EViews计量经济学实验报告-多重共线性的诊断与修正的讨论

1、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）（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”这个问题。设定如下形式的计量

2、经济模型：=+其中，为财政收入CS/亿元；为农业增加值NZ/亿元；为工业增加值GZ/亿元；为建筑业增加值JZZ/亿元；为总人口TPOP/万人；为最终消费CUM/亿元；为受灾面积SZM/千公顷。图1： 19782007年财政收入及其影响因素数据年份财政收入CS/亿元农业增加值NZ/亿元工业增加值GZ/亿元建筑业增加值JZZ/亿元总人口TPOP/万人最终消费CUM/亿元受灾面积SZM/千公顷19781132.31027.51607138.2962592239.15079019791146.41270.21769.7143.8975422633.73937019801159.91371.61996.

3、5195.5987053007.94452619811175.81559.52048.4207.11000723361.53979019821212.31777.42162.3220.71016543714.833130198313671978.42375.6270.61030084126.43471019841642.92316.12789316.71043574846.33189019852004.82564.43448.7417.91058515986.344365198621222788.73967525.71075076821.84714019872199.432334585.866

4、5.81093007804.64209019882357.23865.45777.28101110269839.55087019892664.94265.9648479411270411164.24699119902937.150626858859.411433312090.53847419913149.485342.28087.11015.111582314091.95547219923483.375866.610284.5141511717117203.35133319934348.956963.8141882266.511851721899.94882919945218.19572.71

5、9480.72964.711985029242.25504319956242.212135.824950.63728.812112136748.24582119967407.9914015.429447.64387.412238943919.54698919978651.1414441.932921.44621.612362648140.65342919989875.9514817.634018.44985.812476151588.250145199911444.081477035861.55172.112578655636.949981200013395.2314944.740036552

6、2.31267436151654688200116386.0415781.343580.65931.712762766878.352215200218903.641653747431.36465.512845371691.247119200321715.2517381.754945.57490.812922777449.554506200426396.4721412.7652108694.312998887032.937106200531649.292242076912.910133.813075696918.138818200638760.22404091310.911851.1131448

7、110595.341091200751321.7828095107367.214014.1132129128444.648992利用EV软件，生成、等数据，采用这些数据对模型进行OLS回归。（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 /EV WorkfileExcel多重共线性的数据.xls ；2、在EV主页界面的窗口，输入“ls y c x2 x3 x4 x5 x6 x7”，按“Enter”.出现OLS回归结果,图2： 图2： OLS 回归结果Dependent Variable: YMethod: Least SquaresDate:

8、 10/12/10 Time: 17:07Sample: 1978 2007Included observations: 30VariableCoefficientStd. Errort-StatisticProb.  C-6646.6946454.156-1.0298320.3138X2-0.9706880.330409-2.9378410.0074X31.0846540.2285214.7463970.0001X4-2.7639282.076994-1.3307350.1963X50.0776130.0679741.1418080.2653X6-0.0471190.08

9、1509-0.5780840.5688X70.0075800.0350390.2163290.8306R-squared0.994565    Mean dependent var10049.04Adjusted R-squared0.993147    S.D. dependent var12585.51S.E. of regression1041.849    Akaike info criterion16.93634Sum squared resid24965329&#

10、160;   Schwarz criterion17.26329Log likelihood-247.0452    F-statistic701.4747Durbin-Watson stat2.167410    Prob(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=0.05时，=2.069，不仅X4、X5、X6、X7的系数t检验不显著，而且

11、X2、X4、X6系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、工业增加值外，其他因素对财政收入的影响都不显著，且农业增加值、建筑业增加值、最终消费的回归系数还是负数，这说明很可能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”Group StatisticsCorrelationsOK,出现相关系数矩阵，如图3：图3： 相关系数矩阵X2X3X4X5X6X7X210.972980614561470.9826606234997890.9279784294067450.98896

12、26197246670.226199965872465X30.9729806145614710.9985218083931880.8439002065687580.9926412367117840.129443710336215X40.9826606234997890.99852180839318810.8641521359280510.9960568434415960.154645718404353X50.9279784294067450.8439002065687580.86415213592805110.8888480555469790.387767264808787X60.988962

13、6197246670.9926412367117840.9960568434415960.88884805554697910.185172880851582X70.2261999658724650.1294437103362150.1546457184043530.3877672648087870.1851728808515821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、工业增加值、建筑业增加值、最终消费之间，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

14、、X6、X7的一元回归，结果如下图4：在EV主页界面的窗口，输入“ls y c x2”，“回车键”。Dependent Variable: YMethod: Least SquaresDate: 10/12/10 Time: 17:49Sample: 1978 2007Included observations: 30VariableCoefficientStd. Errort-StatisticProb.  C-4086.5441463.091-2.7930900.0093X21.4541860.11723512.403980.0000R-squared0.846034&

