EViews计量经济学实验报告-多重共线性的诊断与修正

1、时间地点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、对多元线性回归模型的多重共线性的诊断；2、对多元线性回归模型的多重共线性的修正。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”，19782007年的财政收入，农业增加值，工业增加值，建筑业增加值等数据，运用EV软件，做回归分析，判断是否存在多重共线性，以及修正。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）设定如下形式的计量经济模型：（一）模型设定及其估计经分析，影响财政收入的主要因素，除了农业增加值，工业增加值，建筑业增加值以外，还可能与总人口等因素有关研究“农业的发展反而会减少财政收入”

2、这个问题。Y=B+卩X+卩X+卩X+卩X+卩X+卩X+卩1223344556677i其中，Y为财政收入CS/亿元；X为农业增加值NZ/亿元；X为工业增加值GZ/亿元；X为建筑业增加值JZZ/亿元;i234X为总人口TPOP/万人；X为最终消费CUM/亿元；X为受灾面积SZM/千公顷。567图1：年份1978197919801981198219831984198519861987198819891990199119921993199419782007年财政收入及其影响因素数据财政收入CS/亿元1132.31146.41159.91175.81212.313671642.92004.8212221

3、99.42357.22664.92937.13149.483483.374348.955218.1农业增加值NZ/亿元1027.51270.21371.61559.51777.41978.42316.12564.42788.732333865.44265.950625342.25866.66963.89572.7工业增加值GZ/亿元16071769.71996.52048.42162.32375.627893448.739674585.85777.2648468588087.110284.51418819480.7建筑业增加值JZZ/亿元138.2143.8195.5207.1220.7270

4、.6316.7417.9525.7665.8810794859.41015.114152266.52964.7总人口TPOP/万人962599754298705100072101654103008104357105851107507109300111026112704114333115823117171118517119850最终消费CUM/亿元2239.12633.73007.93361.53714.84126.44846.35986.36821.87804.69839.511164.212090.514091.917203.321899.929242.2受灾面积SZM/千公顷5079039

5、37044526397903313034710318904436547140420905087046991384745547251333488295504319956242.212135.824950.63728.812112136748.24582119967407.9914015.429447.64387.412238943919.54698919978651.1414441.932921.44621.612362648140.65342919989875.9514817.634018.44985.812476151588.250145199911444.081477035861.5517

6、2.112578655636.949981200013395.2314944.7400365522.31267436151654688200116386.0415781.343580.65931.712762766878.352215200218903.641653747431.36465.512845371691.247119200321715.2517381.754945.57490.812922777449.554506200426396.4721412.7652108694.312998887032.937106200531649.292242076912.910133.8130756

7、96918.138818200638760.22404091310.911851.1131448110595.341091200751321.7828095107367.214014.1132129128444.648992利用EV软件，生成Y、X、Xi23X、X、X、X等数据，采用这些数据对模型进行OLS回归。4567（二）诊断多重共线性1、双击“Eviews”，进入主页。输入数据：点击主菜单中的File/Open/EVWorkfileExcel一多重共线性的数据.xls；2、在EV主页界面的窗口，输入“lsycx2x3x4x5x6x7”，按“Enter”.出现OLS回归结果，图2：图2：O

8、LS回归结果DependentVariable:YMethod:LeastSquaresDate:10/12/10Time:17:07Sample:19782007Includedobservations:30VariableCoefficientStd.Errort-StatisticProb.C-6646.6946454.156-1.0298320.3138X2-0.9706880.330409-2.9378410.0074X31.0846540.2285214.7463970.0001X4-2.7639282.076994-1.3307350.1963X50.0776130.067974

9、1.1418080.2653X6-0.0471190.081509-0.5780840.5688X70.0075800.0350390.2163290.8306R-squared0.994565Meandependentvar10049.04AdjustedR-squared0.993147S.D.dependentvar12585.51S.E.ofregression1041.849Akaikeinfocriterion16.93634Sumsquaredresid24965329Schwarzcriterion17.26329Loglikelihood-247.0452F-statisti

10、c701.4747Durbin-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a=0.05时，t(n-k)=t(23)=2.069，不仅X4、X5、X6、X7的系数t检验不显著，而且X2、X4、X6系a/20.025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。即除了农业增加值工业增加值X夕卜，其他因素对23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

11、能46存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”一GroupStatisticsCorrelationsOK,出现相关系数矩阵，如图3：图3：相关系数矩阵X2X30.9729806145X40.9826606234X50.9279784294X60.9889626197X70.2261999658X216147997890674524667724650.97298061450.99852180830.84390020650.99264123670.1294437103X36147193188687

