复习多元线性回归模型案例

我国农民收入影响因素的回归分析自改革开放以来,虽然中国经济平均增长速度为9.5但%二元,经济结构给经济发展带来的问题仍然很突出。农村人口占了中国总人口的70%多,农业产业结构不合理,经济不发达,以及农民收入增长缓慢等问题势必成为我国经济持续稳定增长的障碍。正确有效地解决好“三农”问题是中国经济走出困境,实现长期稳定增长的关键。其中,农民收入增长是核心,也是解决“三农”问题的关键。本文力图应用适当的多元线性回归模型,对有关农民收入的历史数据和现状进行分析,寻找其根源,探讨影响农民收入的主要因素,并在此基础上对如何增加农民收入提出相应的政策建议。农民收入水平的度量，通常采用人均纯收入指标。影响农民收入增长的因素是多方面的，既有结构性矛盾因素，又有体制性障碍因素。但可以归纳为以下几个方面：一是农产品收购价格水平。目前农业收入仍是中西部地区农民收入的主要来源。二是农业剩余劳动力转移水平。中国的农业目前仍以农户分散经营为主，农业比较效益低，尽快地把农业剩余劳动力转移出去是有效改善农民收入状况的重要因素。三是城市化、工业化水平。中国多数地区城市化、工业化水平落后于世界平均水平，这种状况极大地影响了农民收入的增长。四是农业产业结构状况。农林牧渔业对农民收入增长贡献率是不同的。随着我国“入世”后农产品市场的开放和人民生活水平的提高、农产品需求市场的改变，农业结构状况直接影响着农民收入的增长。五是农业投入水平。农民收入与财政农业支出、农村集体投入、农户个人投入以及信贷投入都有显著的正相关关系。农业投入是农民收入增长的重要保证。但考虑到农业投入主体的多元性，既有国家、集体和农户的投入，又有银行、企业和外资的投入，考虑到复杂性和可行性，所以对农业投入与农民收入，本文暂不作讨论。因此，以全国为例，把农民收入与各影响因素关系进行线性回归分析，并建立数学模型。一、计量经济模型分析（一）、数据搜集根据以上分析，我们在影响农民收入因素中引入个解释变量。即：X财2

政用于农业的支出的比重，X第二、三产业从业人数占全社会从业人数的比重，3TOC\o"1-5"\h\zX非农村人口比重，X乡村从业人员占农村人口的比重，X农业总产值45 6占农林牧总产值的比重，X农作物播种面积，X农村用电量。7 8—年份年可比价比重比重比重千公顷亿千瓦时资料来源《中国统计年鉴2006》。TOC\o"1-5"\h\z（二）、计量经济学模型建立我们设定模型为下面所示的形式：Y=0+0X+pX+pX+pX+pX+pX+pX+ut1 22 33 44 55 66 77 88t利用Eviews软件进行最小二乘估计，估计结果如下表所示:DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Errort-StatisticProb.C-1102.373375.8283-2.9331840.0136X1-6.6353933.781349-1.7547690.1071

