多重共线性模型

1、多重共线性报告分析背景与意义：农产品的产量及其分布构成在国民生产生活中具有重要意义，它能真切反应国名的日常生活需求什么，因此本次研究就是对于2000年-2008年人均主要工农业产品产量进行分析，主要考虑各解释变量之间是否存在多重共线性，并对其进行修正处理降低多重共线性对结果的影响，从而使结果模型更具代表性，更真切的展示结果，进而有利于国家对农业产品的生产组成的了解以及监控，才能更好的对其调控，促进其稳定、科学的发展。一、数据选择主要人均主要工农业产品产品年份工农业产品产粮食油料糖料水果猪牛羊2000量536.78366.0423.460.4749.3肉37.572001536.81355.89

2、22.5368.0552.3537.992002552.77356.9622.6380.3954.338.492003583.12334.2921.8274.83112.6839.52004618.47362.2223.6673.84118.3640.392005632.99371.2623.672.5123.6541.982006652.91379.8920.1479.78130.4542.652007670.29380.6119.4992.48137.6240.092008710.21399.1322.29101.31145.142.38(来源与中国统计网)二、实验步骤：1、 参数估计，过

3、程如下：(1)先录入数据至eviews,得到下表:obsYX1X2X3X4X52000536780036604002340C00604700049.3000037.570002001636.3100355-89002253000680500052.3500037.990002002552.770035G.960022.6300080.390054.3000039,490002003583J2O0334.2900218200074,03000112680039,50000200461847003622200236600073840001183600403900020056329900371260

4、023600007250000123650041980002006652.9100379.B90020.1400。79.78000130450042,650002007670.2900380.610019.4900092.48000137.620040,090002008710.2100399.130022.29000101.310014510004233000L.C1J(2)在命令窗口输入LSycx1x2x3x4x5,出现下列结果:DependentVanable:YMethodLeastSquaresDate：12/25/11Time：0813Sample:20002008Included

5、observations9VanableCoefficientStdError1StatisticProbC254E102.02E-10-1.2566190.2978X11000000396E-13253E+12000001oooooo398E-12251E+11000001.000000664E-131.51E+12000001oooooo31*33.19E+12000001oooooo5.17E-121.62E+1100000R-squared1.000000Meandependentvar6104333AdjustedR-squared1OOOOQOS.Ddependentvar62.0

6、8072S.E.ofregression137E-11Akaikeinfocnterion-46.95645Sumsquaredresid5.62E-22Schwarzcriterion16.82497Loglikelihood217.3040F-stattstic3.29E+25Durbin-Watsonstat2.395932Prob(F-statistic)oooooooT2、 分析从结果看判断系数R，很高，说明方程很显著，但四个参数t检验值中有三个较显著，有一个不显著，不符合经济理论，显然认为出现了多重线性回归。三、检验计算解释变量之间的简单相关系数。Eviews过程如下：(1)在Qu

7、ick菜单中选GroupStatistics项中的Correlation命令。在出现SeriesList对话框时，直接输入x1X2X3X4,出现解释变量x1x2x3x4之间的相关系数为：CorrelationMatrixX1X2X3X4X1X2X3X4X11.0000000.9822490.9801540.985451X209822491.0000000.9900770981440X309801540.99007710000000.984562X409854510.96144009845621.000000可以看出四个解释变量x1x2x3x4之间的高度相关，必然存在严重的多重共线性。辅助回归检

8、验：解释变量x1x2x3x4之间的辅助回归分别为：在命令窗口分别输入：lsx1cx2;lsx1cx3;lsx1cx4;lsx2cx3;lsx2cx4;lsx3cx4;结果分别为:DependentVariable:X1Method:LeastSquaresDate:11/24/11Time:08:46Sample(adjusted):19781998Includedobservations:21afteradjustingendpointsVariableCoefficientStd.Errort-StatisticProb.C1077.333543.45941.9823620.0621X21

9、3.183760.57759822.825140.0000R-squared0.964814Meandependentvar11725.53AdjustedR-squared0.962962S.D.dependentvar6638.021S.E.ofregression1277.503Akaikeinfocriterion17.23360Sumsquaredresid31008264Schwarzcriterion17.33307Loglikelihood-178.9527F-statistic520.9871Durbin-Watsonstat0.611662Prob(F-statistic)

10、0.000000DependentVariable:X1Method:LeastSquaresDate:11/24/11Time:08:53Sample(adjusted):19781998Includedobservations:21afteradjustingendpointsVariableCoefficientStd.Errort-StatisticProb.C2337.206525.88784.4443050.0003X31.4539730.06746421.551870.0000R-squared0.960702Meandependentvar11725.53AdjustedR-s

11、quared0.958634S.D.dependentvar6638.021S.E.ofregression1350.091Akaikeinfocriterion17.34412Sumsquaredresid34632150Schwarzcriterion17.44360Loglikelihood-180.1133F-statistic464.4832Durbin-Watsonstat0.865011Prob(F-statistic)0.000000DependentVariable:X1Method:LeastSquaresDate:11/24/11Time:09:05Sample(adju

12、sted):19781998Includedobservations:21afteradjustingendpointsVariableCoefficientStd.Errort-StatisticProb.C2405.3699446.9817305.381360863.41634090423873159189e-05X44.60403150.1821678425.27356814.356762641693599746462e-16R-squared0.9711137Meandependentvar11725.528770685714AdjustedR-squared0.9695934S.D.

