我国公路客运量的研究.doc

我国公路客运量的研究报告白一佳 陈华 师群昌 王一竹 张斯蕊 庄云摘要：本文通过建立模型对影响我国公路客运量的因素进行了研究，通过Evies对七个变量进行回归拟合，通过建立模型对样本数据进行回归，分析得到最终模型，并在此基础上细分变量优化模型，引入虚拟变量对城市农村的影响情况进行对比分析，由此提出了最终模型的改进模型，通过样本回归分析得出一定的结论，提出进一步探讨的问题。关键词：公路客运量 OLS回归一背景综述改革开放后，我国国民经济持续高速发展，公路运输需求强劲增长，国家加大了公路基础设施的建设力度。随着道路环境的改善和城乡交流的日益频繁，公路客运量逐年提高。伴随着中国城市化的进程，城乡之间、城际之间的交流日益频繁，这直接支持了公路客运行业的发展。公路客运在我国综合运输体系客运市场中发挥着举足轻重的作用，承担着90%以上的份额，因此对我国公路客运的研究就显得很有现实意义，通过研究我国从改革开放至今的公路客运量发展变化，可以从我国国民经济发展的一个侧面了解到我国二十多年来的交通运输、公共事业建设、人民生活水平、社会生产、流通、分配、消费各环节协调发展等诸多现实经济问题，对于提升个人对国家经济发展认识、研究分析的能力大有好处。因此，本文以1978年为课题研究的时间起点，纵观中国公路、人口、人均收入、客运汽车产量、铁路、民航、水路运输客运量等众多因素对我国公路客运量的推动作用和影响，通过建立多元线性回归方程，进行实证分析，得出对我国公路客运量的显著影响因素。二模型变量选择及预测在模型建立之初，我们选择了七个对公路客运量可能造成影响的因素：客运汽车总量、年底总人口、铁路客运量、水运客运量、民用航空客运量、公路长度及全国总人均收入。从经济常识的角度，初步认为，人口、人均收入作为国民经济衡量的基本要素对公路客运量应该有一定的影响；铁路客运、水运客运、民航客运与公路客运存在替代的经济关系，其三者的客运量要么与公路客运量有负相关的关系，要么与公路客运量的相关关系不大；客运汽车作为公路客运的硬件条件我们也将其引入模型，去考察客运汽车总量与客运量规模间的解释关系；而客运路线的丰富程度势必也将对公路客运量造成影响，在此我们用公路的长度去衡量客运路线的丰富程度。在以上分析的基础上，进行主观的预测，对公路客运量可能造成影响的因素有：年底总人口、全国总人均收入、铁路客运量、客运汽车总量。三模型分析根据对经济现象的分析，建立如下模型描述：其中：（一）、对所选择的样本作散点图得个解释变量与被解释变量的关系如下系列图所示：从图形看出所选择的解释变量x3与x4样本数据与所选择的被解释变量的样本数据间没有明显的相关性，其余解释变量与被解释变量间有明显的线性相关性。所以推测所建模型中x3和x4对y的解释可能不显著。（二）、样本模型的估计1、模型估计对所选择的样本数据运用OLS法回归得：Dependent Variable: YMethod: Least SquaresDate: 12/16/05 Time: 15:08Sample: 1 18Included observations: 18VariableCoefficientStd. Errort-StatisticProb. C-1810996.156801.2-11.549640.0000X1-18.56917178.2442-0.1041780.9191X216.031731.7781879.0157720.0000X33.7978611.1424343.3243600.0077X4-2.6284404.549093-0.5777940.5762X510.8877217.879220.6089590.5561X61357.762726.40071.8691640.0911X7349.150853.140406.5703460.0001R-squared0.998779 Mean dependent var941880.1Adjusted R-squared0.997924 S.D. dependent var413515.1S.E. of regression18842.03 Akaike info criterion22.82667Sum squared resid3.55E+09 Schwarz criterion23.22239Log likelihood-197.4400 F-statistic1168.282Durbin-Watson stat2.666635 Prob(F-statistic)0.000000即：从回归的样本模型的统计量R=0.998779可以看出，模型的拟合优度非常好，从F=1168.282可知解释变量对模型的整体解释显著，然而通过样本数据所得的解释变量x1、x4、x5参数估计值的t值明显不显著，据此推测模型解释变量间可能存在多重共线性。2、多重共线性的检验运用相关系数矩阵检验，相关系数矩阵为：X1X2X3X4X5X6X7X1 1.000000 0.882892 0.407131-0.702549 0.973972 0.960579 0.907679X2 0.882892 1.000000 0.504735-0.504676 0.920224 0.819337 0.924883X3 0.407131 0.504735 1.000000 0.276174 0.330393 0.359901 0.295472X4-0.702549-0.504676 0.276174 1.000000-0.751790-0.739402-0.722706X5 0.973972 0.920224 0.330393-0.751790 1.000000 0.933892 0.974145X6 0.960579 0.819337 0.359901-0.739402 0.933892 1.000000 0.863272X7 0.907679 0.924883 0.295472-0.722706 0.974145 0.863272 1.000000从相关系数矩阵中可以看出，解释变量x1与x2、x5、x6、x7，x2与x5、x6、x7，x5与x6、x7，x6与x7高度相关，说明模型存在多重共线性。