計量經(jīng)濟學課程論文-我國公路客運量的研究報告

1、計量經(jīng)濟學課程論文我國公路客運量的研究報告我國公路客運量的研究報告摘要：本文通過建立模型對影響我國公路客運量的因素進行了研究，通過Evies對七個變量進行回歸擬合，通過建立模型Yt = b0 + b1 X1 + b2 X 2 + b3 X3 + b4 X 4 + b5 X5 + b6 X 6 + b7 X 7 + ut 對樣本數(shù)據(jù)進行回歸，分析得到最終模型Yt = b0 +b1 X 2 + b2 X 6 +b3 X 7 + ut ，并在此基礎上細分變量優(yōu)化模型，引入虛擬變量對城市農村的影響情況進行對比分析，由此提出了最終模型的改進模型Yt = b0 +b1 X 2 +b2 X 7 + ut ，

2、通過樣本回歸分析得出一定的結論，提出進一步探討的問題。關鍵詞：公路客運量OLS回歸一背景綜述改革開放后，我國國民經(jīng)濟持續(xù)高速發(fā)展，公路運輸需求強勁增長，國家加大了公路基礎設施的建設力度。隨著道路環(huán)境的改善和城鄉(xiāng)交流的日益頻繁，公路客運量逐年提高。伴隨著中國城市化的進程，城鄉(xiāng)之間、城際之間的交流日益頻繁，這直接支持了公路客運行業(yè)的發(fā)展。公路客運在我國綜合運輸體系客運市場中發(fā)揮著舉足輕重的作用，承擔著90%以上的份額，因此對我國公路客運的研究就顯得很有現(xiàn)實意義，通過研究我國從改革開放至今的公路客運量發(fā)展變化，可以從我國國民經(jīng)濟發(fā)展的一個側面了解到我國二十多年來的交通運輸、公共事業(yè)建設、人民生活水平

3、、社會生產(chǎn)、流通、分配、消費各環(huán)節(jié)協(xié)調發(fā)展等諸多現(xiàn)實經(jīng)濟問題，對于提升個人對國家經(jīng)濟發(fā)展認識、研究分析的能力大有好處。因此，本文以1978年為課題研究的時間起點，縱觀中國公路、人口、人均收入、客運汽車產(chǎn)量、鐵路、民航、水路運輸客運量等眾多因素對我國公路客運量的推動作用和影響，通過建立多元線性回歸方程，進行實證分析，得出對我國公路客運量的顯著影響因素。二模型變量選擇及預測在模型建立之初，我們選擇了七個對公路客運量可能造成影響的因素：客運汽車總量、年底總人口、鐵路客運量、水運客運量、民用航空客運量、公路長度及全國總人均收入。從經(jīng)濟常識的角度，初步認為，人口、人均收入作為國民經(jīng)濟衡量的基本要素對公路

4、客運量應該有一定的影響；鐵路客運、水運客運、民航客運與公路客運存在替代的經(jīng)濟關系，其三者的客運量要么與公路客運量有負相關的關系，要么與公路客運量的相關關系不大；客運汽車作為公路客運的硬件條件我們也將其引入模型，去考察客運汽車總量與客運量規(guī)模間的解釋關系；而客運路線的豐富程度勢必也將對公路客運量造成影響，在此我們用公路的長度去衡量客運路線的豐富程度。在以上分析的基礎上，進行主觀的預測，對公路客運量可能造成影響的因素有：年底總人口、全國總人均收入、鐵路客運量、客運汽車總量。三模型分析根據(jù)對經(jīng)濟現(xiàn)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 - -公路客運量X1 - -客運汽車總量X 2 - -年底總人口X 3 - -鐵路客運量X 4 - -水運客運量X 5 - -民用航空客運量X 6 - -公路長度X 7 - -全國總人均收入（一）、對所選擇的樣本作散點圖得個解釋變量與被解釋變量的關系如下系列圖所示：1500000150000010000001000000YY50000050000000100200300400500090000100000 110000 120000 130000X1X21500000150000010000001000000

6、YY50000050000008000090000100000 110000 12000001500020000250003000035000X3X41500000150000010000001000000YY500000500000002000 4000 6000 8000 10000080100 120 140 160 180 200X5X615000001000000Y50000000500100015002000X7從圖形看出所選擇的解釋變量 x3 與 x4 樣本數(shù)據(jù)與所選擇的被解釋變量的樣本數(shù)據(jù)間沒有明顯的相關性，其余解釋變量與被解釋變量間有明顯的線性相關性。所以推測所建模型中 x3