X318.229422.066617 8.8208990.0000X42.4300398.370337 0.2903160.7770X5-16.237375.894109 -2.7548470.0187X6-2.1552082.770834 -0.7778190.4531X70.0099620.002328 4.2788100.0013X80.0633890.021276 2.9793480.0125R-squared0.995823Meandependentvar345.5232AdjustedR-squared0.993165S.D.dependentvar139.7117S.E.ofregression11.55028Akaikeinfocriterion8.026857Sumsquaredresid1467.498Schwarzcriterion8.424516Loglikelihood-68.25514F-statistic374.6600Durbin-Watsonstat1.993270Prob（F-statistic）0.000000表1最小二乘估计结果回归分析报告为：Y=-1102.373-6.6354X+18.2294X+2.4300X-16.2374X-2.1552X+0.0100X+0.0634XSe=（375.83）（3.7813j（2.06661）（8.37034｝（5.8941）（2.7708）（0.00233）（0.02l28）t=（-2.933）（-1.755）（8.82090）（0.20316）（-2.755）（-0.778）（4.27881）（2.9793）R2=0.995823R2=0.993165Df=19DW=1.99327F=374.66、计量经济学检验(一)、多重共线性的检验及修正①、检验多重共线性(a)、直观法从“表1最小二乘估计结果”中可以看出，虽然模型的整体拟合的很好，但是x4x6的t统计量并不显著，所以可能存在多重共线性。(b)、相关系数矩阵X2X3X4X5X6X7X8X2X3X4X5X6X7X81.000000-0.717662-0.695257-0.7313260.737028-0.332435-0.594699-0.717662-0.695257-0.7313260.737028-0.332435-0.5946991.0000000.9222860.935992-0.9457010.7422510.8838040.9222860.935992-0.9457010.7422510.8838041.0000000.986050-0.9377510.7539280.9746750.9860501.000000-0.9747500.6874390.940436-0.937751-0.9747501.000000-0.603539-0.8874280.7539280.687439-0.6035391.0000000.7427810.9746750.940436-0.8874280.7427811.000000X2X3X4X5X6X7X8X2X3X4X5X6X7X81.000000-0.717662-0.695257-0.7313260.737028-0.332435-0.594699-0.717662-0.695257-0.7313260.737028-0.332435-0.5946991.0000000.9222860.935992-0.9457010.7422510.8838040.9222860.935992-0.9457010.7422510.8838041.0000000.986050-0.9377510.7539280.9746750.9860501.000000-0.9747500.6874390.940436-0.937751-0.9747501.000000-0.603539-0.8874280.7539280.687439-0.6035391.0000000.7427810.9746750.940436-0.8874280.7427811.000000表2相关系数矩阵从“表2相关系数矩阵”中可以看出，个个解释变量之间的相关程度较高，所以应该存在多重共线性。②、多重共线性的修正—一逐步迭代法

A、A、元回归DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Error t-StatisticProb.C820.3133151.8712 5.4013740.0000X2-51.3783616.18923 -3.1736140.0056R-squared0.372041Meandependentvar345.5232AdjustedR-squared0.335102S.D.dependentvar139.7117S.E.ofregression113.9227Akaikeinfocriterion12.40822Sumsquaredresid220632.4Schwarzcriterion12.50763Loglikelihood-115.8781F-statistic10.07183Durbin-Watsonstat0.644400Prob(F-statistic)0.005554 1表3y对x2的回归结果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Error t-StatisticProb.C-525.889164.11333 -8.2024920.0000X319.460311.416043 13.742740.0000R-squared0.917421Meandependentvar345.5232AdjustedR-squared0.912563S.D.dependentvar139.7117S.E.ofregression41.31236Akaikeinfocriterion10.37950Sumsquaredresid29014.09Schwarzcriterion10.47892Loglikelihood-96.60526F-statistic188.8628Durbin-Watsonstat0.598139Prob(F-statistic)0.000000表4y对x3的回归结果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Error t-StatisticProb.C-223.190569.92322 -3.1919370.0053X418.650862.242240 8.3179560.0000R-squared0.802758Meandependentvar345.5232AdjustedR-squared0.791155S.D.dependentvar139.7117S.E.ofregression63.84760Akaikeinfocriterion11.25018Sumsquaredresid69300.77Schwarzcriterion11.34959Loglikelihood-104.8767F-statistic69.18839

Durbin-Watsonstat0.282182Prob(F-statistic)0.000000DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19表5y对x4的回归结果VariableCoefficientStd.Error t-StatisticProb.C-494.1440118.1449 -4.1825260.0006X515.779782.198711 7.1768320.0000R-squared0.751850Meandependentvar345.5232AdjustedR-squared0.737253S.D.dependentvar139.7117S.E.ofregression71.61463Akaikeinfocriterion11.47978Sumsquaredresid87187.14Schwarzcriterion11.57919Loglikelihood-107.0579F-statistic51.50691Durbin-Watsonstat0.318959Prob(F-statistic)0.000002表6y对x5的回归结果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Error t-StatisticProb.C1288.009143.8088 8.9563950.0000X6-15.523982.351180 -6.6026350.0000R-squared0.719448Meandependentvar345.5232AdjustedR-squared0.702945S.D.dependentvar139.7117S.E.ofregression76.14674Akaikeinfocriterion11.60250Sumsquaredresid98571.54Schwarzcriterion11.70192Loglikelihood-108.2238F-statistic43.59479Durbin-Watsonstat0.395893Prob(F-statistic)0.000004表7y对x6的回归结果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Error t-StatisticProb.C-4417.766681.1678 -6.4855770.0000X70.0315280.004507 6.9949430.0000R-squared0.742148Meandependentvar345.5232AdjustedR-squared0.726980S.D.dependentvar139.7117S.E.ofregression73.00119Akaikeinfocriterion11.51813Sumsquaredresid90595.96Schwarzcriterion11.61754