12、5811784362150.98266062340.99852180830.86415213590.99605684340.1546457184X4997899318812805141596043530.92797842940.84390020650.86415213590.88884805550.3877672648X5067456875828051146979087870.98896261970.99264123670.99605684340.88884805550.1851728808X6246671178441596469791515820.22619996580.1294437103

13、038776726480.1851728808X772465362150435308787515821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X、工业增加值X、建筑业增23加值X、最终消费之间X，相关系数都在0.8以上。46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EV主页界面的窗口，输入“lsycx2”，“回车键”。DependentVariable:YMethod:LeastSquaresDate:10/1

14、2/10Time:17:49Sample:19782007Includedobservations:30VariableCoefficientStd.Errort-StatisticProb.C-4086.5441463.091-2.7930900.0093X21.4541860.11723512.403980.0000R-squared0.846034Meandependentvar10049.04AdjustedR-squared0.840536S.D.dependentvar12585.51S.E.ofregression5025.770Akaikeinfocriterion19.946

15、89Sumsquaredresid7.07E+08Schwarzcriterion20.04030Loglikelihood-297.2033F-statistic153.8588Durbin-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1.4541860.4268173.1868510.8297890.3303540.111530t统计量12.4039828.9016822.677336.20602518.128950

16、.320338R20.8460340.9675670.9483640.5790410.9214940.003651R20.8405360.9664080.9465200.5640060.918690-0.0319322、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5：33DependentVariable:YMethod:LeastSquaresDate:10/13/10Time:01:27Sample:19782007Includedobservations:30VariableCoefficientStd.Errort-StatisticProb.C1976.0

17、86388.24135.0898410.0000X2-1.1053390.105222-10.504860.0000X30.7219890.02887925.000560.0000R-squared0.993624Meandependentvar10049.04AdjustedR-squared0.993152S.D.dependentvar12585.51S.E.ofregression1041.474Akaikeinfocriterion16.82930Sumsquaredresid29286057Schwarzcriterion16.96942Loglikelihood-249.4395

18、F-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：图5.加入新变量的回归结果（一）变量X2X3X4X5X6X7R2X3,X2-1.1053390.7219890.993152(T0.50486)(25.00056)X3,X41.65227-9.2557480.990547(11.46367)(-8.514941)X3,X50.514796-0.2619970.98301(26.29703)(-5.325453)X3,X60.9105

19、03-0.3864590.985025(11.18199)(-5.984236)X3,X70.430639-0.1255790.970053(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。22在X的基础上分别加入其他变量后发现，X，X，X，X，X的系数都为负，与预期估计违背。因24567此这些变量都会引起严重的多重共线性，全部剔除，只保留X。修正的回归结果为：3DependentVariable:YMethod:LeastSquaresDate:10/12/10Time:17:50Sample:19782007

20、Includedobservations:30VariableCoefficientStd.Errort-StatisticProb.C-1075.289570.5337-1.8847080.0699X30.4268170.01476828.901680.0000R-squared0.967567Meandependentvar10049.04AdjustedR-squared0.966408S.D.dependentvar12585.51S.E.ofregression2306.678Akaikeinfocriterion18.38935Sumsquaredresid1.49E+08Schw

21、arzcriterion18.48276Loglikelihood-273.8402F-statistic835.3074Durbin-Watsonstat0.292531Prob(F-statistic)0.000000Y=-1075.289+0.426817Xi3(-1.884708)(28.90168)R2=0.967567R2=0.966408F=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。四、实践结果报告：为研究“农业的发展反而会减少财政收入”的问题，根据19782007年的财政收入，农业增加值，工业增加值，建筑业增加值

22、等数据，运用EV软件，做回归分析，判断是否存在多重共线性，以及修正。最后修正的回归结果为：Y=-1075.289+0.426817Xi3(-1.884708)(28.90168)R2=0.967567R2=0.966408F=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。可决系数为0.967567，较高，说明模型拟合优度高；F值为835.3074，说明整个方程显著；斜率系数的t值28.90168，大于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

23、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:LeastSquaresDate:10/12/10Time:17:49Sample:19782007Includedobservations:30VariableCoefficientStd.Errort-StatisticProb.C-4086.5441463.091-2.7930900.0093X21.4541860.11723512.403980.0000R-squared0.8

24、46034Meandependentvar10049.04AdjustedR-squared0.840536S.D.dependentvar12585.51S.E.ofregression5025.770Akaikeinfocriterion19.94689Sumsquaredresid7.07E+08Schwarzcriterion20.04030Loglikelihood-297.2033F-statistic153.8588Durbin-Watsonstat0.166951Prob(F-statistic)0.000000lsycx3DependentVariable:YMethod:L

