多重共線性模型

1、多重共線性報告分析背景與意義：農(nóng)產(chǎn)品的產(chǎn)量及其分布構(gòu)成在國民生產(chǎn)生活中具有重要意義，它能真切反應(yīng)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(nóng)業(yè)產(chǎn)品產(chǎn)量進(jìn)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(jìn)行修正處理降低多重共線性對結(jié)果的影響，從而使結(jié)果模型更具代表性，更真切的展示結(jié)果，進(jìn)而有利于國家對農(nóng)業(yè)產(chǎn)品的生產(chǎn)組成的了解以及監(jiān)控，才能更好的對其調(diào)控，促進(jìn)其穩(wěn)定、科學(xué)的發(fā)展。一、數(shù)據(jù)選擇主要人均主要工農(nóng)業(yè)產(chǎn)品產(chǎn)品年份工農(nóng)業(yè)產(chǎn)品產(chǎn)糧食油料糖料水果豬牛羊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(來源與中國統(tǒng)計網(wǎng))二、實驗步驟：1、 參數(shù)估計，過

3、程如下：(1)先錄入數(shù)據(jù)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)在命令窗口輸入LSycx1x2x3x4x5,出現(xiàn)下列結(jié)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、 分析從結(jié)果看判斷系數(shù)R，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(jīng)濟(jì)理論，顯然認(rèn)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(guān)系數(shù)。Eviews過程如下：(1)在Qu

7、ick菜單中選GroupStatistics項中的Correlation命令。在出現(xiàn)SeriesList對話框時，直接輸入x1X2X3X4,出現(xiàn)解釋變量x1x2x3x4之間的相關(guān)系數(shù)為：CorrelationMatrixX1X2X3X4X1X2X3X4X11.0000000.9822490.9801540.985451X209822491.0000000.9900770981440X309801540.99007710000000.984562X409854510.96144009845621.000000可以看出四個解釋變量x1x2x3x4之間的高度相關(guān)，必然存在嚴(yán)重的多重共線性。輔助回歸檢

8、驗：解釋變量x1x2x3x4之間的輔助回歸分別為：在命令窗口分別輸入：lsx1cx2;lsx1cx3;lsx1cx4;lsx2cx3;lsx2cx4;lsx3cx4;結(jié)果分別為: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(jié)合經(jīng)濟(jì)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)sycx1”、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