计量经济学课程论文-我国公路客运量的研究报告

1、我国公路客运量的研究报告信息管理与信息系统03级指导老师:鲁万波白一佳 40311006师群昌40311020张斯蕊40311043陈华 40311028土一竹 40311062庄云 40311065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 Yt =用+由Xi +p2 X2 +3 X3+P4 X 4+P 5 X5 +瓦X6 +再X 7 + Ut对样本数据进行回归，分析得到最终模型 Yt = Po +Pi X 2 + P2 X 6 +P3 X 7 + ut ,并在此基

2、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Yt=Po + Pi X 2+P2 X 7 + Ut,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

3、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

4、：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：

5、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：Y=B0+Bl Xi +日2 X2+B3 X3 邛 4 X4 + B5 X5 + B6 X6 + B7 X 7 + u C1其中：Yt-公路客运量,一监运汽车总量2 -年底总人口X3-铁路客运量X4 -水运客运量X5 -民用航空客运量6-公路长度X7 -全国总人均收入（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:1500000100000050000000100200300400500X115000001000000500000090000100000110

6、000120000130000X2150000010000005000008000090000100000110000 120000X31500000100000050000001500020000250003000035000X415000001000000 -Y500000 .0,02000 400060008000 100001500000X51500000 , j 1V ,1000000.Y ,500000-,0.,80100120140160180 200X610000005000000500100015002000X7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

7、的样本数据间没有x3和明显的相关性，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-1810996.156801.2-11.549640.0000X1-18.56917178.244

8、2-0.1041780.9191X216.031731.7781879.0157720.0000X33.7978611.1424343.3243600.0077X4-2.6284404.549093-0.5777940.5762X510.8877217.879220.6089590.5561X61357.762726.40071.8691640.0911X7349.150853.140406.5703460.0001R-squared0.998779Mean dependent var941880.1Adjusted R-squared0.997924S.D. dependent var413

9、515.1S.E. of regression18842.03Akaike info criterion22.82667Sum squared resid3.55E+09Schwarz criterion23.22239Log likelihood-197.4400F-statistic1168.282Durbin-Watson stat2.666635Prob(F-statistic)0.000000(156801.2)(178.24)(1.78)(1.42)(4.55)(17.88)(726.40)(53.14)t =( -11.55)(-0.10)(9.02)(3.32)(-0.58)(

10、0.61)(1.87)(6.57)R 2 =0.9987R 2= 0.9979F =1168.28- 3.80 X 3-2.62X 4 10.88X 5 1357.76X 6 349.15X 7即:Y =1810996-18.57 X 116.03 X 2tDW =2.667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=1168.282x1、x4、x5参数估计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 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X1X2X3X4X5X11.0000000.8828

11、920.407131-0.7025490.973972X20.8828921.0000000.504735-0.5046760.920224X30.4071310.5047351.0000000.2761740.330393X4-0.702549-0.5046760.2761741.000000-0.751790X50.9739720.9202240.330393-0.7517901.000000X60.9605790.8193370.359901-0.7394020.933892X70.9076790.9248830.295472-0.7227060.974145从相关系数矩阵中可以看出，解

12、释变量x1 与 x2、x5、x6、 x7,X6 0.960579 0.819337 0.359901 -0.7394020.933892 1.000000 0.863272X7 0.907679 0.924883 0.295472 -0.7227060.974145 0.863272 1.000000x2 与 x5、x6、x7, x5运用相关系数矩阵检验，相关系数矩阵为: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

13、/05 Time: 15:25Sample: 1 18Included observations: 18VariableCoefficientStd. Errort-StatisticProb.C224417.043625.735.1441430.0001X7759.698140.5134618.751750.0000R-squared0.956478Mean dependent var941880.1Adjusted R-squared0.953758S.D. dependent var413515.1S.E. of regression88922.47Akaike info criteri

14、on25.73336Sum squared resid1.27E+11Schwarz criterion25.83229Log likelihood-229.6002F-statistic351.6280Durbin-Watson stat0.528434Prob(F-statistic)0.000000第二步：X2 x7Dependent Variable: YMethod: Least SquaresDate: 12/16/05 Time: 15:27Sample: 1 18Included observations: 18VariableCoefficientStd. Errort-St

