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量年份工农业产品产量粮食油料糖料水果猪牛羊 肉2000536.78366.0423.460.4749.337.572001536.8

2、1355.8922.5368.0552.3537.992002552.77356.9622.6380.3954.338.492003583.12334.2921.8274.83112.6839.52004618.47362.2223.6673.84118.3640.392005632.99371.2623.672.5123.6541.982006652.91379.8920.1479.78130.4542.652007670.29380.6119.4992.48137.6240.092008710.21399.1322.29101.31145.142.38（来源与中国统计网）二、实验步骤：1、

3、 参数估计，过程如下：（1）先录入数据至eviews，得到下表:obsYX1X2X3X4X52&0053B.7800366.040023.4000060 4700049.3000037.670002001536.8100355.890022.5300068.0500052.3500037.990002&02552.7Z00356.960022.6300080.3900054.3000038490002003583.1200334.290021.8200074.83000112.680039.500002004&18.47003S2.220023.6600073.84000118.360040.

4、390002005&32.9900371.260023.6000072.60000123.G50041.980002Q&6652.9100379.890020.1400079.78000130.460042.650002&07670.2900380.610019.4900092.48000137.620040.0900020DS710.2100399.130022.29000101.3100145.100042.38000(2)在命令窗口输入LS y c x1 x2 x3 x4 x5,出现下列结果:Dependent Variable: YMethod: Least Squares ate:

5、12/25/11 Time: 08:13Sample: 2000 2008Included observations: 9Jk】VariableCoefficientStd. Errort-StatisticProb.C-2.54E-102.02E-10-1.2566190.2978X11 0000003.96E-132.53E+120.00001 0000003.98E-122.51E+110.00001 0000006.64E-131.51E+120.00001 0000003.14E-133.19E+120.00001 0000006.17E-121.&2E+T10.0000R-squa

6、r&d1 000000Mean dependent var610 4333Adjusted R-squared1 000000S.D. dependent var82.08072S E of regression1.3 ZE-11Aka ike infio criterion-46.95646Sum squared resid5.62E-22Schwarz criterion-46.82497Log likelihood217.3040F-statistic3.29E+26Durbin-Watson stat2.395982Prob(F-statisti：0 000000v2、分析 从结果看判

7、断系数RA2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 Quick 菜单中选 Group Statistics 项中的 Correlation 命令。在出现Series List对话框时，直接输入x1 X2 X3 X4,出现解释变量x1 x2 x3 x4之间的相关系数为：Correlation MatrixX1X2X3X4X1X2X3X4X11.0000000.9822490.9801540.985451X20 9822491.0000000 990

8、0770 981440X30 9801540 9900771.0000000 984662X40.9854510 9814400 9845621.000000可以看出四个解释变量x1 x2 x3 x4之间的高度相关，必然存在严重的多重共线性。辅助回归检验：解释变量x1 x2 x3 x4之间的辅助回归分别为：在命令窗口分别输入：ls x1 c x2;ls x1 c x3;ls x1 c x4;ls x2 c x3;ls x2 cx4;ls x3 c x4;结果分别为:Dependent Variable: X1Method: Least SquaresDate: 11/24/11 Time: 0

9、8:46Sample(adjusted): 1978 1998Included observations: 21 after adjusting endpointsVariableCoefficientStd. Error t-StatisticProb.C1077.333543.45941.9823620.0621X213.183760.57759822.825140.0000R-squared0.964814Mean dependent var11725.53Adjusted R-squared0.962962S.D.dependent var6638.021S.E. of regress

10、ion1277.503Akaike info criterion17.23360Sum squared resid31008264Schwarz criterion17.33307Log likelihood-178.9527F-statistic520.9871Durbin-Watson stat0.611662Prob(F-statistic)0.000000Dependent Variable: X1 Method: Least SquaresDate: 11/24/11 Time: 08:53Sample(adjusted): 1978 1998Included observation

11、s: 21 after adjusting endpointsVariableCoefficientStd. Errort-StatisticProb.C2337.206525.88784.4443050.0003X31.4539730.06746421.551870.0000R-squared0.960702Mean dependent var11725.53Adjusted R-squared0.958634S.D.dependent var6638.021S.E. of regression1350.091Akaike info criterion17.34412Sum squared

12、resid34632150Schwarz criterion17.44360Log likelihood-180.1133F-statistic464.4832Durbin-Watson stat0.865011Prob(F-statistic)0.000000Dependent Variable: X1 Method: Least SquaresDate: 11/24/11 Time: 09:05Sample(adjusted): 1978 1998Included observations: 21 after adjusting endpointsVariableCoefficientSt