3、多重共线性的消除运用逐步回归法消除多重共线性：第一步：Dependent Variable: YMethod: Least SquaresDate: 12/16/05 Time: 15:25Sample: 1 18Included observations: 18VariableCoefficientStd. Errort-StatisticProb. C224417.043625.735.1441430.0001X7759.698140.5134618.751750.0000R-squared0.956478 Mean dependent var941880.1Adjusted R-squared0.953758 S.D. dependent var413515.1S.E. of regression88922.47 Akaike info criterion25.73336Sum squared resid1.27E+11 Schwarz criterion25.83229Log likelihood-229.6002 F-statistic351.6280Durbin-Watson stat0.528434 Prob(F-statistic)0.000000第二步：X2 x7Dependent Variable: YMethod: Least SquaresDate: 12/16/05 Time: 15:27Sample: 1 18Included observations: 18VariableCoefficientStd. Errort-StatisticProb. C-1905953.296654.0-6.4248360.0000X7406.146652.954207.6697710.0000X220.835102.8937677.1999910.0000R-squared0.990233 Mean dependent var941880.1Adjusted R-squared0.988931 S.D. dependent var413515.1S.E. of regression43506.46 Akaike info criterion24.35022Sum squared resid2.84E+10 Schwarz criterion24.49861Log likelihood-216.1520 F-statistic760.3815Durbin-Watson stat0.787593 Prob(F-statistic)0.000000第三步： x2 x6 x7Dependent Variable: YMethod: Least SquaresDate: 12/16/05 Time: 15:29Sample: 1 18Included observations: 18VariableCoefficientStd. Errort-StatisticProb. C-1956629.196460.9-9.9593800.0000X7328.316939.038748.4100300.0000X62111.153468.41224.5070420.0005X219.710071.92948810.215180.0000R-squared0.996015 Mean dependent var941880.1Adjusted R-squared0.995161 S.D. dependent var413515.1S.E. of regression28765.19 Akaike info criterion23.56485Sum squared resid1.16E+10 Schwarz criterion23.76271Log likelihood-208.0836 F-statistic1166.384Durbin-Watson stat1.807779 Prob(F-statistic)0.000000第四步：通过加入剩余变量后剔除不显著的变量后得：x2 x3 x6 x7Dependent Variable: YMethod: Least SquaresDate: 12/16/05 Time: 15:31Sample: 1 18Included observations: 18VariableCoefficientStd. Errort-StatisticProb. C-1877325.121383.9-15.466010.0000X7393.156427.2833414.410130.0000X215.968811.40413211.372720.0000X61957.836288.53886.7853460.0000X33.2002030.6488084.9324360.0003R-squared0.998612 Mean dependent var941880.1Adjusted R-squared0.998185 S.D. dependent var413515.1S.E. of regression17616.05 Akaike info criterion22.62114Sum squared resid4.03E+09 Schwarz criterion22.86847Log likelihood-198.5903 F-statistic2338.575Durbin-Watson stat2.590139 Prob(F-statistic)0.000000但从回归后所得的统计量看，加入x3后模型的整体拟合优度改善并不明显，说明x3对y的解释能力不大；同时从经济意义上看，从我们先前的预测得铁路的客运量与公路客运量间应该存在负相关性，然而所估计的系数为正，与经济意义相违背。所以剔除x3，故最后的模型为：4、异方差检验运用arch检验得：ARCH Test:F-statistic0.000226 Probability0.988210Obs*R-squared0.000256 Probability0.987238Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 12/20/05 Time: 20:07Sample(adjusted): 2 18Included observations: 17 after adjusting endpointsVariableCoefficientStd. Errort-StatisticProb. C6.00E+082.28E+082.6317560.0189RESID2(-1)0.0038870.2586790.0150260.9882R-squared0.000015 Mean dependent var6.02E+08Adjusted R-squared-0.066651 S.D. dependent var6.62E+08S.E. of regression6.84E+08 Akaike info criterion43.63541Sum squared resid7.02E+18 Schwarz criterion43.73343Log likelihood-368.9009 F-statistic0.000226Durbin-Watson stat1.997109 Prob(F-statistic)0.988210根据F-statistic与Obs*R-squared的P值可得模型不存在异方差。5、自相关检验由DW=1.807779，给定显著性水平查表，n=18，k=3得下临界值和上临界值为，因为4-1.6961.8077791.696,所以模型不存在自相关性。