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、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19781132.31027.51607138.2962592239.15079019791146.41270.21769.7143.8975422633.73937019801159.91371.61996.5195.5987053007.94452619811175.81559.52048.4207.13361.53979019821212.31777.42162.3220.73714.833130198313671978.42375.6270.64126.43471019841642.92316.12789316.74846.33189019852004.82564.43448.7417.95986.344365198621222788.73967525.76821.84714019872199.432334585.8665.87804.64209019882357.23865.45777.28109839.55087019892664.94265.9648479411164.24699119902937.150626858859.412090.53847419913149.485342.28087.11015.114091.95547219923483.375866.610284.5141517203.35133319934348.956963.8141882266.521899.94882919945218.19572.719480.72964.729242.25504319956242.212135.824950.63728.836748.24582119967407.9914015.429447.64387.443919.54698919978651.1414441.932921.44621.648140.65342919989875.9514817.634018.44985.851588.250145199911444.081477035861.55172.155636.949981200013395.2314944.7400365522.36151654688200116386.0415781.343580.65931.766878.352215200218903.641653747431.36465.571691.247119200321715.2517381.754945.57490.877449.554506200426396.4721412.7652108694.387032.937106200531649.292242076912.910133.896918.138818200638760.22404091310.911851.1.341091200751321.7828095.214014.1.648992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: 10/12/10 Time: 17:07Sample: 1978 2007Included observations: 30VariableCoefficientStd. Errort-StatisticProb.C-6646.6946454.156-1.0.3138X2-0.0.-2.0.0074X.0001X4-2.2.-1.0.1963X.2653X6-0.0.-0.0.5688X.8306R-squared0.Mean dependent var10049.04Adjusted R-squared0.S.D. dependent var12585.51S.E. of regression1041.849Akaike info criterion16.93634Sum squared residSchwarz criterion17.26329Log likelihood-247.0452F-statistic701.4747Durbin-Watson stat2.Prob(F-statistic)0.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X2X3X4X5X6X7X210.1470.97890.67450.46670.2465X30.14710.31880.87580.17840.6215X40.97890.318810.80510.15960.4353X50.67450.87580.805110.69790.8787X60.46670.17840.15960.697910.1582X70.24650.62150.43530.87870.15821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、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-4086.5441463.091-2.0.0093X03980.0000R-squared0.Mean dependent var10049.04Adjusted R-squared0.S.D. dependent var12585.51S.E. of regression5025.770Akaike info criterion19.94689Sum squared resid7.07E+08Schwarz criterion20.04030Log likelihood-297.2033F-statistic153.8588Durbin-Watson stat0.Prob(F-statistic)0.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.0.0.t统计量12.4039828.9016822.677336.18.1289...-0.2、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.C1976.086388.24135.0.0000X2-1.0.-10.504860.0000X00560.0000R-squared0.Mean dependent var10049.04Adjusted R-squared0.S.D. dependent var12585.51S.E. of regression1041.474Akaike info criterion16.82930Sum squared residSchwarz criterion16.96942Log likelihood-249.4395F-statistic2103.946Durbin-Watson stat1.Prob(F-statistic)0.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,X2-1.0.0.（-10.50486）（25.00056）X3,X41.65227-9.0.（11.46367）（-8.）X3,X50.-0.0.98301（26.29703）（-5.）X3,X60.-0.0.（11.18199）（-5.）X3,X70.-0.0.（30.62427）（-2.）经比较，新加入的方程= 0. ，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-1075.289570.5337-1.0.0699X01680.0000R-squared0.Mean dependent var10049.04Adjusted R-squared0.S.D. dependent var12585.51S.E. of regression2306.678Akaike info criterion18.38935Sum squared resid1.49E+08Schwarz criterion18.48276Log likelihood-273.8402F-statistic835.3074Durbin-Watson stat0.Prob(F-statistic)0.= -1075.289 + 0.（-1.） （28.90168）= 0. =0. 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0.亿元。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.（-1.） （28.90168）= 0. =0. 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0.亿元。可决系数为0.