计量经济学多元线性回归模型老师作业要求范本范文

1、计量经济学多元线性回归模型应用作业概述在当今市场上，一国的原油产量与多个因素存在着紧密的联系，例如民用汽车拥有量、宏观经济等都是影响一国原油产量的重要因素。本次将以中国19902006年原油产量与国内民用汽车拥有量、GDP等因素的数据，通过建立计量经济模型来分析上述变量之间的关系，强调的重要性，从而促进国内原油产业的发展。模型构建过程.变量的定义解释变量：X 1民用汽车拥有量，X 2电力产量，X 3国内生产总值，X 4能源消费总量。被解释变量：Y原油产量建立计量经济模型：解释原油产量与民用汽车拥有量、电力产量、国内生产总值、 以及能源消费总量之间的关系。.模型的数学形式设定原油产量与五个解释变

2、量相关关系模型，样本回归模型为：A A AAAAY=+ Xi+ X2i+ X 3i+ X4i + e01234.数据的收集该模型的构建过程中共有四个变量 ，分别是中国从19902006年民用汽车拥有量、 电 力产量、国内生产总值以及能源消费总量，因此为时间序列数据，最后一个即2006年的数据作为预测对比数据，收集的数据如下所示：年份YXIX2X3X4199019745,18551.364983. 2561S667. 398703199120130. 048606.114927. 6682178k 5103783199220271.384691.745148. 28326923. 5109170

3、199320768, 033817.585886,12735333. 9115993199420896, 304941.957005.01148197.9122737199521419. 64410400000.10860793, 7131176199622544. 721100.087691.72871176.6136948199T22906. 931219.098606. 6578373137798199322986. 251319.38821. 7584402. 3132214199922920.171452.94831147189677.1133831200023345. 018160

4、8.919286.41699214.6138553200123365. 651802.0411270. 49109655.2143199200223872. 462053.171164g. 61120332.7151797200324248, 6162382. 9311960.466135822,8174990200425103. 6942693. 7114425. 257159878. 3203227200525940, 3763159.6615852, 45218386L9224632200626305. 6643697. 3517463. 424210871246270Y原油产量（万吨标

5、准煤） XI民用汽车拥有量1万辆） X2电力产量（万吨标准媒） X3国内生产总值（亿元） X4能源消费总量（万吨标准煤）.用OLS法估计模型回归结果，散点图分别如下：Dependent Variable: Y Method: Least Squares Date: 05/04/09 Time： 18:45 Sample: 1990 2006 Included observations: 17VariableCoefficientStd. Error t-StatisticProb.C20425.46531.1592 3B 454600.0000X1-2 1872140.487949 -4.43

6、24650.0007X2-0 1981180.112342 -1.763519111032X30.0822710.00821810010620.0000X40.0011450.0057330.1997650,8450R-squared0.993314Mean tlependerit var22751.10Adjusted R-squared0.991005S.D dependent vr1996.786S E. of regression100.7229Akaike info criterion13,65836Sum squared resid427395.0Schwarz criterion

7、13.80343Log llikelihood-110 2461F-atatistic445.6371Durbin-Watson stat1.961792Prob(F-statistic)0.000000Yi =20425.46-2.1872 X1-0.1981 X2 +0.0823 X3+0.0011 X4d.f.=12 ,R2 =0.9933 , Se=(531.1592) (0.4879) (0.1123) (0.0082) (0.0057) t=(38.4545) (-4.4825) (-1.7635)(10.0106) (0.1998)。C X1g X2* X3x X42500002

8、0000015000010000050000 -0-18000 20000 22000 24000 26000 28000模型的检验及结果的解释、评价.拟合优度检验及统计检验R2 =0.9933,可以看到模型的拟合优度非常高，说明原油产量与上述四个解释变量之间 总体线性关系显著。模型总体T佥验（F检验）：给定显著水平a =0.05,查自由度为（4,12）的F分布表，得 F（4,12）=3.26,可见该模型的F值远大于临界值，因此该回归方程很明显是显著的。但由于X1与X2系数不显著且符号为负，与经济意义不符，因此我们认为解释变量之间存在多重共线性。变量的显著性检验（t检验）：给定显著水平 =0.

