吴洋一经济学08071002422022年本科计量经济学实验课程期末上机考试实验报告

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实验（实训）报告

项目名称建立影响能源消费需求总量的因素模型

所属课程名称计量经济学试验

项目类型多重共线性模型的检验与处理

试验(实训)日期2022

班级08经济（2）

学号0807100242

姓名吴洋一

指导教师项后军

财经学院教务处制

一、试验（实训）概述：

(1)建立对数线性多元回归模型

(2)假如决定用表中全部变量作为解释变量，你预料会遇到多重共线性的问题吗？为什么？

(3)假如有多重共线性，你准备怎样解决这个问题？试写出整个分析和解决过程。

Klein判别法，逐步回归法,OLS

（使用的材料、设备、软件）

1、电脑1人一台。2、Eviews3.1学生版

二、试验（实训）容：

建立并检验影响影响能源消费需求总量的因素模型

理论上认为影响能源消费需求总量的因素主要有经济发展水平、收入水平、产业发展、人民生活水平提高、能源转换技术等因素。为此，收集了中国能源消费总量Y(万吨标准煤)、国生产总值(亿元)X1(代表经济发展水平)、国民总收入(亿元)X2(代表收入水平)、工业增加值(亿元)X3、建筑业增加值(亿元)X4、交通运输邮电业增加值(亿元)X5(代表产业发展水平及产业结构)、人均生活电力消费(千瓦小时)X6(代表人民生活水平提高)、能源加工转换效率(%)X7(代表能源转换技术)等在1985-2022年期间的统计数据，具体如下：

年份

能源消费

国民

总收入

ＧＤＰ

工业

建筑业

交通运输邮电

人均生活

电力消费

能源加工

转换效率

y

X1

X2

X3

X4

X5

X6

X7

1985

76682

8989.1

8964.4

3448.7

417.9

406.9

21.3

68.29

1986

80850

10201.4

10202.2

3967.0

525.7

475.6

23.2

68.32

1987

86632

11954.5

11962.5

4585.8

665.8

544.9

26.4

67.48

1988

92997

14922.3

14928.3

5777.2

810.0

661.0

31.2

66.54

1989

96934

16917.8

16909.2

6484.0

794.0

786.0

35.3

66.51

1990

98703

18598.4

18547.9

6858.0

859.4

1147.5

42.4

67.2

1991

103783

21662.5

21617.8

8087.1

1015.1

1409.7

46.9

65.9

1992

109170

26651.9

26638.1

10284.5

1415.0

1681.8

54.6

66

1993

115993

34560.5

34634.4

14143.8

2284.7

2123.2

61.2

67.32

1994

122737

46670.0

46759.4

19359.6

3012.6

2685.9

72.7

65.2

1995

131176

57494.9

58478.1

24718.3

3819.6

3054.7

83.5

71.05

1996

138948

66850.5

67884.6

29082.6

4530.5

3494.0

93.1

71.5

1997

137798

73142.7

74462.6

32412.1

4810.6

3797.2

101.8

69.23

1998

132214

76967.2

78345.2

33387.9

5231.4

4121.3

106.6

69.44

1999

130119

80579.4

82067.5

35087.2

5470.6

4460.3

118.1

70.45

2000

130297

88254.0

89468.1

39047.3

5888.0

5408.6

132.4

70.96

2022

134914

95727.9

97314.8

42374.6

6375.4

5968.3

144.6

70.41

2022

148222

103935.3

105172.3

45975.2

7005.0

6420.3

156.3

69.78

资料来源：《中国统计年鉴》2022、2000年版，中国统计。

（步骤、记录、数据、程序等）

一、建立对数线性多元回归模型

利用Eviews软件，输入Y、X1、X2、X3、X4、X5、X6、X7等数据，采用这些数据对模型进行OLS回归，结果如表1.1：

表1.1

DependentVariable:Y

Method:LeastSquares

Date:06/14/11Time:10:20

Sample:19852022

Includedobservations:18

Variable

Coefficient

Std.Error

t-Statistic

Prob.

