计量经济学多元线性回归模型(老师作业要求范本)范文

计量经济学•多元线性回归模型应用作业

一、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1990-2006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。

二、模型构建过程

1.变量的定义

解释变量：X1民用汽车拥有量，X2电力产量，X.国内生产总值，X,能源消费总量。

被解释变量：Y原油产量

建立计展经济模型：解释原油产品与民用汽车拥有量、电力产量、国内生产总值、

以及能源消费总量之间的关系。

2.模型的数学形式

设定原油产量与五个解释变量相关美系模型，样本回归模型为：

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y""X”x,"x「四X",

3.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1990—2006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YXIX2X3X4

199019745.18551.364988.25618667.898703

199120130.048606.114927.66821781.5103783

199220271.384691.745148.28826923.5109170

199320768.033817.585886.12735333.9115993

199420896.304941.957005.01148197.9122737

199521419.64410408000.10860793.7131176

199622544.721100.087691.72871176.6138948

199722906.931219.098606.6578973137798

199822986.251319.38821.7584402.3132214

199922920.171452.948311.7189677.1133831

200023345.0181608.919286.41699214.6138553

200123365.651802.0411270.49109655.2143199

200223872.462053.1711648.61120332.7151797

200324248.6162382.9311960.466135822.8174990

200425103.6942693.7114425.257159878.3203227

200525940.3763159.6615852.452183867.9224682

200626305.6643697.3517463.424210871246270

Y原油产量（万吨标准煤）

XI民用汽车拥有量（万辆）

X2电力产量（万吨标准煤）

X3国内生产总值（亿元）

X4能源消费总量（万吨标准煤）

4.用OLS法估计模型

回归结果，散点图分别如下：

DependentVariable:Y

Method:LeastSquares

Date:05/04/09Time:18:45

Sample:19902006

Includedobservations:17

VariableCoefficientStd.Errort-StatisticProb.

20425.46531.159238.454500.0000

-21872140.487949-4.4824650.0007

-01981180.112342-1.7635190.1032

00822710.00821810,010620.0000

00011450.0057330.1997650.8450

R-squared0993314Meandependentvar22751.18

AdjustedR-squared0991085S.D.dependentvar1998.786

S.E.ofregression188.7229Akaikeinfocriterion13,55836

Sumsquaredresid427395.8Schwarzcriterion13.80343

Loglikelihood-110.2461F-statistic445.6871

Durbin-Watsonstat1951792Prob(F-statistic)0.000000

』「()•、

Yi=20425.46-2872X1981X+0.0823X3+0.(X)llX4

d.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

•X1

eX2

*X3

*X4

180002000022000240002600028000

Y

三、模型的检验及结果的解释、评价

2.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。

・模型总体性检验(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,I2)=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a=0.05,查自由度为12的t分布表，得

ta/212=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。

3.多重共线性的检验

⑴相关系数检验法

CorrelationMa”仅

YX1X2X3X4

Y1.0000000.9576960.9676140.9852250.933689

X10.9576961.0000000.9895570.9913360.979697

X20.9676140.9895571.0000000.9928200.971923

X30.9852250.9913360.9928201.0000000.969240

X40.9336890.9796970.9719230.9692401.000000

DependentVariable:Y

Method:LeastSquares

Date:05/04/09Time:21:23

Sample:19902006

Includedobservations:17

VariableCoefficientStd.Errort-StatisticProb.

C19443.20294.334666.058150.0000

X12.0722190.16077712.888770.0000

R-squared0.917182Meandependentvar22751.18

AdjustedR-squared0.911661S.D.dependentvar1998.786

S.E.ofregression594.0769Akaikeinfocriterion15.72203

Sumsquaredresid5293910.Schwarzcriterion15.82005

Loglikelihood-131.6372F-statistic166.1204

Durbin-Watsonstat0.428702Prob(F-statistic)0.000000

DependentVariable:Y

Method:LeastSquares

Date:05/04/09Time:21:26

Sample:19902006

Includedobservations:17

VariableCoefficientStd.Errort-StatisticProb.