9、05,查自由度为12的t分布表，得 ta/2 12=2.179,大于该临界值的的显著变量为X3；其余的解释变量未通过检验，说明这些变量与被解释变量之间不存在显著的线性相关关系。.多重共线性的检验相关系数检验法Correlation hkitiixYX1用X3刈|Y1.0000000.9576960.9676140.9852250.933689X1D.957E961 0000000 9895570.9913360.979697X20.9676140.9895571.0000000.9928200 971923X30.9852250.9913360.9920201,0000000.969240X4

10、0.9336890.9796970 9719230.9692401.000000上图是Eviews输出所有变量的相关系数矩阵,可发现Y与所有解释变量都是正相关的关系,所以进一步确定了上面的回归存在共线性问题。另外，我们发现X2和X3的相关系数很高,两变量很可能存在共线性。多个解释变量的相关性检验由上面的分析可知，X 2和X 3有很高的相关性,那么我们这里就用X3做被解释变量，X 1和X2做解释变量，可得回归模型如下:Dependent Variable: X3 Method Least SquaresDate: 05/OW9 Time:21:53Sample: 1990 2006Include

11、d observations:17VariableCoefficientStd. Error -StatisticProbC-31466.169114.671-34522560.0039X126,2004711.5820122496540.0411X23.53902728490302 9971700.0096R-squared0.989491Mean dependent var91504.11Adjusted R-squared0.9679893.D. dependent var56774.44S.E. of regression6222 083Akaike info criterion20

12、4683SSum squared resid5 42E416Schwarz criterion20,61542Log likelihood-170.9012F-statistic659.0764Durbin-Wart son stat0.694809Prob(F-statistic)0.000000=-31466.18+26.2805 X1+8.5390 X2X3t=(-3.4523) (2.2497) (2.9972)R2 = 0.9895, R2=0.9880,F=659.0764 , DW = 0.6948可以看到，回归模型的拟合优度非常高，F值也远大于临界值。如果将显著水平扩大到 a1

13、0%的话，所有参数都显著，因此可以认为几个解释变量的线性组合，+31466.18-26.2805 V 1-8.5390 V2 定0,因此存在多重共线性。X3四、模型的建立这里我们用 逐步回归法 得到中国原油产量模型。L分别用四个解释变量对 Y进行回归，回归结果分别如下:Dependent Variable: Y Method: Least SquaresDate: 05/04/09 Time: 21:23Sample: 1990 2006Included observations: 17VariableCoefficientStd. Error t-StatisticProb.C19443.2

14、0294.334666.058150.0000X12.0722190.16077712.888770.0000R-squared0.917182Mean dependent var22751.18Adjusted R-squared0.911661S.D. dependentvar1998.786S F nf rpgressinn694 07R9Akaikp infn critArinn15 72203Sum squared resid5293910.Schwarz criterion15,82005Log likelihood-131.6372F-statistic166.1204Durbi

15、n-Watson stat0.428702Prob(F-statistic)0.000000Dependent Variable: Y Method: Least Squares Date: 05/04/09 Time: 21:26Sample: 1990 2006Included observations: 17VariableCoefficientStd. Error t-StatisticProb.C17906.56349.955151.168180.0000X20.5106100.03439514.845550.0000R-squared0.936276Mean dependent v

16、ar22751.18Adjusted R-squared0.932028S.D. dependent var1998.786S.E. of regression521.1132Akaike info criterion15,45994Sum squared resid4073385.Schwarz criterion15.55797Log likelihood-129.4095F-statistic220.3902Durbin-Watson stat0.883430Prob(F-statistic)0.000000Dependent Variable: Y Method: Least Squa

17、res Date: 05/04/09 Time: 21 27 Sample: 1990 2006 Included observalions: 17VariableCoefficientStd. Error t-StatisticProbC19577.311 的2736117.74150.0000X30.0346860 00155722.279530 0000R-squared0.9706B7Mean dependent var22751.18Adjusted R-squared0.968712S D dependent var1998 786S E of regression353 5539

18、Akaike info criterion1468408Sum squared resid1875005Schwarz criterion14 7B210Log likelihood-122.8147F-statistic496 3772Durbin-Watson stat0.742903Prob(F-statistic)0.000000Dependent Variable： YMethod: Least SquaresDate: 05/04/09 Time: 21:27Sample: 1990 2006Included observations: 17VariableCoefficientS

19、td Error t-StartisticProb.C16161.76676.688323.893610.0000X40 044682000442510,O9B640.0000R-squared0 871776Mean dependent war22751.18Adjusted R*squared0.863228S.D. dependent var1958.786S.E of regression739.2064Akaike info criterion16,15916Sum squared resid8196391.Schwarz criterion16.25719Log likelihoo

20、d-135.3529F-statistic101.9626Durbin-Watson slat0.255869ProbfF* statistic)0.000000可以看出，丫与X3拟合优度R2最大，因此将这个方程作为基本方程，然后往里加入其他 变量。2.引入第二个变量Dependent Variable: Y Method: Least SquaresDate: 054/09 Time: 22:31Sample: 1990 2006Included observations: 17Variable Coefficient Std. Error t-Statistic Prob.CX3X1199

