多重共線性模型

1、多重共線性報告分析背景與意義：農產品的產量及其分布構成在國民生產生活中具 有重要意義，它能真切反應國名的日常生活需求什么，因此本次研究 就是對于2000年-2008年人均主要工農業(yè)產品產量進行分析，主要 考慮各解釋變量之間是否存在多重共線性，并對其進行修正處理降低 多重共線性對結果的影響，從而使結果模型更具代表性，更真切的展 示結果，進而有利于國家對農業(yè)產品的生產組成的了解以及監(jiān)控，才 能更好的對其調控，促進其穩(wěn)定、科學的發(fā)展。一、數(shù)據(jù)選擇主要人均主要工農業(yè)產品產量年份工農業(yè)產品產量糧食油料糖料水果豬牛羊 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（來源與中國統(tǒng)計網）二、實驗步驟：1、

3、 參數(shù)估計，過程如下：（1）先錄入數(shù)據(jù)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)在命令窗口輸入LS y c x1 x2 x3 x4 x5,出現(xiàn)下列結果: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 從結果看判

7、斷系數(shù)RA2很高，說明方程很顯著，但四個參數(shù)t檢驗值 中有三個較顯著，有一個不顯著，不符合經濟理論，顯然認為出現(xiàn)了 多重線性回歸。三、檢驗計算解釋變量之間的簡單相關系數(shù)。Eviews過程如下：(1)在 Quick 菜單中選 Group Statistics 項中的 Correlation 命令。在出現(xiàn)Series List對話框時，直接輸入x1 X2 X3 X4,出現(xiàn)解釋變量x1 x2 x3 x4之間的相關系數(shù)為：Correlation MatrixX1X2X3X4X1X2X3X4X11.0000000.9822490.9801540.985451X20 9822491.0000000 990

8、0770 981440X30 9801540 9900771.0000000 984662X40.9854510 9814400 9845621.000000可以看出四個解釋變量x1 x2 x3 x4之間的高度相關，必然存在嚴重的多重共線性。輔助回歸檢驗：解釋變量x1 x2 x3 x4之間的輔助回歸分別為：在命令窗口分別輸入：ls x1 c x2;ls x1 c x3;ls x1 c x4;ls x2 c x3;ls x2 cx4;ls x3 c x4;結果分別為: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)0.000000六個回歸方程均存在高度顯著，擬合優(yōu)度高，具有共線性。四、修正運用OLS方法逐一求Y對各個解釋變量的回歸。結合經濟意義 和統(tǒng)計檢驗選出擬合效果最好的一元線性回歸方程。分別輸入“l(fā)s 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“l(fā)s 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“l(fā)s 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