13、d. Error t-StatisticProb.C2405.3699446.981730 5.381360863.41634090423873159189e-05X44.60403150.18216784 25.27356814.356762641693599746462e-16R-squared0.9711137Mean dependent var11725.528770685714Adjusted R-squared0.9695934S.D.dependent var6638.0216074316668S.E. of regression1157.5030Akaike info crit

14、erion17.03631115205737Sum squared resid25456451.Schwarz criterion17.13578211889011Log likelihood-176.88126F-statistic638.7532102449431Durbin-Watson stat0.5080094Prob(F-statistic)4.356762037226462e-16Dependent Variable: X2Method: Least SquaresDate: 11/24/11 Time: 09:05Sample(adjusted): 1978 1998Inclu

15、ded observations: 21 after adjusting endpointsVariableCoefficientStd. Error t-StatisticProb.C101.121627.774743.6407760.0017X30.1094240.00356330.710380.0000R-squared0.980252Mean dependent var807.6753Adjusted R-squared0.979213S.D.dependent var494.5626S.E. of regression71.30498Akaike info criterion11.4

16、6220Sum squared resid96603.61Schwarz criterion11.56168Log likelihood-118.3531F-statistic943.1276Durbin-Watson stat2.211553Prob(F-statistic)0.000000Dependent Variable: X2Method: Least SquaresDate: 11/24/11 Time: 09:05Sample(adjusted): 1978 1998Included observations: 21 after adjusting endpointsVariab

17、leCoefficientStd. Errort-StatisticProb.C116.108137.576143.0899430.0060X40.3416250.01531422.307720.0000R-squared0.963224Mean dependent var807.6753Adjusted R-squared0.961288S.D.dependent var494.5626S.E. of regression97.30710Akaike info criterion12.08401Sum squared resid179904.8Schwarz criterion12.1834

18、9Log likelihood-124.8821F-statistic497.6345Durbin-Watson stat0.530959Prob(F-statistic)0.000000Dependent Variable: X3 Method: Least SquaresDate: 11/24/11 Time: 09:06Sample(adjusted): 1978 1998Included observations: 21 after adjusting endpointsVariableCoefficientStd. Errort-StatisticProb.C179.7667310.

19、32270.5792900.5692X43.1008740.12647224.518200.0000R-squared0.969362Mean dependent var6457.012Adjusted R-squared0.967749S.D.dependent var4474.829S.E. of regression803.6109Akaike info criterion16.30650Sum squared resid12270021Schwarz criterion16.40598Log likelihood-169.2183F-statistic601.1422Durbin-Wa

20、tson stat0.896788Prob(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“ls y c x1”、Dependent Variable: YMethod: Least SquaresDate: 11/24/11 Time: 09:25Sample(adjusted): 1978 1998Included observations: 21 after adjusting endpointsVariable Coeff

21、icient Std. Error t-Statistic Prob.C-2241.475648.0392-3.4588570.0026X12.0093540.04837641.536570.0000R-squared0.989107Mean dependent var21319.26Adjusted R-squared0.988534S.D.dependent var13411.38S.E. of regression1436.083Akaike info criterion17.46762Sum squared resid39184332Schwarz criterion17.56710L

22、og likelihood-181.4100F-statistic1725.286Durbin-Watson stat0.520820Prob(F-statistic)0.000000“ls y c x2”、Dependent Variable: YMethod: Least SquaresDate: 11/24/11 Time: 09:13Sample(adjusted): 1978 1998Included observations: 21 after adjusting endpointsVariableCoefficientStd. Error t-StatisticProb.C-43

23、6.7055675.4209-0.6465680.5256X226.936520.71784937.523940.0000R-squared0.986686Mean dependent var21319.26Adjusted R-squared0.985985S.D.dependent var13411.38S.E. of regression1587.703Akaike info criterion17.66836Sum squared resid47895234Schwarz criterion17.76784Log likelihood-183.5178F-statistic1408.0

24、46Durbin-Watson stat1.194877Prob(F-statistic)0.000000“ls y c x3”Dependent Variable: YMethod: Least SquaresDate: 11/24/11 Time: 09:18Sample(adjusted): 1978 1998Included observations: 21 after adjusting endpointsVariableCoefficientStd. Error t-StatisticProb.C2065.912540.80643.8200590.0012X32.9817740.06937842.978820.0000R-squared0.989819Mean dependent var21319.26Adjusted R-squared0.989283S.D.dependent var13411.38S.E. of regression1388.391Akaike info c