21、64.140.073106-2.381973104.285219047890.00657511.118750.404103 -5 8944690.00000.00000.0000R-scjuared0.991575Mean dependent var22751 18Adjusted R-squared0 990372S D. dependent! var1998.7B6S.E. of regression196.1269Akaike info criterion13.55419Sum squared resid533520.9Schwarz criterion13.70122Log likel

22、ihood-1112.2106F-statistic623.9967Durbin-Watson st st1.979233Prob(F* statistic)0 000000如上图所示，引入变量 X1后，X 1的系数通不过显著性检验。Dependent Variable: Y Wethad: Least SquaresDate: O5/D47a9 Time: 22:35Sample: 1990 2005Included observations: 17VariableCoefficientStd. Error t-StatisticProt).C20909.10611 544334.190E5

23、0.0000X30 0604260.0115535.2301S50 0001X2-0 3666140.173173 -2.2440600.0415R-squared0 976427Mean dependent var22751.18Adjusted R-squared0.975345S.D. dependent var1998.786S E. of regression313B446Akaike info criterion14,49446Sum squared resid1378978Schwarz criterion14,64150Lag likelihood-120.2029F-stat

24、istic317.4841Durbin-Watson stat1.134309Prob(F-statistic；i0 000000如上图所示，引入变量 X2后，其系数也通不过显著性检验。Dependent Variable: YMethod: Least SquaresDte: 05/04/09 Time: 22:37Sample: 1990 2006Included observations: 17Vanable Coefficient Std. Error Statistic Prob.CX3X420956.430,0466450016772649 493332.2E5B110056578

25、,2461420.007669 -2.1912940.00000.00000.0467R*squared0978108Mean dependent var22751 18Adjusted R-squared0.974980S D, dependent var1998 796S.E. of regression316.1604Akaike info criterion14,50916Sum squared resid1399403.Schwarz criterion14,65620Log likelihood-120.3279F-statistic312.7479Durbin-Watson st

26、at1.W5811Prob(F-statistic)0.000000引入变量X4后，其系数同样通不过显著性检验。综上所述，本次模型只引入变量X3,其最终输出结果如下:3Dependent Variable： YMethod: Least SquaresDate: 05/04/09 Time: 21:27Sampla: 1990 2006Included observations: 17VariableCoefficientStd. Error t-StatisticProbC19577.31伯6 273611774150.0000用0.034B360.00155722279530.0000R-

27、squared0.970667Mean dependent var22751.18Adjusted R-squared0.963712S.D. dependent var1998 786S E of regression353.5539Akaike info criterion14,68403Sum squared resid1375006.Schwarz criterion14.70210Log likelihood-122.8147F-statistic496.3772Durbin-Watson stat0.742903Prob(F-statistic)0.000000模型的最终结果为AY

28、 = 19577.31+0.0347X3R2 =0.9707,(117.7415) (22.2795)= 0.9687, F=496.3772, DW=0.7429五、异方差检验（怀特检验）White Heteraskedasticity Test:F-st artistic0.313118Probability0.7361530bs*R-squ3ned0 727872Probability0.694936Test Equation:Dependent Variable: RESIDEMethod: Least SquaresDate: 05/04/09 Time: 22:53Sample:

29、1990 2006Included observations: 17n*R 2 =0.7279 / 20 05（1）=3.841,模型存在一阶自相关。同理，可通过LM检验法检验是否存在二阶自相关，具体如下:Bneusch-Godfrey Serial Correlation LM Test:F-statisticObs*R-squared2.802700512172BProbabilityProbability0.0972700.077238Test Equation:Dependent Variable: RESIDMethod: Least SquaresDate: 05/0W9 Time

30、: 23:12Presample missing value lagged residuals set to zero.VariableCoefficientStd. Error t-StatisticProbC59.380B0152.4D5B0.3896220.7031X3-0.0008850W1469 -0.E025180 5572RESID(-1)0 6399420 3170722.0182680.0647RESID(-2)-0 0126740319160 -0.0397110.9689R-squared0 301278Mean dependent var-L10E-12Adjusted

31、 R-squared0.140035S.D. dependent var342.3271S.E of regression317.4547Akaike info criterion14,66007Sum squared resid1310107Schwarz criterion14 75692Log likelihood-119.7674F-statistic1.068467Durbin-Walson stat1.670097Prob(F-statistic)018476122LM=n*R =5,1217 7。5.991,模型不存在二阶自相关。七、科一奥迭代法修正Breusch-Godfrey

32、 Serial Correlation LM Test:F-st atisticObs*R-squaned0.2437400.678973ProbabilityProbability0.7070140.71213BTest Equation:Dependent Variable: RESIDMethod: Least SquaresDate： 05/04/09 Time： 23:28Presample missing value lagged residuals set to zeroVariableCoefficientStd. Error t-StatisticProb.C219.1657714.56120.306714 7648X3-0.0011420 004650 -0.2456140.8105AR0.1462060 333491