15、atistic Prob.C-1905953.296654.0-6.4248360.0000X7X2406.146620.8351052.954207.6697712.8937677.1999910.00000.0000R-squared0.990233Mean dependent var941880.1Adjusted R-squared0.988931S.D. dependent var413515.1S.E. of regression43506.46Akaike info criterion24.35022Sum squared resid2.84E+10Schwarz criteri

16、on24.49861Log likelihood-216.1520F-statistic760.3815Durbin-Watson stat0.787593Prob(F-statistic)0.000000x2 x6 x7Dependent Variable: YMethod: Least SquaresDate: 12/16/05 Time: 15:29Sample: 1 18Included observations: 18VariableCoefficient Std. Error t-Statistic Prob.C-1956629.196460.9-9.9593800.0000X73

17、28.316939.038748.4100300.0000X62111.153468.41224.5070420.0005X219.710071.92948810.215180.0000R-squared0.996015Mean dependent var941880.1Adjusted R-squared0.995161S.D. dependent var413515.1S.E. of regression28765.19Akaike info criterion23.56485Sum squared resid1.16E+10Schwarz criterion23.76271Log lik

18、elihood-208.0836F-statistic1166.384Durbin-Watson stat1.807779Prob(F-statistic)0.000000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-1877325.121383.9-15.466010.0000

19、X7393.156427.2833414.410130.0000X215.968811.40413211.372720.0000X61957.836288.53886.7853460.0000X33.2002030.6488084.9324360.0003R-squared0.998612Mean dependent var941880.1Adjusted R-squared0.998185S.D. dependent var413515.1S.E. of regression17616.05Akaike info criterion22.62114Sum squared resid4.03E

20、+09Schwarz criterion22.86847Log likelihood-198.5903F-statistic2338.575Durbin-Watson stat2.590139Prob(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：Yt =-1956629+328.32 X 2 2111.15 X 6 19.71X 7 (196460.9

21、) (39.04 ) ( 468.41)( 1.93)t= (9.96)(8.41)(4.51)(10.22)2- 2R =0.996015R =0.995161F =1166.384DW =1.8077794、异方差检验运用arch检验得：ARCH Test:F-statisticObs*R-squared0.0002260.000256ProbabilityProbability0.9882100.987238Test Equation:Dependent Variable: RESIDA2Method: Least SquaresDate: 12/20/05 Time: 20:07Sam

22、ple(adjusted): 2 18Included observations: 17 after adjusting endpointsVariableCoefficientStd. Errort-StatisticProb.C6.00E+082.28E+082.6317560.0189RESIDA2(-1)0.0038870.2586790.0150260.9882R-squared0.000015Mean dependent var6.02E+08Adjusted R-squared-0.066651S.D. dependent var6.62E+08S.E. of regressio

23、n6.84E+08Akaike info criterion43.63541Sum squared resid7.02E+18Schwarz criterion43.73343Log likelihood-368.9009F-statistic0.000226Durbin-Watson stat1.997109Prob(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 a =0.05查表，n=18 , k=3得下临界值和上临界值为d l =0.933, du =1

24、.696,因为 4-1.696>1.807779>1.696, 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19.71万人；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328.32万人；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2111.15万人。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：150000015000001000000 -1000000 -500000-500000-0,10000 20000

25、300004000050000 60000.,76000 78000 80000 82000 84000 86000 88000X21X22150000015000001000000 .1000000 .500000.500000 .0_010002000300002000400060008000 10000X72X71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:Yt -二 0 7工1 X21 k工2 X 6 上工3 X71 - utC3Yt

26、= ：, 1 二.工2 D0 , ：1 D0 X 22 ,: 2 X 22，： 3 X 72，：4 X 6Ut其中:0 t 与1995D0 =1 t 1995X -心路客运量21 一 ”底城镇居民人口数X71 - 镇居民人均收入(二)、样本模型的估计X6X22X72公路长度-年底农村居民人口数- -农村居民人均收入(1)对模型。2的估计 1 .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: 1

