多重共线性检验与修正

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1、问题:选収粮食生产为例，由经济学理论和实际可以知道，影响粮食生产y的因素有：农业化肥施用量xl，粮食播种曲‘积x2,成灾面积x3,农业机械总动力x4,农业劳动力x5,由此建立以下方程：y=P0+P1X1+32X2+33X3+P4X4+35X5，木目关数据女卩下：obsYX1X2X3X4X5

2、198338728.001659.800114047.019209.3018022.0031645.10[198440731.001739.800112884.015264.0019497.0031685.00198537911.001775.8001088

3、45.022705.30209130030351.50198639151.001930.600110933.023656.0022950.0030467.00198740208.001999.300111628.020392.7024836.0030870.00198839408002141.500110123.023944.7026575.0031455.70198940755.002357.100112205.024448.7028067.0032440.50199044624.002590.300113466.017819.3028708

4、.0033330.40199143529.002806.100112314.027814.0029389.0034186.30199244264.002930.200110560.025894.7030308.0034037.00199345649.003151.900110509023133.0031817.0033258.20199444510.003317.900109544.031383.0033802.0032690.30199546662.003593.700110060.0222670036118.0032334.50199650

5、454.003827.900112548.021233.0038547.0032260.40199749417.003980.700112912.030309.0042016.0032434.90199851230004083.700113787.025181.0045208.0032626.40199950839.004124.300113161.026731.0048996.0032911.80200046218.004146.400108463.034374.0052574.0032797.50解：1、检验多重共线性(1)在命令栏巾输入：

6、Isycxlx2x3x4x5,则有;CoefficientStdErrort-StatisticProb.C-131846211743.11-112275402835XI6.1748960.64083696356920.0000X204230160104157406133100016X3-01870300049958•374374400028X4-0.0922540058135158688601385X5•00086100173446•004964009612R-squared0.987160Meandependentvar44127.11Ad

7、justedR-squared0981810SDdependentvar4409100SEofregression5946485Akaikeinfocrrtenon1587502Sumsquaredresd4243283.Schwarzcrrtenon16.17181Loglikelihood-1368752Hannan-Quinncriter1591594F-statistic1845210Durbin-Watsonstat1837323Prob(F-statistic)0000000DependentVanable:YMethodLeast

8、SquaresDate:11/18/15Time:18:32Sample:19832000Includedobservations18可以看到，可决系数R2和F值都很高，二自变量xl到x5的t值均较小，并且x4和x5的t检验不显著，说明方程很可能存在多重共线性。(2)对自变量做相关性分析：Wxlx5作为组打开，viewcovarianceanalysiscorrelation,姑果如下:X1X2X3X4X5X11000000-0000271062088309602780545450X2•00002711.000000•0433350•0.047

9、3880.166159X30.620883-0.4333501.0000000.6711320.349993X40960278-0.047388067