15、#160;   Mean dependent var10049.04Adjusted R-squared0.840536    S.D. dependent var12585.51S.E. of regression5025.770    Akaike info criterion19.94689Sum squared resid7.07E+08    Schwarz criterion20.04030Log likelihood-297.203

16、3    F-statistic153.8588Durbin-Watson stat0.166951    Prob(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参数估计值1.4541860.4268173.1868510.8297890.3303540.111530t统计量12.4039828.9016822.677336.20602518.128950.3203380.8460340.9675670.9483640

17、.5790410.9214940.0036510.8405360.9664080.9465200.5640060.918690-0.0319322、其中，加入的最大，以为基础，顺次加入其他变量逐步回归。结果如下图5：Dependent Variable: YMethod: Least SquaresDate: 10/13/10 Time: 01:27Sample: 1978 2007Included observations: 30VariableCoefficientStd. Errort-StatisticProb.  C1976.086388.24135.089841

18、0.0000X2-1.1053390.105222-10.504860.0000X30.7219890.02887925.000560.0000R-squared0.993624    Mean dependent var10049.04Adjusted R-squared0.993152    S.D. dependent var12585.51S.E. of regression1041.474    Akaike info criterion16.82930Sum sq

19、uared resid29286057    Schwarz criterion16.96942Log likelihood-249.4395    F-statistic2103.946Durbin-Watson stat1.662637    Prob(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X2X3X4X5X6X7X3,X2-1.1053390.7219890

20、.993152（-10.50486）（25.00056）X3,X41.65227-9.2557480.990547（11.46367）（-8.514941）X3,X50.514796-0.2619970.98301（26.29703）（-5.325453）X3,X60.910503-0.3864590.985025（11.18199）（-5.984236）X3,X70.430639-0.1255790.970053（30.62427）（-2.099504）经比较，新加入的方程= 0.993152 ，改进最大， 但是得系数为负，这显然不符题意。在的基础上分别加入其他变量后发现，的系数都为负，与预

21、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。修正的回归结果为：Dependent Variable: YMethod: Least SquaresDate: 10/12/10 Time: 17:50Sample: 1978 2007Included observations: 30VariableCoefficientStd. Errort-StatisticProb.  C-1075.289570.5337-1.8847080.0699X30.4268170.01476828.901680.0000R-squared0.967567 &#

22、160;  Mean dependent var10049.04Adjusted R-squared0.966408    S.D. dependent var12585.51S.E. of regression2306.678    Akaike info criterion18.38935Sum squared resid1.49E+08    Schwarz criterion18.48276Log likelihood-273.8402 

23、   F-statistic835.3074Durbin-Watson stat0.292531    Prob(F-statistic)0.000000= -1075.289 + 0.426817（-1.884708） （28.90168）= 0.967567 =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。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

24、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。最后修正的回归结果为：= -1075.289 + 0.426817（-1.884708） （28.90168）= 0.967567 =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。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

25、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：ls y c x2Dependent Variable: YMethod: Least SquaresDate: 10/12/10 Time: 17:49Sample: 1978 2007Included observations: 30VariableCoefficientStd. Errort-StatisticProb.  C-4086.5441463.091-2.7930900.0093X21.4541860.1172

26、3512.403980.0000R-squared0.846034    Mean dependent var10049.04Adjusted R-squared0.840536    S.D. dependent var12585.51S.E. of regression5025.770    Akaike info criterion19.94689Sum squared resid7.07E+08    Schwarz crite

27、rion20.04030Log likelihood-297.2033    F-statistic153.8588Durbin-Watson stat0.166951    Prob(F-statistic)0.000000ls y c x3Dependent Variable: YMethod: Least SquaresDate: 10/12/10 Time: 17:50Sample: 1978 2007Included observations: 30VariableCoefficientStd. Erro

28、rt-StatisticProb.  C-1075.289570.5337-1.8847080.0699X30.4268170.01476828.901680.0000R-squared0.967567    Mean dependent var10049.04Adjusted R-squared0.966408    S.D. dependent var12585.51S.E. of regression2306.678    Akaike info c

29、riterion18.38935Sum squared resid1.49E+08    Schwarz criterion18.48276Log likelihood-273.8402    F-statistic835.3074Durbin-Watson stat0.292531    Prob(F-statistic)0.000000ls y c x4Dependent Variable: YMethod: Least SquaresDate: 10/12/10 Tim