，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-4086.5441463.091-2.0.0093X03980.0000R-squared0.Mean dependent var10049.04Adjusted R-squared0.S.D. dependent var12585.51S.E. of regression5025.770Akaike info criterion19.94689Sum squared resid7.07E+08Schwarz criterion20.04030Log likelihood-297.2033F-statistic153.8588Durbin-Watson stat0.Prob(F-statistic)0.ls y c x3Dependent Variable: YMethod: Least SquaresDate: 10/12/10 Time: 17:50Sample: 1978 2007Included observations: 30VariableCoefficientStd. Errort-StatisticProb.C-1075.289570.5337-1.0.0699X01680.0000R-squared0.Mean dependent var10049.04Adjusted R-squared0.S.D. dependent var12585.51S.E. of regression2306.678Akaike info criterion18.38935Sum squared resid1.49E+08Schwarz criterion18.48276Log likelihood-273.8402F-statistic835.3074Durbin-Watson stat0.Prob(F-statistic)0.ls y c x4Dependent Variable: YMethod: Least SquaresDate: 10/12/10 Time: 17:50Sample: 1978 2007Included observations: 30VariableCoefficientStd. Errort-StatisticProb.C-1235.177727.9896-1.0.1008X77330.0000R-squared0.Mean dependent var10049.04Adjusted R-squared0.S.D. dependent var12585.51S.E. of regression2910.486Akaike info criterion18.85437Sum squared resid2.37E+08Schwarz criterion18.94778Log likelihood-280.8155F-statistic514.2614Durbin-Watson stat0.Prob(F-statistic)0.ls y c x5 Dependent Variable: YMethod: Least SquaresDate: 10/12/10 Time: 17:51Sample: 1978 2007Included observations: 30VariableCoefficientStd. Errort-StatisticProb.C-86420.4215618.35-5.0.0000X.0000R-squared0.Mean dependent var10049.04Adjusted R-squared0.S.D. dependent var12585.51S.E. of regression8310.188Akaike info criterion20.95269Sum squared resid1.93E+09Schwarz criterion21.04611Log likelihood-312.2904F-statistic38.51474Durbin-Watson stat0.Prob(F-statistic)0.ls y c x6Dependent Variable: YMethod: Least SquaresDate: 10/12/10 Time: 17:51Sample: 1978 2007Included observations: 30VariableCoefficientStd. Errort-StatisticProb.C-2026.867934.3495-2.0.0387X28950.0000R-squared0.Mean dependent var10049.04Adjusted R-squared0.S.D. dependent var12585.51S.E. of regression3588.750Akaike info criterion19.27334Sum squared resid3.61E+08Schwarz criterion19.36675Log likelihood-287.1000F-statistic328.6589Durbin-Watson stat0.Prob(F-statistic)0.ls y c x7Dependent Variable: YMethod: Least SquaresDate: 10/12/10 Time: 18:36Sample: 1978 2007Included observations: 30VariableCoefficientStd. Errort-StatisticProb.C4934.61616135.440.0.7620X.7511R-squared0.Mean dependent var10049.04Adjusted R-squared-0.S.D. dependent var12585.51S.E. of regression12784.87Akaike info criterion21.81425Sum squared resid4.58E+09Schwarz criterion21.90767Log likelihood-325.2138F-statistic0.Durbin-Watson stat0.Prob(F-statistic)0.2、 以为基础，顺次加入其他变量逐步回归。X3、X2:Dependent Variable: YMethod: Least SquaresDate: 10/13/10 Time: 01:27Sample: 1978 2007Included observations: 30VariableCoefficientStd. Errort-StatisticProb.C1976.086388.24135.0.0000X2-1.0.-10.504860.0000X00560.0000R-squared0.Mean dependent var10049.04Adjusted R-squared0.S.D. dependent var12585.51S.E. of regression1041.474Akaike info criterion16.82930Sum squared residSchwarz criterion16.96942Log likelihood-249.4395F-statistic2103.946Durbin-Watson stat1.Prob(F-statistic)0.X3、X4:Dependent Variable: YMethod: Least SquaresDate: 10/13/10 Time: 01:27Sample: 1978 2007Included observations: 30VariableCoefficientStd. Errort-StatisticProb.C-241.4297318.0985-0.0.4544X63670.0000X4-9.1.-8.0.0000R-squared0.Mean dependent var10049.04Adjusted R-squared0.S.D. dependent var12585.51S.E. of regression1223.617Akaike info criterion17.15165Sum squared residSchwarz criterion17.29177Log likelihood-254.2747F-statistic1520.477Durbin-Watson stat1.Prob(F-statistic)0.X3、X5:Dependent Variable: YMethod: Least SquaresDate: 10/13/10 Time: 01:28Sample: 1978 2007Included observations: 30VariableCoefficientStd. Errort-StatisticProb.C27090.895304.5145.0.0000X97030.0000X5-0.0.-5.0.0000R-squared0.Mean dependent var10049.04Adjusted R-squared0.S.D. dependent var12585.51S.E. of regression1640.462Akaike info criterion17.73798Sum squared resid