C17906.56349.955151.168180.0000

X20.5106100.03439514.845550.0000

R-squared0.936276Meandependentvar22751.18

AdjustedR-squared0.932028S.D.dependentvar1998.786

S.E.ofregression621.1132Akaikeinfocriterion16.45994

Sumsquaredresid4073385.Schwarzcriterion15.55797

Loglikelihood-129.4095F-statistic220.3902

Durbin-Watsonstat0.883430Prob(F-statistic)0.000000

DependentVariable:Y

Method:LeastSquares

Date:05/04/09Time:21:27

Sample:19902006

Includedobservations:17

VariableCoefficientStd.Errort-StatisticProb.

C19577.31166.2736117.74150.0000

X30.0346860.00155722.279530.0000

R-squared0.970667Meandependentvar22751.18

AdjustedR-squared0.968712S.D.dependentvar1998.786

S.E.ofregression353.5539Akaikeinfocriterion14.68408

Sumsquaredresid1875005.Schwarzcriterion14.78210

Loglikelihood-122.8147F-statistic496.3772

Durbin-Watsonstat0.742903Prob(F-statistic)0.000000

DependentVariable:Y

Method:LeastSquares

Date:05/04/09Time:21:27

Sample:19902006

Includedobservations:17

VariableCoefficientStd.Errort-StatisticProb.

C16161.76676.688323.883610.0000

X40.0446820.00442510.098640.0000

R-squared0.871776Meandependentvar22751.18

AdjustedR-squared0.863228S.D.dependentvar1998.786

S.E.ofregression739.2064Akaikeinfocriterion16,15916

Sumsquaredresid8'96391.Schwarzcriterion16.25719

Loglikelihood-135.3529F-statistic101.9826

Durbin-Watsonstat0.255859Prob(F-statistic)0.000000

可以看出，Y与X3拟合优度R: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

DependentVariable:Y

Method:LeastSquares

Date:05/04A)9Time:22:31

Sample:19902006

Includedobservations:17

VariableCoeiicientStd.Errort-StatisticProb.

C19864.14104.2852190.478900000

X30.0731060.00657511.118750.0000

X1-2.3819730.404103-5.8944690.0000

R-squared0.991575Meandependentvar22751.18

AdjustedR-squared0.990372S.D.dependentvar1998.786

S.E.ofregression196.1269Akaikeinfocriterion13.55419

Sumsquaredresid538520.9Schwarzcriterion13.70122

Loglikelihood-112.2106F-statistic823.8987

Durbin-Watsonstat1.979233Prob(F-statistic)0.000000

如上图所示，引入变量X1后，X1的系数通不过显著性检验。

DependentVariable:Y

Method:LeastSquares

Date:05/04/09Time:22:35

Sample:19902006

Includedobservations:17

VariableCoefficientStd.Errort-StatisticProb.

C20909.10611.544334.190650.0000

X30.0604260.0115535.2301850.0001

X2-0.3886140.173173-2.2440800.0415

R-squared0.978427Meandependentvar22751.18

AdjustedR-squared0.975345S.D.dependentvar1998.786

S.E.ofregression313.8446Akaikeinfocriterion14.49446

Sumsquaredresid1378978.Schwarzcriterion14.64150

Loglikelihood-120.2029F-statistic317.4841

Durbin-Watsonstat1.134309Prob(F-statistic)0.000000

如上图所示，引入变量X2后，其系数也通不过显著性检验。

DependentVariable:Y

Method:LeastSquares

Date:05/04/D9Time:22:37

Sample:19902006

Includedobservations:17

VariableCoefficientStd.Errort-StatisticProb.

C2C956.43649.493332.265810.0000

X30.0466450.0056578.2461420.0000

X4-0.0167720.007689-2.1812940.0467

R-squared0.978108Meandependentvar22751.18

AdjustedR-squared0.974980S.D.dependentvar1998.786

S.E.ofregression316.1604Akaikeinfocriterion14,50916

Sumsquaredresid1399403.Schwarzcriterion14.65620

Loglikelihood-120.3279F-statistic312.7479

Durbin-Watsonstat1.105811Prob(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X,,其最终输出结果如下:

DependentVariable:Y

Method:LeastSquares

Date:05/04/09Time:21:27

Sample:19902006

Includedobservations:17

VariableCoefficientStd.Errort-StatisticProb.