C

-80155.52

108510.7

-0.738688

0.4771

X1

36.84232

11.64146

3.164750

0.0101

X2

-28.23350

11.33756

-2.490262

0.0320

X3

-10.32637

4.845876

-2.130961

0.0589

X4

-17.52643

17.94658

-0.976589

0.3518

X5

-34.49995

18.88123

-1.827209

0.0976

X6

336.4866

992.1418

0.339152

0.7415

X7

1952.573

1535.832

1.271345

0.2324

R-squared

0.964563

Meandependentvar

114898.3

AdjustedR-squared

0.939758

S.D.dependentvar

22162.37

S.E.ofregression

5439.605

Akaikeinfocriterion

20.34190

Sumsquaredresid

2.96E+08

Schwarzcriterion

20.73762

Loglikelihood

-175.0771

F-statistic

38.88476

Durbin-Watsonstat

1.842204

Prob(F-statistic)

0.000002

EstimationCommand:

=====================

LSYCX1X2X3X4X5X6X7

EstimationEquation:

=====================

Y=C(1)+C(2)*X1+C(3)*X2+C(4)*X3+C(5)*X4+C(6)*X5+C(7)*X6+C(8)*X7

SubstitutedCoefficients:

=====================

Y=-80155.51982+36X1-28X2-10X3-17.526428*X4-34X5+336.4865768*X6+1952.572512*X7

二、假如决定用表中全部变量作为解释变量，你预料会遇到多重共线性的问题吗？为什么？

由表1.1可见，该模型R2=0.964563，可决系数很高，F检验值38.88476,明显显著。但是当时,2.228，不仅X1、X2、X3、X4、X5、X6、X7的t检验不显著，而且X2、X3、X4、X5系数的符号与预期的相反，这说明很可能存在严重的多重共线性。

计算各解释变量的相关系数，选择X1、X2、X3、X4、X5、X6、X7数据，点〞view/correlations〞得相关系数矩阵（如表1.2）：

表1.2

由相关系数矩阵可以看出：各解释变量相互之间的相关系数较高，证明确实存在严重多重共线性。

三、消除多重共线性

采用逐步回归的方法，去检验和解决多重共线性问题。分别作Y对X1、X2、X3、X4、X5、X6、X7的一元回归，

DependentVariable:Y

Method:LeastSquares

Date:06/14/11Time:10:46

Sample:19852022

Includedobservations:18

Variable

Coefficient

Std.Error

t-Statistic

Prob.

C

85243.95

3524.481

24.18624

0.0000

X1

0.624974

0.061545

10.15481

0.0000

R-squared

0.865682

Meandependentvar

114898.3

AdjustedR-squared

0.857287

S.D.dependentvar

22162.37

S.E.ofregression

8372.365

Akaikeinfocriterion

21.00770

Sumsquaredresid

1.12E+09

Schwarzcriterion

21.10663

Loglikelihood

-187.0693

F-statistic

103.1201

Durbin-Watsonstat

0.253364

Prob(F-statistic)

0.000000

DependentVariable:Y

Method:LeastSquares

Date:06/14/11Time:10:46

Sample:19852022

Includedobservations:18

Variable

Coefficient

Std.Error

t-Statistic

Prob.

C

85469.49

3523.767

24.25515

0.0000

X2

0.612846

0.060668

10.10163

0.0000

R-squared

0.864456

Meandependentvar

114898.3

AdjustedR-squared

0.855985

S.D.dependentvar

22162.37

S.E.ofregression

8410.478

Akaikeinfocriterion

21.01678

Sumsquaredresid

1.13E+09

Schwarzcriterion

21.11571

Loglikelihood

-187.1511

F-statistic

102.0429

Durbin-Watsonstat

0.254758

Prob(F-statistic)

0.000000

DependentVariable:Y

Method:LeastSquares

Date:06/14/11Time:10:47

Sample:19852022

Includedobservations:18

Variable

Coefficient

Std.Error

t-Statistic

Prob.

C

87111.43

3531.741

24.66529

0.0000

X3

1.370007

0.141557

9.678113

0.0000

R-squared

0.854102

Meandependentvar

AdjustedR-squared

0.844984

S.D.dependentvar

S.E.ofregression

8725.793

Akaikeinfocriterion

Sumsquaredresid

1.22E+09

Schwarzcriterion

Loglikelihood

-187.8135

F-statistic

Durbin-Watsonstat

0.238854

Prob(F-statistic)

DependentVariable:Y

Method:LeastSquares

Date:06/14/11Time:10:48

Sample:19852022

Includedobservations:18

Variable

Coefficient

Std.Error

t-Statistic

Prob.