6模型结论从所取样本的估计模型得出：全国人均总收入每增加一元RMB，其他因素不变时，公路客运总量平均提高万人；全国总人口每增加一万人，其他因素不变时，公路客运总量平均提高万人；公路总长度每增加一万公里，其他因素不变时，公路客运总量平均提高万人。四模型改进（一）、对所选择的样本作散点图得分类后的解释变量与被解释变量的关系如下系列图所示：考虑到全国人均收入与全国总人口存在区域差异，即可把人口范围细分为城镇和农村。因此，在上述模型的基础上，我们进一步考虑各细化因素的影响程度，以及农村人口由于政策因素而呈现的二次型，建立如下模型： 其中： （二）、样本模型的估计（1）对模型的估计模型估计选择的样本数据运用OLS法回归得：Dependent Variable: YMethod: Least SquaresDate: 12/24/05 Time: 23:23Sample: 1 10Included observations: 10VariableCoefficientStd. Errort-StatisticProb. C453987.7709790.90.6396080.5461X6-11946.309828.607-1.2154620.2698X2141.153768.5584004.8085810.0030X71121.882734.826153.4997470.0128R-squared0.995571 Mean dependent var641103.1Adjusted R-squared0.993356 S.D. dependent var290572.5S.E. of regression23684.97 Akaike info criterion23.27224Sum squared resid3.37E+09 Schwarz criterion23.39328Log likelihood-112.3612 F-statistic449.5276Durbin-Watson stat2.133751 Prob(F-statistic)0.000000即：上述结果，虽然方程有相当高的拟合优度和F值，但解释变量的t值并不显著，且x6违背经济意义，由此推测模型的解释变量间可能存在多重共线性。多重共线性的检验：X21X71X6X2110.9681937631010.938423544908X710.96819376310110.9467378499X60.9384235449080.94673784991从相关矩阵可以看出解释变量间存在高度的相关。多重共线性的消除：运用逐步回归得到消除后的结果为：Dependent Variable: YMethod: Least SquaresDate: 12/24/05 Time: 23:25Sample: 1 10Included observations: 10VariableCoefficientStd. Errort-StatisticProb. C-406302.355062.37-7.3789480.0002X2131.185342.52828612.334580.0000X7182.0646012.214326.7187190.0003R-squared0.994480 Mean dependent var641103.1Adjusted R-squared0.992903 S.D. dependent var290572.5S.E. of regression24479.23 Akaike info criterion23.29236Sum squared resid4.19E+09 Schwarz criterion23.38314Log likelihood-113.4618 F-statistic630.5537Durbin-Watson stat1.603479 Prob(F-statistic)0.000000由此得到方程：异方差检验：Arch x21 x71ARCH Test:F-statistic0.090948 Probability0.771738Obs*R-squared0.115433 Probability0.734042Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 12/24/05 Time: 23:29Sample(adjusted): 2 10Included observations: 9 after adjusting endpointsVariableCoefficientStd. Errort-StatisticProb. C5.08E+082.58E+081.9700260.0895RESID2(-1)-0.1155490.383151-0.3015750.7717R-squared0.012826 Mean dependent var4.54E+08Adjusted R-squared-0.128199 S.D. dependent var5.25E+08S.E. of regression5.58E+08 Akaike info criterion43.31014Sum squared resid2.18E+18 Schwarz criterion43.35397Log likelihood-192.8956 F-statistic0.090948Durbin-Watson stat2.056760 Prob(F-statistic)0.771738可判断模型不存在异方差。自相关检验：在置信度为0.1的水平下，模型不存在自相关。5模型结论：从所取样本的估计模型得出：城市人均总收入每增加一元RMB，其他因素不变时，公路客运总量平均提高万人；城市总人口每增加一万人，其他因素不变时，公路客运总量平均提高万人。（）.对模型的估计模型估计选择的样本数据运用OLS法回归得：Dependent Variable: YMethod: Least SquaresDate: 12/25/05 Time: 22:09Sample: 1 18Included observations: 18VariableCoefficientStd. Errort-StatisticProb. C-5456506.1075174.-5.0749980.0003D05950910.3298356.1.8042050.0963D0*X22-68.0856238.50329-1.7683060.1024X2269.9251914.624444.7813940.0004X7277.7181728.688032.7090800.0190X61245.9103307.8190.3766560.7130R-squared0.988681 Mean dependent var941880.1Adjusted R-squared0.983965 S.D. dependent var413515.1S.E. of regression52363.89 Akaike info criterion24.83102Sum squared resid3.29E+10 Schwarz criterion25.12781Log likelihood-217.4792 F-statistic209.6303Durbin-Watson stat1.527338 Prob(F-statistic)0.000000即：上述结果，虽然方程有较高的拟合优度和F值，但个别解释变量的t值并不显著，由此推测模型的解释变量间可能存在多重共线性。