27、0VariableCoefficientStd. Errort-StatisticProb.C453987.7709790.90.6396080.5461X6-11946.309828.607-1.2154620.2698X2141.153768.5584004.8085810.0030X71121.882734.826153.4997470.0128R-squared0.995571Mean dependent var641103.1Adjusted R-squared0.993356S.D. dependent var290572.5S.E. of regression23684.97Ak

28、aike info criterion23.27224Sum squared resid3.37E+09Schwarz criterion23.39328Log likelihood-112.3612F-statistic449.5276Durbin-Watson stat2.133751Prob(F-statistic)0.000000即：?Y = 453987.7+41.15376 X -11946.30 X +121.8827Xt21671(0.639608 ) (4.808581 ) ( -1.215462 ) ( 3.499747)R2 = 0.995571 F=449.5276DW

29、=2.133751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。X21X71X6X2110.9681937631010.938423544908X710.96819376310110.9467378499X60.9384235449080.946737849912 .多重共线性的检验：从相关矩阵可以看出解释变量间存在高度的相关。3 .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 Squares Date: 12/24/05 Time

30、: 23:25Sample: 1 10Included observations: 10由此得到方程:VariableCoefficientStd. Errort-StatisticProb.C-406302.355062.37-7.3789480.0002X2131.185342.52828612.334580.0000X7182.0646012.214326.7187190.0003R-squared0.994480Mean dependent var641103.1Adjusted R-squared0.992903S.D. dependent var290572.5S.E. of re

31、gression24479.23Akaike info criterion23.29236Sum squared resid4.19E+09Schwarz criterion23.38314Log likelihood-113.4618F-statistic630.5537Durbin-Watson stat1.603479Prob(F-statistic)0.000000Yt =-406302.3+31.18534 X 21 +82.06460X71(-7,378948 ) (12.33458) (6.718719)R= 0.994480F=630,5537DW=1.6034793 .异方差

32、检验：Arch x21 x71ARCH Test:F-statisticObs*R-squared0.0909480.115433ProbabilityProbability0.7717380.734042Test Equation:Dependent Variable: RESIDA2Method: Least SquaresDate: 12/24/05 Time: 23:29Sample(adjusted): 2 10Included observations: 9 after adjusting endpointsVariableCoefficientStd. Errort-Statis

33、ticProb.C5.08E+082.58E+081,9700260.0895RESIDA2(-1)-0.1155490.383151-0.3015750.7717R-squared0.012826Mean dependent var4.54E+08Adjusted R-squared-0.128199S.D. dependent var5.25E+08S.E. of regression5.58E+08Akaike info criterion43,31014Sum squared resid2.18E+18Schwarz criterion43,35397Log likelihood-19

34、2.8956F-statistic0.090948Durbin-Watson stat2.056760Prob(F-statistic)0.771738可判断模型不存在异方差。4 .自相关检验：在置信度为0.1的水平下，DW=1.603479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82.0646万人；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31.18534万人。(2),对模型。3的估计1 .模型估计选择的样本数据运用OLS法回归得：Dependent Variable: YMethod

35、: Least SquaresDate: 12/25/05 Time: 22:09Sample: 1 18Included observations: 18VariableCoefficientStd. Errort-StatisticProb.C-5456506.1075174.-5.0749980.0003D05950910.3298356.1.8042050.0963D0*X22-68.0856238,50329-1.7683060.1024即:X2269.9251914.624444.7813940.0004X7277.7181728.688032.7090800.0190X61245

36、.9103307.8190.3766560.7130R-squared0.988681Mean dependent var941880.1Adjusted R-squared0.983965S.D.dependent var413515.1S.E. of regression52363.89Akaike info criterion24.83102Sum squared resid3.29E+10Schwarz criterion25.12781Log likelihood-217.4792F-statistic209.6303Durbin-Watson stat1.527338Prob(F-

37、statistic)0.000000Y=-5456506+5950910D -68.08562D X +69.92519X1245.910X +77.71817Xt002222672(-5.074998 ) (1.804205 ) (-1.768306 ) (4.781394) (0.376656)( 2.709080)R= 0.988681 F=209.6303DW=1.527338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。2 .多重共线性的检验D0D0*X22X22X72X6D010.998996948031-0.3

38、716625096950.878283144760.790165566279D0*X22 ().9989969480311-0.3421454499550.8634536867410.764711913402X220.371662509695 -C.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