C

88024.82

3384.305

26.00972

0.0000

X4

8.805949

0.890155

9.892599

0.0000

R-squared

0.859481

Meandependentvar

AdjustedR-squared

0.850698

S.D.dependentvar

S.E.ofregression

8563.442

Akaikeinfocriterion

Sumsquaredresid

1.17E+09

Schwarzcriterion

Loglikelihood

-187.4755

F-statistic

Durbin-Watsonstat

0.244443

Prob(F-statistic)

DependentVariable:Y

Method:LeastSquares

Date:06/14/11Time:10:48

Sample:19852022

Includedobservations:18

Variable

Coefficient

Std.Error

t-Statistic

Prob.

C

87474.56

3855.295

22.68946

0.0000

X5

10.14708

1.160865

8.740963

0.0000

R-squared

0.826848

Meandependentvar

AdjustedR-squared

0.816026

S.D.dependentvar

S.E.ofregression

9505.923

Akaikeinfocriterion

Sumsquaredresid

1.45E+09

Schwarzcriterion

Loglikelihood

-189.3549

F-statistic

Durbin-Watsonstat

0.291497

Prob(F-statistic)

DependentVariable:Y

Method:LeastSquares

Date:06/14/11Time:10:49

Sample:19852022

Includedobservations:18

Variable

Coefficient

Std.Error

t-Statistic

Prob.

C

79984.11

4307.686

18.56777

0.0000

X6

464.9711

49.90741

9.316675

0.0000

R-squared

0.844359

Meandependentvar

114898.3

AdjustedR-squared

0.834631

S.D.dependentvar

22162.37

S.E.ofregression

9012.457

Akaikeinfocriterion

21.15504

Sumsquaredresid

1.30E+09

Schwarzcriterion

21.25397

Loglikelihood

-188.3954

F-statistic

86.80043

Durbin-Watsonstat

0.270852

Prob(F-statistic)

0.000000

DependentVariable:Y

Method:LeastSquares

Date:06/14/11Time:10:49

Sample:19852022

Includedobservations:18

Variable

Coefficient

Std.Error

t-Statistic

Prob.

C

-342804.1

151437.7

-2.263664

0.0378

X7

6689.491

2212.428

3.023597

0.0081

R-squared

0.363618

Meandependentvar

114898.3

AdjustedR-squared

0.323844

S.D.dependentvar

22162.37

S.E.ofregression

18223.83

Akaikeinfocriterion

22.56329

Sumsquaredresid

5.31E+09

Schwarzcriterion

22.66222

Loglikelihood

-201.0696

F-statistic

9.142136

Durbin-Watsonstat

0.500653

Prob(F-statistic)

0.008072

结果如表1.3所示：

表1.3

变量

X1

X2

X3

X4

X5

X6

X7

参数估计值

0.624974

0.612846

1.370007

8.805949

10.14708

464.9711

6689.491

t统计量

10.15481

10.10163

9.678113

9.892599

8.740963

9.316675

3.023597

0.865682

0.864456

0.854102

0.859481

0.826848

0.844359

0.363618

按的大小排序为：X1、X2、X4、X3、X6、X5、X7。

以X1为基础，顺次参与其他变量逐步回归。首先参与X2回归结果为：

DependentVariable:Y

Method:LeastSquares

Date:06/14/11Time:11:06

Sample:19852022

Includedobservations:18

Variable

Coefficient

Std.Error

t-Statistic

Prob.

C

82091.42

4623.981

17.75341

0.0000

X1

10.28141

9.207935

1.116582

0.2817

X2

-9.475974

9.035652

-1.048732

0.3109

R-squared

0.874858

Meandependentvar

AdjustedR-squared

0.858172

S.D.dependentvar

S.E.ofregression

8346.365

Akaikeinfocriterion

Sumsquaredresid

1.04E+09

Schwarzcriterion

Loglikelihood

-186.4325

F-statistic

Durbin-Watsonstat

0.309126

Prob(F-statistic)

Y=82091.42296+10X1-9.475973692*X2

t=(1.116582)(-1.048732)R2=0.874858

当取时，，X2参数的t检验不显著，故剔除X2，

再参与X3回归得

DependentVariable:Y

Method:LeastSquares

Date:01/03/10Time:13:44

Sample:19852022

Includedobservations:18

Variable

Coefficient

Std.Error

t-Statistic

Prob.