多重共线性的检验D0D0*X22X22X72X6D010.998996948031-0.3716625096950.878283144760.790165566279D0*X220.9989969480311-0.3421454499550.8634536867410.764711913402X22-0.371662509695-0.3421454499551-0.322713375095-0.502528541506X720.878283144760.863453686741-0.32271337509510.9467378499X60.7901655662790.764711913402-0.5025285415060.94673784991从相关矩阵看，个别变量间存在很高的相关性。多重共线性的消除：通过逐步回归得到如下结果：第一步：Dependent Variable: YMethod: Least SquaresDate: 12/25/05 Time: 21:46Sample: 1 18Included observations: 18VariableCoefficientStd. Errort-StatisticProb. C352643.347262.157.4614320.0000X72153.445010.2779014.929600.0000R-squared0.933024 Mean dependent var941880.1Adjusted R-squared0.928838 S.D. dependent var413515.1S.E. of regression110309.8 Akaike info criterion26.16441Sum squared resid1.95E+11 Schwarz criterion26.26334Log likelihood-233.4797 F-statistic222.8931Durbin-Watson stat0.434010 Prob(F-statistic)0.000000留x72第二步 ：Dependent Variable: YMethod: Least SquaresDate: 12/25/05 Time: 22:01Sample: 1 18Included observations: 18VariableCoefficientStd. Errort-StatisticProb. C-2375663.484871.8-4.8995700.0002X72164.99756.35163825.977160.0000X2232.572785.7793835.6360300.0000R-squared0.978517 Mean dependent var941880.1Adjusted R-squared0.975653 S.D. dependent var413515.1S.E. of regression64522.96 Akaike info criterion25.13844Sum squared resid6.24E+10 Schwarz criterion25.28684Log likelihood-223.2460 F-statistic341.6186Durbin-Watson stat0.952903 Prob(F-statistic)0.000000留x72 x22第三步 Dependent Variable: YMethod: Least SquaresDate: 12/25/05 Time: 22:03Sample: 1 18Included observations: 18VariableCoefficientStd. Errort-StatisticProb. C-2414088.505274.8-4.7777730.0003D030585.2067056.750.4561090.6553X72159.912012.9194112.377650.0000X2233.111146.0544445.4688990.0001R-squared0.978832 Mean dependent var941880.1Adjusted R-squared0.974296 S.D. dependent var413515.1S.E. of regression66296.85 Akaike info criterion25.23480Sum squared resid6.15E+10 Schwarz criterion25.43266Log likelihood-223.1132 F-statistic215.7906Durbin-Watson stat0.944512 Prob(F-statistic)0.000000Dependent Variable: YMethod: Least SquaresDate: 12/25/05 Time: 22:03Sample: 1 18Included observations: 18VariableCoefficientStd. Errort-StatisticProb. C-2396782.502043.1-4.7740550.0003X72160.913512.2894313.093650.0000X2232.886126.0029145.4783600.0001D0*X220.3041500.7749330.3924850.7006R-squared0.978751 Mean dependent var941880.1Adjusted R-squared0.974198 S.D. dependent var413515.1S.E. of regression66423.18 Akaike info criterion25.23861Sum squared resid6.18E+10 Schwarz criterion25.43647Log likelihood-223.1475 F-statistic214.9529Durbin-Watson stat0.943698 Prob(F-statistic)0.000000Dependent Variable: YMethod: Least SquaresDate: 12/25/05 Time: 22:04Sample: 1 18Included observations: 