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Eviews多重共线性检验及补救_eviews多重共线性检验

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Eviews多重共线性检验及补救

关键词:eviews多重共线性eviews多重共线性操作多重共线性检验eviews判断多重共线性

目的:1、正确使用EVIEWS

      2、能根据计算结果进行多重共线性检验和出现多重共线性时的补救。

      3、数据为demo data2

 

实例:我国钢材供应量分析(多重共线性检验及补救)

 

    通过分析我国改革开放以来(1978-1997)钢材供应量的历史资料,可以建立一个单一方程模型。根据理论及对现实情况的认识,影响我国钢材供应量Y(万吨)的主要因素有:原油产量X1(万吨),生铁产量X2(万吨),原煤产量X3(万吨),电力产量X4(亿千瓦小时),固定资产投资X5(亿元),国内生产总值X6(亿元),铁路运输量X7(万吨)。

Eviews多重共线性检验及补救_eviews多重共线性检验


设模型的函数形式为:

一、运用OLS估计法对上式中参数进行估计,EVIEWS操作步骤为:

1、  在FILE菜单中选择NEW-WORKFILE,输入起止时间。

2、  在主窗口菜单选QUICK-EMPTY GROUP,在编辑数据区输入Y  X1 X2 X3 X4 X5 X6 X7所对应的数据。

3、  在主窗口菜单选在QUICK-ESTIMATE EQUATION,对参数做OSL估计,输出结果见下表:

Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

139.2362

718.2493

0.193855

0.8495

X1

-0.051954

0.090753

-0.572483

0.5776

X2

0.127532

0.132466

0.962751

0.3547

X3

-24.29427

97.48792

-0.249203

0.8074

X4

0.863283

0.186798

4.621475

0.0006

X5

0.330914

0.105592

3.133889

0.0086

X6

-0.070015

0.025490

-2.746755

0.0177

X7

0.002305

0.019087

0.120780

0.9059

R-squared

0.999222

    Mean dependent var

5153.350

Adjusted R-squared

0.998768

    S.D. dependent var

2511.950

S.E. of regression

88.17626

    Akaike info criterion

12.08573

Sum squared resid

93300.63

    Schwarz criterion

12.48402

Log likelihood

-112.8573

    F-statistic

2201.081

Durbin-Watson stat

1.703427

    Prob(F-statistic)

0.000000

 

Y = 139.2361608 – 0.05195439459*X1 + 0.1275320853*X2 – 24.294272*X3 + 0.8632825292*X4 + 0.330913843*X5 – 0.07001518918*X6 + 0.002305379405*X7

 

二、分析

由F=2201.081>F0.05(7,12)=2.91(显著性水平a=0.05),表明模型从整体上看钢材供应量与解释变量之间线性关系显著。

三、检验

计算解释变量之间的简单相关系数。EVIEWS过程如下:

1、主菜单QUICK-GROUP STATISTICS-CORRRELATION,在对话框中输入X1 X2 X3 X4 X5 X6 X7,结果如下:

 

 

X1

X2

X3

X4

X5

X6

X7

               

X1

1.000000

0.921956

0.975474

0.931882

0.826401

0.845837

0.986815

X2

0.921956

1.000000

0.964400

0.994921

0.969686

0.972530

0.931689

X3

0.975474

0.964400

1.000000

0.974809

0.894963

0.913344

0.982943

X4

0.931882

0.994921

0.974809

1.000000

0.959613

0.969105

0.945444

X5

0.826401

0.969686

0.894963

0.959613

1.000000

0.996169

0.827643

X6

0.845837

0.972530

0.913344

0.969105

0.996169

1.000000

0.846079

X7

0.986815

0.931689

0.982943

0.945444

0.827643

0.846079

1.000000

 

2、由上表可以看出,解释变量之间存在高度线性相关性。尽管方程整体线性回归拟合较好,但X1 X2 X3 X7变量的参数t值并不显著, X3 X6 系数的符号与经济意义相悖。表明模型确实存在严重的多重共线性。

四、修正

1、运用OLS方法逐一求Y对各个解释变量的回归。结合经济意义和统计检验选出拟合效果最好的一元线性回归方程。

 

Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

-10123.78

1528.060

-6.625250

0.0000

X1

1.181784

0.116936

10.10629

0.0000

R-squared

0.850171

    Mean dependent var

5153.350

 

Adjusted R-squared

0.841847

    S.D. dependent var

2511.950

 

S.E. of regression

998.9623

    Akaike info criterion

16.74595

 

Sum squared resid

17962663

    Schwarz criterion

16.84552

 

Log likelihood

-165.4595

    F-statistic

102.1371

 

Durbin-Watson stat

0.217842

    Prob(F-statistic)

0.000000

 


Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

-618.7199

108.3930

-5.708116

0.0000

X2

0.926212

0.016019

57.82017

0.0000

R-squared

0.994645

    Mean dependent var

5153.350

Adjusted R-squared

0.994347

    S.D. dependent var

2511.950

S.E. of regression

188.8610

    Akaike info criterion

13.41454

Sum squared resid

642032.9

    Schwarz criterion

13.51411

Log likelihood

-132.1454

    F-statistic

3343.172

Durbin-Watson stat

0.962290

    Prob(F-statistic)

0.000000


Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

-3770.942

581.6642

-6.483023

0.0000

X3

926.7178

58.38537

15.87243

0.0000

R-squared

0.933317

    Mean dependent var

5153.350

Adjusted R-squared

0.929612

    S.D. dependent var

2511.950

S.E. of regression

666.4367

    Akaike info criterion

15.93641

Sum squared resid

7994483.