30、e: 17:50Sample: 1978 2007Included observations: 30VariableCoefficientStd. Errort-StatisticProb.  C-1235.177727.9896-1.6966950.1008X43.1868510.14053022.677330.0000R-squared0.948364    Mean dependent var10049.04Adjusted R-squared0.946520    S.D. depend

31、ent var12585.51S.E. of regression2910.486    Akaike info criterion18.85437Sum squared resid2.37E+08    Schwarz criterion18.94778Log likelihood-280.8155    F-statistic514.2614Durbin-Watson stat0.215531    Prob(F-statistic

32、)0.000000ls y c x5 Dependent Variable: YMethod: Least SquaresDate: 10/12/10 Time: 17:51Sample: 1978 2007Included observations: 30VariableCoefficientStd. Errort-StatisticProb.  C-86420.4215618.35-5.5332600.0000X50.8297890.1337076.2060250.0000R-squared0.579041    Mean dep

33、endent var10049.04Adjusted R-squared0.564006    S.D. dependent var12585.51S.E. of regression8310.188    Akaike info criterion20.95269Sum squared resid1.93E+09    Schwarz criterion21.04611Log likelihood-312.2904    F-stat

34、istic38.51474Durbin-Watson stat0.132458    Prob(F-statistic)0.000001ls y c x6Dependent Variable: YMethod: Least SquaresDate: 10/12/10 Time: 17:51Sample: 1978 2007Included observations: 30VariableCoefficientStd. Errort-StatisticProb.  C-2026.867934.3495-2.1692810.0387X60

35、.3303540.01822218.128950.0000R-squared0.921494    Mean dependent var10049.04Adjusted R-squared0.918690    S.D. dependent var12585.51S.E. of regression3588.750    Akaike info criterion19.27334Sum squared resid3.61E+08    

36、Schwarz criterion19.36675Log likelihood-287.1000    F-statistic328.6589Durbin-Watson stat0.189127    Prob(F-statistic)0.000000ls y c x7Dependent Variable: YMethod: Least SquaresDate: 10/12/10 Time: 18:36Sample: 1978 2007Included observations: 30VariableCoeffic

37、ientStd. Errort-StatisticProb.  C4934.61616135.440.3058250.7620X70.1115300.3481620.3203380.7511R-squared0.003651    Mean dependent var10049.04Adjusted R-squared-0.031932    S.D. dependent var12585.51S.E. of regression12784.87    A

38、kaike info criterion21.81425Sum squared resid4.58E+09    Schwarz criterion21.90767Log likelihood-325.2138    F-statistic0.102616Durbin-Watson stat0.065981    Prob(F-statistic)0.7510912、 以为基础，顺次加入其他变量逐步回归。X3、X2:Dependent Variable: YMethod: L

39、east SquaresDate: 10/13/10 Time: 01:27Sample: 1978 2007Included observations: 30VariableCoefficientStd. Errort-StatisticProb.  C1976.086388.24135.0898410.0000X2-1.1053390.105222-10.504860.0000X30.7219890.02887925.000560.0000R-squared0.993624    Mean dependent var10049.0

40、4Adjusted R-squared0.993152    S.D. dependent var12585.51S.E. of regression1041.474    Akaike info criterion16.82930Sum squared resid29286057    Schwarz criterion16.96942Log likelihood-249.4395    F-statistic2103.946Durb

41、in-Watson stat1.662637    Prob(F-statistic)0.000000X3、X4:Dependent Variable: YMethod: Least SquaresDate: 10/13/10 Time: 01:27Sample: 1978 2007Included observations: 30VariableCoefficientStd. Errort-StatisticProb.  C-241.4297318.0985-0.7589780.4544X31.6522700.14413111.46

42、3670.0000X4-9.2557481.087001-8.5149410.0000R-squared0.991199    Mean dependent var10049.04Adjusted R-squared0.990547    S.D. dependent var12585.51S.E. of regression1223.617    Akaike info criterion17.15165Sum squared resid40425409 

43、0;  Schwarz criterion17.29177Log likelihood-254.2747    F-statistic1520.477Durbin-Watson stat1.669559    Prob(F-statistic)0.000000X3、X5:Dependent Variable: YMethod: Least SquaresDate: 10/13/10 Time: 01:28Sample: 1978 2007Included observations: 30Vari

44、ableCoefficientStd. Errort-StatisticProb.  C27090.895304.5145.1071380.0000X30.5147960.01957626.297030.0000X5-0.2619970.049197-5.3254530.0000R-squared0.984182    Mean dependent var10049.04Adjusted R-squared0.983010    S.D. dependent var12585.51S.E. of regression1640.462    Akaike info criterion17.73798Sum squared resid72660152    Schwarz criterion17.87810Log likelihood-263.0698    F-statistic839.9479Durbin