C

69047.09

5858.239

11.78632

0.0000

X1

6.684434

1.921197

3.479306

0.0034

X3

-13.37710

4.239913

-3.155040

0.0065

R-squared

0.919261

Meandependentvar

114898.3

AdjustedR-squared

0.908496

S.D.dependentvar

22162.37

S.E.ofregression

6704.025

Akaikeinfocriterion

20.60982

Sumsquaredresid

6.74E+08

Schwarzcriterion

20.75821

Loglikelihood

-182.4883

F-statistic

85.39239

Durbin-Watsonstat

0.826375

Prob(F-statistic)

0.000000

Y=69047.08508+6.684434324*X1-13X3

t=(3.479306)(-3.155040)R2=0.919261

当取时，，X3参数通过t检验，

再参与X4回归得

DependentVariable:Y

Method:LeastSquares

Date:01/03/10Time:13:48

Sample:19852022

Includedobservations:18

Variable

Coefficient

Std.Error

t-Statistic

Prob.

C

70482.84

6619.407

10.64791

0.0000

X1

6.493408

2.004407

3.239566

0.0059

X3

-14.25390

4.667455

-3.053892

0.0086

X4

8.327015

16.12832

0.516298

0.6137

R-squared

0.920770

Meandependentvar

114898.3

AdjustedR-squared

0.903792

S.D.dependentvar

22162.37

S.E.ofregression

6874.191

Akaikeinfocriterion

20.70207

Sumsquaredresid

6.62E+08

Schwarzcriterion

20.89993

Loglikelihood

-182.3186

F-statistic

54.23356

Durbin-Watsonstat

0.920223

Prob(F-statistic)

0.000000

Y=70482.84388+6X1-14X3+8.327015085*X4

t=(3.239566)(-3.053892)（0.516298）R2=0.920770

当取时，，X4参数的t检验不显著，故剔除X4，

再参与X5回归得

DependentVariable:Y

Method:LeastSquares

Date:01/03/10Time:13:53

Sample:19852022

Includedobservations:18

Variable

Coefficient

Std.Error

t-Statistic

Prob.

C

65480.88

5394.770

12.13785

0.0000

X1

8.163830

1.812581

4.503980

0.0005

X3

-14.90018

3.797770

-3.923403

0.0015

X5

-13.22339

5.753094

-2.298483

0.0375

R-squared

0.941382

Meandependentvar

114898.3

AdjustedR-squared

0.928821

S.D.dependentvar

22162.37

S.E.ofregression

5912.807

Akaikeinfocriterion

20.40076

Sumsquaredresid

4.89E+08

Schwarzcriterion

20.59862

Loglikelihood

-179.6068

F-statistic

74.94427

Durbin-Watsonstat

1.171072

Prob(F-statistic)

0.000000

Y=65480.88431+8.163829785*X1-14X3-13X5

t=(4.503980)(-3.923403)（-2.298483）R2=0.941382

当取时，，X5参数通过t检验，

再参与X6回归得

DependentVariable:Y

Method:LeastSquares

Date:01/03/10Time:13:57

Sample:19852022

Includedobservations:18

Variable

Coefficient

Std.Error

t-Statistic

Prob.

C

64354.22

12094.41

5.320991

0.0001

X1

8.030362

2.269021

3.539131

0.0036

X3

-14.66223

4.543937

-3.226767

0.0066

X5

-14.90441

17.07428

-0.872916

0.3985

X6

95.57242

909.5162

0.105081

0.9179

R-squared

0.941431

Meandependentvar

114898.3

AdjustedR-squared

0.923410

S.D.dependentvar

22162.37

S.E.ofregression

6133.405

Akaikeinfocriterion

20.51102

Sumsquaredresid

4.89E+08

Schwarzcriterion

20.75835

Loglikelihood

-179.5992

F-statistic

52.24043

Durbin-Watsonstat

1.150509

Prob