    Schwarz criterion

16.03598

Log likelihood

-157.3641

    F-statistic

251.9341

Durbin-Watson stat

0.477559

    Prob(F-statistic)

0.000000


Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

-34.32474

91.75324

-0.374098

0.7127

X4

0.884047

0.014146

62.49381

0.0000

R-squared

0.995412

    Mean dependent var

5153.350

 

Adjusted R-squared

0.995157

    S.D. dependent var

2511.950

 

S.E. of regression

174.8044

    Akaike info criterion

13.25985

 

Sum squared resid

550018.2

    Schwarz criterion

13.35942

 

Log likelihood

-130.5985

    F-statistic

3905.476

 

Durbin-Watson stat

0.824221

    Prob(F-statistic)

0.000000

 

Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

2896.350

211.0245

13.72518

0.0000

X5

0.572451

0.036983

15.47892

0.0000

R-squared

0.930123

    Mean dependent var

5153.350

Adjusted R-squared

0.926241

    S.D. dependent var

2511.950

 

S.E. of regression

682.2088

    Akaike info criterion

15.98319

 

Sum squared resid

8377359.

    Schwarz criterion

16.08276

 

Log likelihood

-157.8319

    F-statistic

239.5971

 

Durbin-Watson stat

0.181794

    Prob(F-statistic)

0.000000

 


Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

2720.664

205.3405

13.24952

0.0000

X6

0.108665

0.006568

16.54535

0.0000

R-squared

0.938303

    Mean dependent var

5153.350

Adjusted R-squared

0.934875

    S.D. dependent var

2511.950

S.E. of regression

641.0376

    Akaike info criterion

15.85869

Sum squared resid

7396725.

    Schwarz criterion

15.95827

Log likelihood

-156.5869

    F-statistic

273.7485

Durbin-Watson stat

0.259927

    Prob(F-statistic)

0.000000


Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

-9760.099

1317.227

-7.409582

0.0000

X7

0.106826

0.009326

11.45524

0.0000

R-squared

0.879375

    Mean dependent var

5153.350

 

Adjusted R-squared

0.872673

    S.D. dependent var

2511.950

 

S.E. of regression

896.3356

    Akaike info criterion

16.52915

 

Sum squared resid

14461517

    Schwarz criterion

16.62872

 

Log likelihood

-163.2915

    F-statistic

131.2225

 

Durbin-Watson stat

0.183657

    Prob(F-statistic)

0.000000

 


经分析在7个一元回归模型中钢材供应量Y对电力产量X4的线性关系强,拟合度好,即:

Y = -34.32474492 + 0.8840472792*X4

                      (-0.374098)    (62.49381)

R2= 0.995412   S.E.=174.8044,F=3905.476

截距项不显著,去掉,重新估计:

Y = 0.8792594492*X4

2、逐步回归。

将其余解释变量逐一代入上式,得如下模型:

Y = -0.005935225118*X1 + 0.8906555628*X4

                                                          (-0.604681)    (45.03888)   

R2= 0.995469   S.E.=173.7270,    F=3954.290

式中X1不显著,删去,继续:

Y = 0.1741981867*X2 + 0.6978252624*X4

                                                            (1.879546)    (7.217200)   

R2= 0.996135   S.E.=160.4431,    F=4639.290

 

Y = 0.2753793175*X2 + 0.5595511241*X4 + 0.04060861466*X5

                                              (3.082485)        (5.637333)         (2.615818)

R2= 0.997244   S.E.=139.4060,    F=3075.985

 

Y = 0.466836912*X2 + 0.5219953469*X4 – 0.03080496295*X5 – 0.004998894793*X7

(3.245804)      (5.366654)       (-0.674009)       (-1.651391)

R2= 0.997646   S.E.=132.8222,    F=2259.899

X7不符合经济意义,应去掉。

 

所以:

Y = 0.2753793175*X2 + 0.5595511241*X4 + 0.04060861466*X5

3.082485)        (5.637333)         (2.615818

R2= 0.997244   S.E.=139.4060,    F=3075.985

即为最优模型。

Dependent Variable: Y

Method: Least Squares

Date: 10/17/05   Time: 22:53

Sample: 1978 1997

Included observations: 20

Variable

Coefficient

Std. Error

t-Statistic

Prob.

X2

0.275379

0.089337

3.082485

0.0068

X4

0.559551

0.099258

5.637333

0.0000

X5

0.040609

0.015524

2.615818

0.0181

R-squared

0.997244

    Mean dependent var

5153.350

Adjusted R-squared

0.996920

    S.D. dependent var

2511.950

S.E. of regression

139.4060

    Akaike info criterion

12.85014

Sum squared resid

330378.5

    Schwarz criterion

12.99950

Log likelihood

-125.5014

    F-statistic

3075.985

Durbin-Watson stat

0.790639

    Prob(F-statistic)

0.000000

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