LoglikelihoodDurbin-Watsonstat-107.42220.572651F-statisticProb(F-statistic)48.929230.000002DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19表8y对x7的回归结果VariableCoefficientStd.Error t-StatisticProb.C140.162528.96616 4.8388350.0002X80.1198270.014543 8.2395030.0000R-squared0.799739Meandependentvar345.5232AdjustedR-squared0.787959S.D.dependentvar139.7117S.E.ofregression64.33424Akaikeinfocriterion11.26536Sumsquaredresid70361.21Schwarzcriterion11.36478Loglikelihood-105.0209F-statistic67.88941Durbin-Watsonstat0.203711Prob(F-statistic)0.000000—1表9y对x8的回归结果综合比较表3~9的回归结果，发现加入x3的回归结果最好。以x3为基础顺次加入其他解释变量，DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19进行二元回归，具体的回归结果如下表10~15所示：VariableCoefficientStd.Error t-StatisticProb.C-754.4481149.1701 -5.0576370.0001X321.788651.932689 11.273750.0000X213.450708.012745 1.6786630.1126R-squared0.929787Meandependentvar345.5232AdjustedR-squared0.921010S.D.dependentvar139.7117S.E.ofregression39.26619Akaikeinfocriterion10.32254Sumsquaredresid24669.34Schwarzcriterion10.47167Loglikelihood-95.06417F-statistic105.9385Durbin-Watsonstat0.595954Prob(F-statistic)0.000000表10加入x2的回归结果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Error t-StatisticProb.C-508.678175.73220 -6.7168020.0000

X317.882003.752121 4.7658370.0002X41.7533513.844305 0.4560900.6545R-squared0.918481Meandependentvar345.5232AdjustedR-squared0.908291S.D.dependentvar139.7117S.E.ofregression42.30965Akaikeinfocriterion10.47185Sumsquaredresid28641.71Schwarzcriterion10.62097Loglikelihood-96.48254F-statistic90.13613Durbin-Watsonstat0.596359Prob(F-statistic)0.000000表11加入x4的回归结果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Error t-StatisticProb.C-498.155067.21844 -7.4109860.0000X323.975163.967183 6.0433700.0000X5-4.3205663.553466 -1.2158740.2417R-squared0.924405Meandependentvar345.5232AdjustedR-squared0.914956S.D.dependentvar139.7117S.E.ofregression40.74312Akaikeinfocriterion10.39639Sumsquaredresid26560.02Schwarzcriterion10.54551Loglikelihood-95.76570F-statistic97.82772Durbin-Watsonstat0.607882Prob(F-statistic)0.000000表12加入x5的回归结果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Error t-StatisticProb.C-1600.965346.9265 -4.6147090.0003X329.937683.534753 8.4695280.0000X69.9801353.184176 3.1342910.0064R-squared0.948835Meandependentvar345.5232AdjustedR-squared0.942440S.D.dependentvar139.7117S.E.ofregression33.51927Akaikeinfocriterion10.00606Sumsquaredresid17976.66Schwarzcriterion10.15518Loglikelihood-92.05754F-statistic148.3576Durbin-Watsonstat1.125188Prob(F-statistic)0.000000表13加入x6的回归结果DependentVariable:YMethod:LeastSquaresSample:19862004