25、eastSquaresDate:10/12/10Time:17:50Sample:19782007Includedobservations:30VariableCoefficientStd.Errort-StatisticProb.C-1075.289570.5337-1.8847080.0699X30.4268170.01476828.901680.0000R-squared0.967567Meandependentvar10049.04AdjustedR-squared0.966408S.D.dependentvar12585.51S.E.ofregression2306.678Akaik

26、einfocriterion18.38935Sumsquaredresid1.49E+08Schwarzcriterion18.48276Loglikelihood-273.8402F-statistic835.3074Durbin-Watsonstat0.292531Prob(F-statistic)0.000000lsycx4DependentVariable:YMethod:LeastSquaresDate:10/12/10Time:17:50Sample:19782007Includedobservations:30VariableCoefficientStd.Errort-Stati

27、sticProb.C-1235.177727.9896-1.6966950.1008X43.1868510.14053022.677330.0000R-squared0.948364Meandependentvar10049.04AdjustedR-squared0.946520S.D.dependentvar12585.51S.E.ofregression2910.486Akaikeinfocriterion18.85437Sumsquaredresid2.37E+08Schwarzcriterion18.94778Loglikelihood-280.8155F-statistic514.2

28、614Durbin-Watsonstat0.215531Prob(F-statistic)0.000000lsycx5DependentVariable:YMethod:LeastSquaresDate:10/12/10Time:17:51Sample:19782007Includedobservations:30VariableCoefficientStd.Errort-StatisticProb.C-86420.4215618.35-5.5332600.0000X50.8297890.1337076.2060250.0000R-squared0.579041Meandependentvar

29、10049.04AdjustedR-squared0.564006S.D.dependentvar12585.51S.E.ofregression8310.188Akaikeinfocriterion20.95269Sumsquaredresid1.93E+09Schwarzcriterion21.04611Loglikelihood-312.2904F-statistic38.51474Durbin-Watsonstat0.132458Prob(F-statistic)0.000001lsycx6DependentVariable:YMethod:LeastSquaresDate:10/12

30、/10Time:17:51Sample:19782007Includedobservations:30VariableCoefficientStd.Errort-StatisticProb.C-2026.867934.3495-2.1692810.0387X60.3303540.01822218.128950.0000R-squared0.921494Meandependentvar10049.04AdjustedR-squared0.918690S.D.dependentvar12585.51S.E.ofregression3588.750Akaikeinfocriterion19.2733

31、4Sumsquaredresid3.61E+08Schwarzcriterion19.36675Loglikelihood-287.1000F-statistic328.6589Durbin-Watsonstat0.189127Prob(F-statistic)0.000000lsycx7DependentVariable:YMethod:LeastSquaresDate:10/12/10Time:18:36Sample:19782007Includedobservations:30VariableCoefficientStd.Errort-StatisticProb.C4934.616161

32、35.440.3058250.7620X70.1115300.3481620.3203380.7511R-squared0.003651Meandependentvar10049.04AdjustedR-squared-0.031932S.D.dependentvar12585.51S.E.ofregression12784.87Akaikeinfocriterion21.81425Sumsquaredresid4.58E+09Schwarzcriterion21.90767Loglikelihood-325.2138F-statistic0.102616Durbin-Watsonstat0.

33、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:10/13/10Time:01:27Sample:19782007Includedobservations:30VariableCoefficientStd.Errort-StatisticProb.C1976.086388.24135.0898410.0000X2-1.1053390.105222-10.504860.0000X30.7219890.02887925.000560.0000R

34、-squared0.993624Meandependentvar10049.04AdjustedR-squared0.993152S.D.dependentvar12585.51S.E.ofregression1041.474Akaikeinfocriterion16.82930Sumsquaredresid29286057Schwarzcriterion16.96942Loglikelihood-249.4395F-statistic2103.946Durbin-Watsonstat1.662637Prob(F-statistic)0.000000X3、X4:DependentVariabl

35、e:YMethod:LeastSquaresDate:10/13/10Time:01:27Sample:19782007Includedobservations:30VariableCoefficientStd.Errort-StatisticProb.C-241.4297318.0985-0.7589780.4544X31.6522700.14413111.463670.0000X4-9.2557481.087001-8.5149410.0000R-squared0.991199Meandependentvar10049.04AdjustedR-squared0.990547S.D.depe

36、ndentvar12585.51S.E.ofregression1223.617Akaikeinfocriterion17.15165Sumsquaredresid40425409Schwarzcriterion17.29177Loglikelihood-254.2747F-statistic1520.477Durbin-Watsonstat1.669559Prob(F-statistic)0.000000X3、X5:DependentVariable:YMethod:LeastSquaresDate:10/13/10Time:01:28Sample: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.E.ofregression16