计量经济学课程论文-我国公路客运量的研究报告

1、计量经济学课程论文我国公路客运量的研究报告我国公路客运量的研究报告摘要：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 = b0 + b1 X1 + b2 X 2 + b3 X3 + b4 X 4 + b5 X5 + b6 X 6 + b7 X 7 + ut 对样本数据进行回归，分析得到最终模型Yt = b0 +b1 X 2 + b2 X 6 +b3 X 7 + ut ，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Yt = b0 +b1 X 2 +b2 X 7 + ut ，

2、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

3、、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

4、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：Yt = b0 + b1 X1 + b2 X 2 + b3 X 3 + b4

5、 X 4 + b5 X 5 + b6 X 6 + b7 X 7 + ut1其中：Yt - -公路客运量X1 - -客运汽车总量X 2 - -年底总人口X 3 - -铁路客运量X 4 - -水运客运量X 5 - -民用航空客运量X 6 - -公路长度X 7 - -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：1500000150000010000001000000YY50000050000000100200300400500090000100000 110000 120000 130000X1X21500000150000010000001000000

6、YY50000050000008000090000100000 110000 12000001500020000250003000035000X3X41500000150000010000001000000YY500000500000002000 4000 6000 8000 10000080100 120 140 160 180 200X5X615000001000000Y50000000500100015002000X7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

7、 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: Y Method: Least Squares Included observations: 18 VariableCoefficientStd. Errort-StatisticProb.C-1810996.156801.2-11.549640.0000X1-18.56917178.2442-0.1041780.9191X216.031731.7781879.0157720.0000X33.7978611.1424343.3243600.0

8、077X4-2.6284404.549093-0.5777940.5762X510.8877217.879220.6089590.5561X61357.762726.40071.8691640.0911X7349.150853.140406.5703460.0001Date: 12/16/05Time: 15:08 Sample: 1 18R-squared0.998779Mean dependent var941880.1Adjusted R-squared0.997924S.D. dependent var413515.1S.E. of regression18842.03Akaike i

9、nfo criterion22.82667Sum squared resid3.55E+09Schwarz criterion23.22239Log likelihood-197.4400F-statistic1168.282Durbin-Watson stat2.666635Prob(F-statistic)0.000000即：tY = -1810996-18.57X1+16.03X 2 + 3.80X 3-2.62X 4 +10.88X 5 +1357.76 X 6 + 349.15X 7(156801.2) (178.24)(1.78)(1.42) (4.55)(17.88)(726.4

10、0)(53.14)t = (-11.55)(-0.10)(9.02)(3.32) (-0.58)(0.61)(1.87)(6.57)R2 = 0.9987DW = 2.667R2 = 0.9979F = 1168.28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：X1X2X3X4X5X6X7X11.0000000.882892

11、0.407131-0.7025490.9739720.9605790.907679X20.8828921.0000000.504735-0.5046760.9202240.8193370.924883X30.4071310.5047351.0000000.2761740.3303930.3599010.295472X4-0.702549-0.5046760.2761741.000000-0.751790-0.739402-0.722706X50.9739720.9202240.330393-0.7517901.0000000.9338920.974145X60.9605790.8193370.

12、359901-0.7394020.9338921.0000000.863272X70.9076790.9248830.295472-0.7227060.9741450.8632721.000000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: Y Method: Least Squares Included observations: 18 VariableCoefficient

13、Std. Errort-StatisticProb.C224417.043625.735.1441430.0001X7759.698140.5134618.751750.0000Date: 12/16/05Time: 15:25 Sample: 1 18R-squared0.956478Mean dependent var941880.1Adjusted R-squared0.953758S.D. dependent var413515.1S.E. of regression88922.47Akaike info criterion25.73336Sum squared resid1.27E+

14、11Schwarz criterion25.83229Log likelihood-229.6002F-statistic351.6280Durbin-Watson stat0.528434Prob(F-statistic)0.000000第二步：X2 x7Dependent Variable: YMethod: Least SquaresDate: 12/16/05Time: 15:27 Sample: 1 18Included observations: 18VariableCoefficientStd. Errort-StatisticProb.C-1905953.296654.0-6.