Includedobservations:19VariableCoefficientStd.Error t-StatisticProb.C-2153.028327.1248 -6.5816730.0000X314.404971.358355 10.604720.0000X70.0122680.002447 5.0140150.0001R-squared0.967884Meandependentvar345.5232AdjustedR-squared0.963869S.D.dependentvar139.7117S.E.ofregression26.55648Akaikeinfocriterion9.540364Sumsquaredresid11283.94Schwarzcriterion9.689485Loglikelihood-87.63345F-statistic241.0961Durbin-Watsonstat0.690413Prob(F-statistic)0.000000表14加入x7的回归结果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Error t-StatisticProb.C-400.5635103.0301 -3.8878320.0013X315.542712.916358 5.3294930.0001X80.0292330.019233 1.5199290.1480R-squared0.927840Meandependentvar345.5232AdjustedR-squared0.918820S.D.dependentvar139.7117S.E.ofregression39.80687Akaikeinfocriterion10.34990Sumsquaredresid25353.40Schwarzcriterion10.49902Loglikelihood-95.32401F-statistic102.8643Durbin-Watsonstat0.559772Prob(F-statistic)0.000000表15加入x8的回归结果综合表10〜15所示，加入x7的模型的R最大似x3、x7为基础顺次加入其他解释变量，进行三元回归，具体回归结果如下表16~20所示：DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Error t-StatisticProb.C-2133.921340.6965 -6.2634060.0000X314.960232.094645 7.1421340.0000X70.0118430.002786 4.2509080.0007X22.1952436.170403 0.3557700.7270R-squared0.968153Meandependentvar345.5232AdjustedR-squared0.961783S.D.dependentvar139.7117S.E.ofregression27.31242Akaikeinfocriterion9.637224

Sumsquaredresid11189.52Schwarzcriterion9.836053Loglikelihood-87.55363F-statistic151.9988Durbin-Watsonstat0.712258Prob(F-statistic)0.000000表16加入x2的回归结果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Error t-StatisticProb.C-2226.420353.4425 -6.2992430.0000X315.667292.443113 6.4128390.0000X70.0127030.002589 4.9063730.0002X4-1.6013622.553294 -0.6271750.5400R-squared0.968705Meandependentvar345.5232AdjustedR-squared0.962445S.D.dependentvar139.7117S.E.ofregression27.07472Akaikeinfocriterion9.619741Sumsquaredresid10995.60Schwarzcriterion9.818571Loglikelihood-87.38754F-statistic154.7677Durbin-Watsonstat0.704178Prob(F-statistic)0.000000表17加入x4的回归结果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Error t-StatisticProb.C-2110.381306.2690 -6.8906130.0000X318.601562.617381 7.1069370.0000X70.0121390.002285 5.3116650.0001X5-3.9648782.163262 -1.8328230.0868R-squared0.973760Meandependentvar345.5232AdjustedR-squared0.968512S.D.dependentvar139.7117S.E.ofregression24.79152Akaikeinfocriterion9.443544Sumsquaredresid9219.289Schwarzcriterion9.642373Loglikelihood-85.71367F-statistic185.5507Durbin-Watsonstat0.733972Prob(F-statistic)0.000000表18加入x5的回归结果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Error t-StatisticProb.C-2418.859323.7240 -7.4719790.0000

X320.998873.397120 6.1813740.0000X70.0099200.002495 3.9766600.0012X65.3591842.571950 2.0837050.0547R-squared0.975093Meandependentvar345.5232AdjustedR-squared0.970112S.D.dependentvar139.7117S.E.ofregression24.15359Akaikeinfocriterion9.391407Sumsquaredresid8750.940Schwarzcriterion9.590236Loglikelihood-85.21837F-statistic195.7489Durbin-Watsonstat1.084023Prob(F-statistic)0.000000表19加入x6的回归结果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Error t-StatisticProb.C-2013.355361.8657 -5.5638180.0001X313.015782.032420 6.4040780.0000X70.0116150.002558 4.5403220.0004X80.0123750.013416 0.9224010.3709R-squared0.969608Meandependentvar345.5232AdjustedR-squared0.963529S.D.dependentvar139.7117S.E.ofregression26.68115Akaikeinfocriterion9.590455Sumsquaredresid10678.26Schwarzcriterion9.789285Loglikelihood-87.10933F-statistic159.5158Durbin-Watsonstat0.672264Prob(F-statistic)0.000000表20加入x8的回归结果综合上述表16〜20的回归结果所示，其中加入x6的回归结果最好，以x3x6x7为基础一次加入其他解释变量，作四元回归估计，估计结果如表21~24所示:DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Error t-StatisticProb.C-2405.108339.7396 -7.0792690.0000X321.268503.699787 5.7485730.0001X65.3105432.665569 1.9922730.0662X70.0096890.002766 3.5033860.0035X21.3026055.655390 0.2303300.8212R-squared0.975187Meandependentvar345.5232AdjustedR-squared0.968098S.D.dependentvar139.7117S.E.ofregression24.95411Akaikeinfocriterion9.492888