18VariableCoefficientStd. Errort-StatisticProb. C-3333059.719412.6-4.6330290.0004X72130.323721.019186.2002290.0000X2240.494927.1232655.6848820.0001X63592.7752088.1331.7205680.1073R-squared0.982267 Mean dependent var941880.1Adjusted R-squared0.978467 S.D. dependent var413515.1S.E. of regression60679.57 Akaike info criterion25.05773Sum squared resid5.15E+10 Schwarz criterion25.25559Log likelihood-221.5196 F-statistic258.4966Durbin-Watson stat1.077225 Prob(F-statistic)0.000000第三步的回归中虽然各个引入的变量t值均不显著担任然暂留x6，继续回归。第四步：Dependent Variable: YMethod: Least SquaresDate: 12/25/05 Time: 22:05Sample: 1 18Included observations: 18VariableCoefficientStd. Errort-StatisticProb. C-4054005.783040.4-5.1772620.0002X7289.7871730.057432.9871870.0105X2247.321317.6637196.1747180.0000X65735.0912287.4492.5072000.0262D0119447.167233.411.7766040.0990R-squared0.985731 Mean dependent var941880.1Adjusted R-squared0.981341 S.D. dependent var413515.1S.E. of regression56485.28 Akaike info criterion24.95148Sum squared resid4.15E+10 Schwarz criterion25.19881Log likelihood-219.5633 F-statistic224.5224Durbin-Watson stat1.451476 Prob(F-statistic)0.000000Dependent Variable: YMethod: Least SquaresDate: 12/25/05 Time: 22:06Sample: 1 18Included observations: 18VariableCoefficientStd. Errort-StatisticProb. C-4012963.778026.2-5.1578770.0002X2246.745107.5680056.1766740.0000X7290.7511330.075563.0174380.0099X65787.2962324.8222.4893510.0271D0*X221.3698020.7881681.7379580.1058R-squared0.985610 Mean dependent var941880.1Adjusted R-squared0.981183 S.D. dependent var413515.1S.E. of regression56724.22 Akaike info criterion24.95992Sum squared resid4.18E+10 Schwarz criterion25.20725Log likelihood-219.6393 F-statistic222.6075Durbin-Watson stat1.441605 Prob(F-statistic)0.000000引入变量后发现他们都不显著，但不能确定是新引入变量的影响还是后引入变量的影响，于是在进一步回归有：Dependent Variable: YMethod: Least SquaresDate: 12/25/05 Time: 22:14Sample: 1 18Included observations: 18VariableCoefficientStd. Errort-StatisticProb. C-5539369.1017098.-5.4462480.0001D06896284.2068140.3.3345340.0054D0*X22-79.2160223.85477-3.3207620.0055X2272.3516912.688325.7022270.0001X7282.0059925.448743.2223990.0067R-squared0.988547 Mean dependent var941880.1Adjusted R-squared0.985023 S.D. dependent var413515.1S.E. of regression50606.11 Akaike info criterion24.73167Sum squared resid3.33E+10 Schwarz criterion24.97899Log likelihood-217.5850 F-statistic280.5194Durbin-Watson stat1.524092 Prob(F-statistic)0.000000由此得到估计方程为：则：异方差检验ARCH Test:F-statistic0.107898 Probability0.747090Obs*R-squared0.121411 Probability0.727509Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 12/25/05 Time: 22:52Sample(adjusted): 2 18Included observations: 17 after adjusting endpointsVariableCoefficientStd. Errort-StatisticProb. C1.62E+098.72E+081.8608590.0825RESID2(-1)0.0848970.2584540.3284790.7471R-squared0.007142 Mean dependent var1.77E+09Adjusted R-squared-0.059049 S.D. dependent var2.99E+09S.E. of regression3.08E+09 Akaike info criterion46.64214Sum squared resid1.42E+