7、 和 x4 對 y 的解釋可能不顯著。（二）、樣本模型的估計1、模型估計對所選擇的樣本數(shù)據(jù)運用 OLS 法回歸得：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從回歸的樣本模型的統(tǒng)計量 R=0.998779 可以看出，模型的擬合優(yōu)度非常好，從 F=1168.282可知解釋變量對模型的整體解釋顯著，然而通過樣本數(shù)據(jù)所得的解釋變量 x1、x4、x5 參數(shù)估計值的t 值明顯不顯著，據(jù)此推測模型解釋變量間可能存在多重共線性。2、多重共線性的檢驗運用相關系數(shù)矩陣檢驗，相關系數(shù)矩陣為：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從相關系數(shù)矩陣中可以看出，解釋變量 x1 與 x2、x5、x6、x7，x2 與 x5、x6、x7，x5 與x6、x7，x6 與 x7 高度相關，說明模型存在多重共線性。3、多重共線性的消除運用逐步回歸法消除多重共線性：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：通過加入剩余變量后剔除不顯著的變量后得：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但從回歸后所得的統(tǒng)計量看，加入 x3 后模型的整體擬合優(yōu)度改善并不明顯，說明 x3 對 y的解釋能力不大；同時從經(jīng)濟意義上看，從我們先前的預測得鐵路的客運量與公路客運量間應該存在負相關性，然而所估計的系數(shù)為正，與經(jīng)濟意義相違背。所以剔除 x3，故最后的模型為：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、異方差檢驗R2 = 0.996015DW = 1.807779R2 = 0.995161F = 1166.384運用 arch 檢驗得：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根據(jù) F-statistic 與 Obs*R-squared 的 P 值可得模型不存在異方差。5、自相關檢驗由 DW=1.807779，給定顯著性水平a = 0.05 查表，n=18，k=3 得下臨界值和上臨界值為dl = 0.933, du = 1.696 ，因為

24、4-1.696>1.807779>1.696,所以模型不存在自相關性。6模型結論從所取樣本的估計模型得出：全國人均總收入每增加一元RMB，其他因素不變時，公路客運總量平均提高19.71萬人；全國總人口每增加一萬人，其他因素不變時，公路客運總量平均提高328.32 萬人；公路總長度每增加一萬公里，其他因素不變時，公路客運總量平均提高2111.15 萬人。四模型改進（一）、對所選擇的樣本作散點圖得分類后的解釋變量與被解釋變量的關系如下系列圖所示：1500000150000010000001000000YY500000500000010000 20000 30000 40000 5000

25、0 60000076000 78000 80000 82000 84000 86000 88000X21X221500000150000010000001000000YY50000050000000100020003000002000 4000 6000 8000 10000X71X72考慮到全國人均收入與全國總人口存在區(qū)域差異，即可把人口范圍細分為城鎮(zhèn)和農村。因此，在上述模型的基礎上，我們進一步考慮各細化因素的影響程度，以及農村人口由于政策因素而呈現(xiàn)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 - -公路客運量X 21 - -年底城鎮(zhèn)居民人口數(shù)X 71 - -城鎮(zhèn)居民人均收入（二）、樣本模型的估計（1）對模型2 的估計 模型估計選擇的樣本數(shù)據(jù)運用 OLS 法回歸得：X 6 - -公路長度X 22 - -年底農村居民人口數(shù)X 72 - -農村居民人均收入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上述結果，雖然方程有相當高的擬合優(yōu)度和 F 值，但解釋變量的 t 值并不顯著，且 x6 違背經(jīng)濟意義，由此推測模型的解釋變量間可能存在多重共線性。多重共線性的檢驗：X21X71X6X2110.9681937631010.938423544908X710.96819376310110.9467378499X60.9384235449080.94673784991從相關矩陣可以看出解釋變量間存在高度的相關。 多重共線性的消除：運用逐步回歸得到消除后的結果為：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異方差檢驗：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可判斷模型不存在異方差。 自相關檢驗：在置信度為 0.1 的水平下， DW=1.603479 模型不存在自相關。5模型結論：從所取樣本的估計模型得出：城市人均總收入每增加一元RMB，其他因素不變時，公路客運總量平均提高82.0646 萬人；城市總人口每增加一萬人，其他因素不變時，公路客運總量平均提高31.18534 萬人。（）.對模型3 的估計 模型估計選擇的樣本數(shù)據(jù)運用 OLS 法回歸得：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上述結果，雖然方程有較高的擬合優(yōu)度和 F 值，但個別解釋變量的 t 值并不顯著，由此推測模型的解釋變量間可能存在多重共線性。多重共線性的檢驗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從相關矩陣看，個別變量間存在很高的相關性。 多重共線性的消除：通過逐步回歸得到如下結果：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第三步的回歸中雖然各個引入的變量 t 值均不顯著擔任然暫留 x6，繼續(xù)回歸。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