Sumsquaredresid8717.904Schwarzcriterion9.741424Loglikelihood-85.18244F-statistic137.5567Durbin-Watsonstat1.082771Prob(F-statistic)0.000000表21加入x2的回归结果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Error t-StatisticProb.C-2401.402316.2980 -7.5922150.0000X322.105703.420783 6.4621740.0000X69.0890333.781330 2.4036600.0307X70.0070860.003247 2.1820050.0466X44.4176783.348889 1.3191470.2083R-squared0.977847Meandependentvar345.5232AdjustedR-squared0.971517S.D.dependentvar139.7117S.E.ofregression23.57887Akaikeinfocriterion9.379513Sumsquaredresid7783.481Schwarzcriterion9.628049Loglikelihood-84.10537F-statistic154.4909Durbin-Watsonstat1.580301Prob(F-statistic)0.000000—1表22加入x4的回归结果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Error t-StatisticProb.C-2375.188430.7065 -5.5146310.0001X320.834933.657414 5.6966290.0001X64.6291965.252860 0.8812720.3930X70.0102170.003171 3.2219530.0061X5-0.6936924.304485 -0.1611560.8743R-squared0.975139Meandependentvar345.5232AdjustedR-squared0.968036S.D.dependentvar139.7117S.E.ofregression24.97818Akaikeinfocriterion9.494817Sumsquaredresid8734.736Schwarzcriterion9.743353Loglikelihood-85.20076F-statistic137.2849Durbin-Watsonstat1.023211Prob(F-statistic)0.000000 1表23加入x5的回归结果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19

VariableCoefficientStd.Error t-StatisticProb.C-2212.242259.5324 -8.5239510.0000X322.066292.662231 8.2886470.0000X69.5956532.380088 4.0316380.0012X70.0061150.002260 2.7059780.0171X80.0369230.011239 3.2853540.0054R-squared0.985936Meandependentvar345.5232AdjustedR-squared0.981918S.D.dependentvar139.7117S.E.ofregression18.78702Akaikeinfocriterion8.925144Sumsquaredresid4941.332Schwarzcriterion9.173681Loglikelihood-79.78887F-statistic245.3639Durbin-Watsonstat2.186293Prob(F-statistic)0.000000—1表24加入x8的回归结果综合表21〜24所示的回归结果，其中加入x8的回归结果最好，以x3x6x7x8为基础顺次加入其他的解释变量，其回归结果如表25~27所示：DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Errort-StatisticProb.C-2207.020272.6061-8.0960050.0000X322.174952.9031907.6381330.0000X69.5667312.4800573.8574640.0020X70.0060280.0024512.4589490.0287X80.0368460.0116743.1561950.0076X20.5358114.4226450.1211520.9054R-squared0.985952Meandependentvar345.5232AdjustedR-squared0.980549S.D.dependentvar139.7117S.E.ofregression19.48522Akaikeinfocriterion9.029279Sumsquaredresid4935.759Schwarzcriterion9.327523Loglikelihood-79.77815F-statistic182.4791Durbin-Watsonstat2.180501Prob(F-statistic)0.000000表25加入x2的回归结果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Errort-StatisticProb.C-1373.136279.4825-4.9131370.0003X320.093301.92848610.419210.0000X60.4804012.8459720.1688000.8686

X70.0084970.001692 5.0214100.0002X80.0605020.009873 6.1281460.0000X5-11.232922.844094 -3.9495600.0017R-squared0.993607Meandependentvar345.5232AdjustedR-squared0.991148S.D.dependentvar139.7117S.E.ofregression13.14457Akaikeinfocriterion8.241984Sumsquaredresid2246.136Schwarzcriterion8.540228Loglikelihood-72.29885F-statistic404.1009Durbin-Watsonstat1.704834Prob(F-statistic)0.000000表26加入x5的回归结果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Error t-StatisticProb.C-2056.366236.8112 -8.6835690.0000X320.602202.413096 8.5376610.0000X65.2648342.804292 1.8774200.0831X70.0088530.002306 3.8394460.0020X80.0717420.018026 3.9800360.0016X4-9.8612314.279624 -2.3042280.0384R-squared0.990014Meandependentvar345.5232AdjustedR-squared0.986174S.D.dependentvar139.7117S.E.ofregression16.42798Akaikeinfocriterion8.687938Sumsquaredresid3508.420Schwarzcriterion8.986182Loglikelihood-76.53541F-statistic257.7752Durbin-Watsonstat1.965748Prob(F-statistic)0.000000表27加入x4的回归结果据表25~27所示，分别加入x2x4x5后R均有所增加，但是参数的T检验均不显著，所以最终的计量模型如下表所示：DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Error t-StatisticProb.C-2212.242259.5324 -8.5239510.0000X322.066292.662231 8.2886470.0000X69.5956532.380088 4.0316380.0012X70.0061150.002260 2.7059780.0171X80.0369230.011239 3.2853540.0054R-squared0.985936Meandependentvar345.5232

