。984236）—0.125579（30。62427）（-2。099504)经比较，新加入X的方程R2=0.993152，改进最大，但是X得系数为负，这显然不符题意。2 在X的基础上分别加入其他变量后发现，XX2 3 2 4

，X ，X6

的系数都为负，与预期估计违背。因此这些变量都会引起严重的多重共线性，全部剔除，只保留X3DependentVariable：Method:LeastSquaresDate：10/12/10 Time:Sample：19782007Includedobservations:30

。修正的回归结果为：Variable

Coefficient

Std.Error t—Statistic Prob.C X3 0

570。5337 -1。8847080.014768 。90168

0.06990.0000R—squaredAdjustedR—squaredS.E.ofregressionSumsquaredresidLoglikelihoodDurbin—Watsonstat

0967567 Meandependentvar0966408 S。D。dependent2306678 Akaikeinfocriterion149E+08 Schwarzcriterion-2738402 F-statistic0292531 Prob（F-statistic)

100490412585.513893518.48276835.30740.000000=-1075。289+ 0.426817Xi 3（-1。884708）（28。90168）R2=0。967567 R2=0.966408 F=835.3074这说明在其他因素不变的情况下，工业增加值每增加10.426817亿元。四、实践结果报告:1978－2007增加值等数据，运用EV最后修正的回归结果为：=—1075.289+ 0.426817Xi 3(-1.884708）（28.90168）R2=0.967567 R2=0.966408 F=835。3074这说明在其他因素不变的情况下,工业增加值每增加1亿元，财政收入平均增加0.426817亿元。0.967567835。3074，说明整个方程显著;t28。t统计量，t检验显著，符合题意.逐步回归后的结果虽然实现了减轻多重共线性的目的,但反映农业增加值，建筑业增加值的X2，X3等也一并从模型中剔除出去了,可能会带来设定偏误,这是在使用逐步回归时需要注意的问题。附加:1、分别作Y对X2、X3、X4、X5、X6、X7的一元回归，结果如下：lsycx2DependentVariable:YMethod:LeastDate：10/12/10 Time：Sample:19782007Includedobservations：30Variable

Coefficient

Std.Error t—Statistic Prob。—4086C 544

1463。091 -2。

0.0093X2 1.454186 0.117235 12.40398 0.0000R—squaredAdjustedR-squaredS。E.ofregressionSumsquaredresidLoglikelihoodDurbin—Watsonstat

0.846034 Meandependentvar0840536 S。D。dependent5025770 Akaikeinfocriterion7.07E+08 Schwarzcriterion-297.2033 F-statistic0.166951 Prob（F-statistic)

100490412585.519468904030153.8588000000lsycx3DependentVariable：Method:LeastSquaresDate:10/12/10 Time：Sample:19782007Includedobservations:30VariableCX3

Coefficient-10750

Std.570。0。

t-Statistic-1.88470828。

Prob。0.0699。0000R—squared0.967567Meandependentvar10049.04AdjustedR-squared0.966408S。D.dependentvar12585.51S。E.ofregression2306。678Akaikeinfocriterion18.38935Sumsquaredresid1.49E+08Schwarzcriterion18。48276—273。Loglikelihood8402F—statistic835。3074Durbin—Watsonstat0.292531Prob（F-statistic)0。000000lsycx4DependentVariable:YMethod：LeastSquaresDate：10/12/10 Time:17：50Sample：19782007Includedobservations:30VariableCoefficientStd。Errort-StatisticProb.C—1235。177727.9896-1。6966950.1008X43。1868510.14053022。677330.0000R—squaredAdjustedR—squared

0948364 Meandependentvar0.946520 S.D。dependent

100490412585.51S.EofregressionSumsquaredresidLoglikelihoodDurbin—Watsonstat

2910.486 Akaikeinfocriterion2.37E+08 Schwarzcriterion—280.8155 F-statistic0215531 Prob（F-statistic)

854379477851426140.000000lsycx5DependentVariable：Method:LeastSquaresDate:10/12/10 Time：Sample：19782007Includedobservations:30VariableCoefficientStd.Errort-StatisticProb。C。4215618。35-5。5332600。0000X50。8297890.1337076。2060250。0000R—squared0。579041Meandependentvar10049.04AdjustedR—squared0。564006S.D.dependentvar12585。51S。Eofregression8310.188Akaikeinfocriterion20。95269SumsquaredresidLoglikelihood1.93E+09—312.2904SchwarzcriterionF—statistic21.0461138.51474Durbin—Watsonstat0。132458Prob(F—statistic）0.000001lsycx6DependentVariable：YMethod：LeastDate:10/12/10 Time：Sample：19782007Includedobservations:30Variable

Coefficient Std

t—Statistic Prob.C -2026X6 0.330354

934.3495—2。0.018222

0.03870.0000R-squaredAdjustedR—squared

0921494 Meandependentvar0918690 S.D。dependent

10049041258551S。E。ofregression 3588750 Akaikeinfocriterion 19.27334SumsquaredresidLoglikelihood

361E+08 Schwarzcriterion—287.100 F—statistic

3667532865890Durbin—Watsonstat 0189127 Prob(F—statistic) 0.000000lsycx7DependentVariable:YMethod:LeastDate：10/12/10 Time：Sample：19782007Includedobservations：30Variable

Coefficient Std

t—Statistic

Prob。C 4934X7 0

16135。0。

。3058250.320338

。76200.7511R-squaredAdjustedR-squaredS。E.ofregressionSumsquaredresid003651-012784.874.58E+09MeandependentvarS。D.dependentAkaikeinfocriterionSchwarzcriterion100490412585518142590767—325。Loglikelihood2138F-statistic0。102616Durbin-Watsonstat0。065981Prob（F-statistic）0.7510912、以X3为基础，顺次加入其他变量逐步回归。X3、X2：DependentVariable：YMethod：LeastSquaresDate:10/13/10 Time:Sample:19782007Includedobservations:30VariableCoefficientStd。Errort-StatisticProb.C1976.086388.24135.0898410。0000X2。1053390.105222—10.504860。0000X30。7219890.02887925.000560。0000R-squared0.993624Meandependentvar10049。04AdjustedR—squared0。993152S.D.dependentvar12585.51S。Eofregression1041。474Akaikeinfocriterion16.82930Sumsquaredresid29286057Schwarzcriterion16.96942Loglikelihood-249.4395F—statistic2103.946Durbin—Watsonstat1.662637Prob（F—statistic)0.000000X3、X4:DependentVariable:YMethod：LeastSquaresDate：10/13/10 Time:01：27Sample：19782007Includedobservations：30Variable

Coefficient Std

t-Statistic

Prob.C-2414297318。0985-0。7589780。4544X31.6522700.14413111.463670.0000X4—9.2557481。087001—8.5149410。0000R—squared0.991199Meandependentvar10049.04AdjustedR—squared0.990547S.D.dependentvar12585.51S。E.ofregression1223。617Akaikeinfocriterion17。15165SumsquaredresidLoglikelihood40425409—254.2747SchwarzcriterionF—statistic17.291771520477Durbin—Watsonstat1.669559Prob（F—statistic）0.000000X3、X5：DependentVariable：Method:LeastSquaresDate：10/13/10 Time：Sample：19782007Includedobservations:30VariableCoefficientStd.Errort-StatisticProb.C27090.895304.5145.1071380.0000X30.5147960。01957626.297030.0000X5—0.2619970。049197—5。3254530.0000R-squared0.984182Meandependentvar10049.04AdjustedR-squared0。983010S。D。dependentvar12585.51S。Eofregression1640.462Ak