39、高的相关性。3 .多重共线性的消除:通过逐步回归得到如下结果: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-squared0.933024Mean dependent var941880.1Adjusted R-s

40、quared0.928838S.D. dependent var413515.1S.E. of regression110309.8Akaike info criterion26.16441Sum squared resid1.95E+11Schwarz criterion26.26334Log likelihood-233.4797F-statistic222.8931Durbin-Watson stat0.434010Prob(F-statistic)0.000000留x72第二步Dependent Variable: YMethod: Least SquaresDate: 12/25/0

41、5 Time: 22:01Sample: 1 18Included observations: 18VariableCoefficientStd. Errort-StatisticProb.C-2375663.484871.8-4.8995700.0002X72164.99756.35163825.977160.0000X2232.572785.7793835.6360300.0000R-squared0.978517Mean dependent var941880.1Adjusted R-squared0.975653S.D. dependent var413515.1S.E. of reg

42、ression64522.96Akaike info criterion25.13844Sum squared resid6.24E+10Schwarz criterion25.28684Log likelihood-223.2460F-statistic341.6186Durbin-Watson stat0.952903Prob(F-statistic)0.000000留 x72 x22第三步Dependent Variable: YMethod: Least SquaresDate: 12/25/05 Time: 22:03Sample: 1 18Included observations

43、: 18VariableCoefficientStd. Errort-StatisticProb.C-2414088.505274.8-4.7777730.0003D030585.2067056.750.4561090.6553X72159.912012.9194112.377650.0000X2233.111146.0544445.4688990.0001R-squared0.978832Mean dependent var941880.1Adjusted R-squared0.974296S.D. dependent var413515.1S.E. of regression66296.8

44、5Akaike info criterion25.23480Sum squared resid6.15E+10Schwarz criterion25.43266Log likelihood-223.1132F-statistic215.7906Durbin-Watson stat0.944512Prob(F-statistic)0.000000Dependent Variable: YMethod: Least SquaresDate: 12/25/05 Time:22:03Sample: 1 18Included observations: 18VariableCoefficientStd.

45、 Errort-StatisticProb.C-2396782.502043.1-4.7740550.0003X72160.913512.2894313.093650.0000X2232.886126.0029145.4783600.0001D0*X220.3041500.7749330.3924850.7006R-squared0.978751Mean dependent var941880.1Adjusted R-squared0.974198S.D. dependent var413515.1S.E. of regression66423.18Akaike info criterion2

46、5.23861Sum squared resid6.18E+10Schwarz criterion25.43647Log likelihood-223.1475F-statistic214.9529Durbin-Watson stat0.943698Prob(F-statistic)0.000000Dependent Variable: YMethod: Least SquaresDate: 12/25/05 Time:22:04Sample: 1 18Included observations: 18VariableCoefficientStd. Errort-StatisticProb.C

47、-3333059.719412.6-4.6330290.0004X72130.323721.019186.2002290.0000X2240.494927.1232655.6848820.0001X63592.7752088.1331.7205680.1073R-squared0.982267Mean dependent var941880.1Adjusted R-squared0.978467S.D. dependent var413515.1S.E. of regression60679.57Akaike info criterion25.05773Sum squared resid5.1

48、5E+10Schwarz criterion25.25559Log likelihood-221.5196F-statistic258.4966Durbin-Watson stat1.077225Prob(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 Squares Date: 12/25/05 Time: 22:05Sample: 1 18Included observations: 18VariableCoefficientStd. Errort-S

49、tatisticProb.C-4054005.783040.4-5.1772620.0002X7289.7871730.057432.9871870.0105X2247.321317.6637196.1747180.0000X65735.0912287.4492.5072000.0262D0119447.167233.411.7766040.0990R-squared0.985731Mean dependent var941880.1Adjusted R-squared0.981341S.D. dependent var413515.1S.E. of regression56485.28Aka

50、ike info criterion24.95148Sum squared resid4.15E+10Schwarz criterion25.19881Log likelihood-219.5633F-statistic224.5224Durbin-Watson stat1.451476Prob(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-squared0.985610Mean dependent var941880.1Adj