C19577.31166.2736117.74150.0000

X30.0346860.00155722.279530.0000

R-squared0.970667Meandependentvar22751.18

AdjustedR-squared0.968712S.D.dependentvar1998.786

S.E.ofregression353.5539Akaikeinfocriterion14.68408

Sumsquaredresid1875005.Schwarzcriterion14,78210

Loglikelihood-122.8147F-statistic496.3772

Durbin-Watsonstat0.742903Prob(F-statistic)0.000000

模型的最终结果为

Y=19577.31+0.0347

(117.7415)(22.2795)

R2=0.9707,*=0.9687,F=496.3772,DW=0.7429

五、异方差检验（怀特检验）

WhiteHeteroskedasticityTest:

F-statistic0.313118Probability0.736153

Obs*R-squared0.727872Probability0.694936

TestEquation:

DependentVariable:RESIDA2

Method:LeastSquares

Date:05/04/09Time:22:53

Sample:19902006

Includedobservations:17

VariableCoefficientStd.Errort-StatisticProb.

C172673.899625.641.7332260.1050

X3-1.6309602.141675-0.7615350.4590

X3A2761E-069.62E-060.7913240.4420

R-squared0.042816Meandependentvar110294.4

AdjustedR-squared-0.093925S.D.dependentvar122707.1

S.E.ofregression128340.4Akaikeinfocriterion26.52155

Sumsquaredresid2.31E+11Schwarzcriterion26,66858

Loglikelihood-222.4331F-statistic0.313118

Durbin-Watsonstat1.106513Prob(F-statistic)0.736153

n*R2=0.7279<⑵=5.991,不存在异方差。

六、自相关检验及修正

Breusch-GodfreySerialCorrelationLMTest:

F-statistic6.034154Probability0.027698

Obs*R-squared5.120287Probability0.023648

TestEquation:

DependentVariable:RESID

Method:LeastSquares

Date:05/04/09Time:23:06

Presamplemissingvaluelaggedresidualssettozero.

VariableCoefficientStd.Errort-StatisticProb.

C60.06185145.93720.4115590.6869

X3-0.0008950.001395-0.6412350.5317

RESID(-1)0.6331800.2577622.4564520.0277

R-squared0.301193Meandependentvar-1.10E-12

AdjustedR-squared0.201364S.D.dependentvar342.3271

S.E.ofregression305.9255Akaikeinfocriterion14,44335

Sumsquaredresid1310266.Schwarzcriterion14.59038

Loglikelihood-119.7684F-statistic3.017077

Durbin-Watsonstat1.658208Prob(F-statistic)0.081377

LM=n*R2=5.1203>(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:

Breusch-GodfreySerialCorrelationLMTest:

F-statistic2.802700Probability0.097270

Obs*R-squared5.121728Probability0.077238

TestEquation:

DependentVariable:RESID

Method:LeastSquares

Date:05/04/09Time:23:12

Presamplemissingvaluelaggedresidualssettozero.

VariableCoefficientStd.Errort-StatisticProb.

C59,38060152.40560.3896220.7031

X3-0.0008850.001469-0.6025180.5572

RESID(-1)0.6399420.3170722.0182880.0647

RESID(-2)-0.0126740.319160-0.0397110.9689

R-squared0.301278Meandependentvar-1.10E-12

AdjustedR-squared0.140035S.D.dependentvar342.3271

SE.ofregression317.4547Akaikeinfocriterion14.56087

Sumsquaredresid1310107.Schwarzcriterion14.75692

Loglikelihood-r9.7674F-statistic1.868467

Durbin-Watsonstat1.670097Prob(F-statistic)0.184761

。2

LMBRF⑵7</。,。产991，模型不存在二阶自相关,

七、科一奥迭代法修正

Breusch-GodfreySerialCorrelationLMTest:

F-statistic0.243740Probability0.787814

Obs*R-squared0.678973Probability0.712136

TestEquation:

DependentVariable:RESID

Method:LeastSquares

Date:05/0W9Time:23:28

Presamplemissingvaluelaggedresidualssettozero.

VariableCoefficientStd.Errort-StatisticProb.

C