15、4248360.0000X7406.146652.954207.6697710.0000X220.835102.8937677.1999910.0000R-squared0.990233Mean dependent var941880.1Adjusted R-squared0.988931S.D. dependent var413515.1S.E. of regression43506.46Akaike info criterion24.35022Sum squared resid2.84E+10Schwarz criterion24.49861Log likelihood-216.1520F

16、-statistic760.3815Durbin-Watson stat0.787593Prob(F-statistic)0.000000第三步：x2 x6 x7Dependent Variable: YMethod: Least SquaresDate: 12/16/05Time: 15:29 Sample: 1 18 Included observations: 18 VariableCoefficientStd. Errort-StatisticProb.C-1956629.196460.9-9.9593800.0000X7328.316939.038748.4100300.0000X6

17、2111.153468.41224.5070420.0005X219.710071.92948810.215180.0000R-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 likelihood-208.0836F-statistic1166

18、.384Durbin-Watson stat1.807779Prob(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: Y Method: Least SquaresR-squared0.998612Mean dependent var941880.1Adjusted R-squared0.998185S.D. dependent var413515.1S.E. of regression17616.05Akaike info criterion22.62114Sum squared resid

19、4.03E+09Schwarz criterion22.86847Log likelihood-198.5903F-statistic2338.575Durbin-Watson stat2.590139Prob(F-statistic)0.000000Date: 12/16/05Time: 15:31 Sample: 1 18 Included observations: 18 VariableCoefficientStd. Errort-StatisticProb.C-1877325.121383.9-15.466010.0000X7393.156427.2833414.410130.000

20、0X215.968811.40413211.372720.0000X61957.836288.53886.7853460.0000X33.2002030.6488084.9324360.0003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：tY = -1956629+328.32X 2 + 2111.15X 6 +19.71X 7（196460.9）(39.04) (468.41)(

21、1.93)t= (9.96)(8.41) (4.51)(10.22)4、异方差检验R2 = 0.996015DW = 1.807779R2 = 0.995161F = 1166.384运用 arch 检验得：ARCH Test:F-statistic0.000226Probability0.988210 Obs*R-squared0.000256Probability0.987238Test Equation:Dependent Variable: RESID2 Method: Least SquaresDate: 12/20/05Time: 20:07 Sample(adjusted): 2

22、 18 VariableCoefficientStd. Errort-StatisticProb.C6.00E+082.28E+082.6317560.0189RESID2(-1)0.0038870.2586790.0150260.9882 Included observations: 17 after adjusting endpointsR-squared0.000015Mean dependent var6.02E+08Adjusted R-squared-0.066651S.D. dependent var6.62E+08S.E. of regression6.84E+08Akaike

23、 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dl = 0.933, du = 1.696 ，因为

24、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：1500000150000010000001000000YY500000500000010000 20000 30000 40000 5000

25、0 60000076000 78000 80000 82000 84000 86000 88000X21X221500000150000010000001000000YY50000050000000100020003000002000 4000 6000 8000 10000X71X72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 = a0 + a1 X 21 + a2 X 6 + a3 X 71 + ut2Yt = a1 + a2 D0 +

26、b1D0 X 22 + b2 X 22 + b3 X 72 + b4 X 6 + ut3其中：=ì0D0íî1t £ 1995t > 1995Yt - -公路客运量X 21 - -年底城镇居民人口数X 71 - -城镇居民人均收入（二）、样本模型的估计（1）对模型2 的估计 模型估计选择的样本数据运用 OLS 法回归得：X 6 - -公路长度X 22 - -年底农村居民人口数X 72 - -农村居民人均收入Dependent Variable: Y Method: Least Squares Included observations: 10 Va

27、riableCoefficientStd. Errort-StatisticProb.C453987.7709790.90.6396080.5461X6-11946.309828.607-1.2154620.2698X2141.153768.5584004.8085810.0030X71121.882734.826153.4997470.0128Date: 12/24/05Time: 23:23 Sample: 1 10R-squared0.995571Mean dependent var641103.1Adjusted R-squared0.993356S.D. dependent var2

28、90572.5S.E. of regression23684.97Akaike 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+41.15376X -11946.30X +121.8827Xt216 71（0.639608）（4.808581）（-1.215462）（3.499747）R

29、2 = 0.995571F=449.5276DW=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。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: Y Method: Least Sq

30、uares Included observations: 10 VariableCoefficientStd. Errort-StatisticProb.C-406302.355062.37-7.3789480.0002X2131.185342.52828612.334580.0000X7182.0646012.214326.7187190.0003Date: 12/24/05Time: 23:25 Sample: 1 10R-squared0.994480Mean dependent var641103.1Adjusted R-squared0.992903S.D. dependent va

31、r290572.5S.E. of regression24479.23Akaike info criterion23.29236Sum squared resid4.19E+09Schwarz criterion23.38314Log likelihood-113.4618F-statistic630.5537Durbin-Watson stat1.603479Prob(F-statistic)0.000000由此得到方程：tY = -406302.3+31.18534X 21 +82.06460X 71（-7.378948）（12.33458）（6.718719）R2 = 0.994480F

32、=630.5537DW=1.603479异方差检验：Archx21 x71ARCH Test:F-statistic0.090948Probability0.771738 Obs*R-squared0.115433Probability0.734042Test Equation:Dependent Variable: RESID2 Method: Least SquaresDate: 12/24/05Time: 23:29 Sample(adjusted): 2 10 VariableCoefficientStd. Errort-StatisticProb.C5.08E+082.58E+081