13、dependentvar6638.0216074316668S.E.ofregression1157.5030Akaikeinfocriterion17.03631115205737Sumsquaredresid25456451.Schwarzcriterion17.13578211889011Loglikelihood-176.88126F-statistic638.7532102449431Durbin-Watsonstat0.5080094Prob(F-statistic)4.356762037226462e-16DependentVariable:X2Method:LeastSquar

14、esDate:11/24/11Time:09:05Sample(adjusted):19781998Includedobservations:21afteradjustingendpointsVariableCoefficientStd.Errort-StatisticProb.C101.121627.774743.6407760.0017X30.1094240.00356330.710380.0000R-squared0.980252Meandependentvar807.6753AdjustedR-squared0.979213S.D.dependentvar494.5626S.E.ofr

15、egression71.30498Akaikeinfocriterion11.46220Sumsquaredresid96603.61Schwarzcriterion11.56168Loglikelihood-118.3531F-statistic943.1276Durbin-Watsonstat2.211553Prob(F-statistic)0.000000DependentVariable:X2Method:LeastSquaresDate:11/24/11Time:09:05Sample(adjusted):19781998Includedobservations:21afteradj

16、ustingendpointsVariableCoefficientStd.Errort-StatisticProb.C116.108137.576143.0899430.0060X40.3416250.01531422.307720.0000R-squared0.963224Meandependentvar807.6753AdjustedR-squared0.961288S.D.dependentvar494.5626S.E.ofregression97.30710Akaikeinfocriterion12.08401Sumsquaredresid179904.8Schwarzcriteri

17、on12.18349Loglikelihood-124.8821F-statistic497.6345Durbin-Watsonstat0.530959Prob(F-statistic)0.000000DependentVariable:X3Method:LeastSquaresDate:11/24/11Time:09:06Sample(adjusted):19781998Includedobservations:21afteradjustingendpointsVariableCoefficientStd.Errort-StatisticProb.C179.7667310.32270.579

18、2900.5692X43.1008740.12647224.518200.0000R-squared0.969362Meandependentvar6457.012AdjustedR-squared0.967749S.D.dependentvar4474.829S.E.ofregression803.6109Akaikeinfocriterion16.30650Sumsquaredresid12270021Schwarzcriterion16.40598Loglikelihood-169.2183F-statistic601.1422Durbin-Watsonstat0.896788Prob(

19、F-statistic)0.000000六个回归方程均存在高度显著，拟合优度高，具有共线性。四、修正运用OLS方法逐一求Y对各个解释变量的回归。结合经济意义和统计检验选出拟合效果最好的一元线性回归方程。分别输入“lsycx1”、DependentVariable:YMethod:LeastSquaresDate:11/24/11Time:09:25Sample(adjusted):19781998Includedobservations:21afteradjustingendpointsVariableCoefficientStd.Errort-StatisticProb.C-2241.475

20、648.0392-3.4588570.0026X12.0093540.04837641.536570.0000R-squared0.989107Meandependentvar21319.26AdjustedR-squared0.988534S.D.dependentvar13411.38S.E.ofregression1436.083Akaikeinfocriterion17.46762Sumsquaredresid39184332Schwarzcriterion17.56710Loglikelihood-181.4100F-statistic1725.286Durbin-Watsonsta

21、t0.520820Prob(F-statistic)0.000000Isycx2”、DependentVariable:YMethod:LeastSquaresDate:11/24/11Time:09:13Sample(adjusted):19781998Includedobservations:21afteradjustingendpointsVariableCoefficientStd.Errort-StatisticProb.C-436.7055675.4209-0.6465680.5256X226.936520.71784937.523940.0000R-squared0.986686

22、Meandependentvar21319.26AdjustedR-squared0.985985S.D.dependentvar13411.38S.E.ofregression1587.703Akaikeinfocriterion17.66836Sumsquaredresid47895234Schwarzcriterion17.76784Loglikelihood-183.5178F-statistic1408.046Durbin-Watsonstat1.194877Prob(F-statistic)0.000000lsycx3”DependentVariable:YMethod:Least

23、SquaresDate:11/24/11Time:09:18Sample(adjusted):19781998Includedobservations:21afteradjustingendpointsVariableCoefficientStd.Errort-StatisticProb.C2065.912540.80643.8200590.0012X32.9817740.06937842.978820.0000R-squared0.989819Meandependentvar21319.26AdjustedR-squared0.989283S.D.dependentvar13411.38S.E.ofregression1388.391Akaikein