AdjustedR-squared0.981918S.D.dependentvar139.7117S.E.ofregression18.78702Akaikeinfocriterion8.925144Sumsquaredresid4941.332Schwarzcriterion9.173681Loglikelihood-79.78887F-statistic245.3639Durbin-Watsonstat2.186293Prob（F-statistic）0.000000表28多重共线性修正后的最终模型回归分析报告为：Y=-2212.242+22.0663X+9.5956X+0.00612X+0.03692XSe=（259.5324）（2.6622）（2.3801（0.00226/（0.011239）t=（-8.523951）（8.28865）（4.032）（2.70598）（3.285354）R2=0.985936R2=0.981918Df=19DW=2.186293F=245.3639（二）、异方差的检验A、相关图形分析图1图图#图9从图中可以看出大部分点落在1、3象限，表明存在正自相关。从图中可以看出，随着t的变化逐次变化，并不频繁改变符号，而是正的后面跟着几个负的，表明存在正自相关。综上所述，说明模型存在自相关性。②自相关的修正——德宾两步法将广义方程表示为：Yt=4（1-P）+%X3+^3X6+口4X7+P5X8-P%X3一一P^3X6.1-p^4X7--p^5X8,1+pYt-1+vtt—1 t—1 t—1 t—1将上述式子作为一个多元模型进行普通最小二乘估计，将Y1的P作为的p估计值。t—1DependentVariable:YMethod:LeastSquaresSample(adjusted):19872003Includedobservations:17afteradjustingendpointsVariableCoefficientStd.Errort-StatisticProb.C-2604.5511325.611-1.9647930.0902X37.1311006.6275901.0759720.3176X68.1289833.4627792.3475320.0513X70.0195220.0070682.7620590.0280X8-0.0067280.0718170.0936870.9280X3(1)17.369733.9158844.4357100.0030X6(-1)3.3799903.0459851.1096540.3038X7(-1)-0.0124860.0032633.8268870.0065X8(-1)0.0950230.1146970.8284660.4347Y(-1)-0.2081230.495599 -0.4199420.6871R-squared0.997436Meandependentvar348.9382AdjustedR-squared0.994140S.D.dependentvar132.8918S.E.ofregression10.17327Akaikeinfocriterion7.766572Sumsquaredresid724.4683Schwarzcriterion8.256698Loglikelihood-56.01586F-statistic302.5781Durbin-Watsonstat2.420889Prob(F-statistic)0.000000 1表31广义方程估计结果由上表可知P=-0.208123,下一步使用广义差分法进行修正:令Y=Y令Y=Y-PY,X=X-PX,X=X-PX,X1t t—1 31 3t 3t-1 61 6t 6t-1 71p=B(1-p),p=p,p=p,p=p,p=p;11 1 21 2 31 3 41 4 51 5则模型可表示为：=X7t-PX,X=X-PX;7t-1 81 8t 8t-1Y=p+pX+pX+pX+pX+v1 11 21 31 31 61 41 71 51 81tDependentVariable:Y+Y(-1)*0.208123Method:LeastSquaresSample(adjusted):19872004Includedobservations:18afteradjustingendpointsVariableCoefficientStd.Error t-StatisticProb.C-2681.442307.9863 -8.7063680.0000X3+X3(-1)*0.20812323.587662.433154 9.6942750.0000X6+X6(-1)*0.20812311.094402.238039 4.9571990.0003X7+X7(-1)*0.2081230.0050620.002144 2.3613690.0345X8+X8(-1)*0.2081230.0412480