33、.9700260.0895RESID2(-1)-0.1155490.383151-0.3015750.7717 Included observations: 9 after adjusting endpointsR-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 criterion4

34、3.35397Log likelihood-192.8956F-statistic0.090948Durbin-Watson stat2.056760Prob(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， 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。（）.对模型3 的估计 模型估计选择的样本数据运用 OLS 法回归得：Dep

35、endent Variable: Y Method: Least SquaresDate: 12/25/05Time: 22:09 Sample: 1 18 Included observations: 18 VariableCoefficientStd. Errort-StatisticProb.C-5456506.1075174.-5.0749980.0003D05950910.3298356.1.8042050.0963D0*X22-68.0856238.50329-1.7683060.1024R-squared0.988681Mean dependent var941880.1Adju

36、sted 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-statistic)0.000000即：X2269.9251914.624444.7813940.0004X7277.7181728.68803

37、2.7090800.0190X61245.9103307.8190.3766560.7130Y = -5456506+5950910D -68.08562D X +69.92519X +1245.910X +77.71817Xt00 22226 72（-5.074998）(1.804205）(-1.768306）（4.781394）(0.376656) (2.709080)R2 = 0.988681F=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。多重共线性的检验D0D0*X22

38、X22X72X6D010.998996948031-0.3716625096950.878283144760.790165566279D0*X220.9989969480311-0.3421454499550.8634536867410.764711913402X22-0.371662509695-0.3421454499551-0.322713375095-0.502528541506X720.878283144760.863453686741-0.32271337509510.9467378499X60.7901655662790.764711913402-0.5025285415060.

39、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: Y Method: Least Squares Included observations: 18 VariableCoefficientStd. Errort-StatisticProb.C352643.347262.157.4614320.0000X72153.445010.2779014.929600.0000Date: 12/25/05Time: 21:46 Sample: 1 18R-squared0.933024Mean de

40、pendent var941880.1Adjusted R-squared0.928838S.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: Y

41、Method: Least SquaresDate: 12/25/05Time: 22:01 Sample: 1 18 Included observations: 18 VariableCoefficientStd. Errort-StatisticProb.C-2375663.484871.8-4.8995700.0002X72164.99756.35163825.977160.0000X2232.572785.7793835.6360300.0000R-squared0.978751Mean dependent var941880.1Adjusted R-squared0.974198S

42、.D. dependent var413515.1S.E. of regression66423.18Akaike info criterion25.23861Sum squared resid6.18E+10Schwarz criterion25.43647Log likelihood-223.1475F-statistic214.9529Durbin-Watson stat0.943698Prob(F-statistic)0.000000Dependent Variable: Y Method: Least SquaresDate: 12/25/05Time: 22:04 Sample:

43、1 18 Included observations: 18 VariableCoefficientStd. Errort-StatisticProb.C-3333059.719412.6-4.6330290.0004X72 130.323721.019186.2002290.0000R-squared0.978517Mean dependent var941880.1Adjusted R-squared0.975653S.D. dependent var413515.1S.E. of regression64522.96Akaike info criterion25.13844Sum squ

44、ared 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 Squares Included observations: 18 VariableCoefficientStd. Errort-StatisticProb.C-2414088.505274.8-4.7777730.0003D0305

45、85.2067056.750.4561090.6553X72159.912012.9194112.377650.0000X2233.111146.0544445.4688990.0001Date: 12/25/05Time: 22:03 Sample: 1 18R-squared0.978832Mean dependent var941880.1Adjusted R-squared0.974296S.D. dependent var413515.1S.E. of regression66296.85Akaike info criterion25.23480Sum squared resid6.

46、15E+10Schwarz criterion25.43266Log likelihood-223.1132F-statistic215.7906Durbin-Watson stat0.944512Prob(F-statistic)0.000000Dependent Variable: YMethod: Least SquaresDate: 12/25/05Time: 22:03 Sample: 1 18 Included observations: 18 VariableCoefficientStd. Errort-StatisticProb.C-2396782.502043.1-4.774

47、0550.0003X72160.913512.2894313.093650.0000X2232.886126.0029145.4783600.0001D0*X220.3041500.7749330.3924850.7006R-squared0.982267Mean dependent var941880.1Adjusted R-squared0.978467S.D. dependent var413515.1S.E. of regression60679.57Akaike info criterion25.05773Sum squared resid5.15E+10Schwarz criter

48、ion25.25559Log likelihood-221.5196F-statistic258.4966Durbin-Watson stat1.077225Prob(F-statistic)0.000000X2240.494927.1232655.6848820.0001X63592.7752088.1331.7205680.1073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: Y Method: Least SquaresDate: 12/25/05Time: 22:05 Sample: 1 18Included

49、 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-squared0.985731Mean dependent var941880.1Adjusted R-squared0.981341S.D. dependent var413515.1S.E. of regression56485.28Akaike info criterion24.95148Sum squared resid4.15E+10Schwar