吳洋一經(jīng)濟學(xué)08071002422022年本科計量經(jīng)濟學(xué)實驗課程期末上機考試實驗報告

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實驗（實訓(xùn)）報告

項目名稱建立影響能源消費需求總量的因素模型

所屬課程名稱計量經(jīng)濟學(xué)試驗

項目類型多重共線性模型的檢驗與處理

試驗(實訓(xùn))日期2022

班級08經(jīng)濟（2）

學(xué)號0807100242

姓名吳洋一

指導(dǎo)教師項后軍

財經(jīng)學(xué)院教務(wù)處制

一、試驗（實訓(xùn)）概述：

(1)建立對數(shù)線性多元回歸模型

(2)假如決定用表中全部變量作為解釋變量，你預(yù)料會遇到多重共線性的問題嗎？為什么？

(3)假如有多重共線性，你準備怎樣解決這個問題？試寫出整個分析和解決過程。

Klein判別法，逐步回歸法,OLS

（使用的材料、設(shè)備、軟件）

1、電腦1人一臺。2、Eviews3.1學(xué)生版

二、試驗（實訓(xùn)）容：

建立并檢驗影響影響能源消費需求總量的因素模型

理論上認為影響能源消費需求總量的因素主要有經(jīng)濟發(fā)展水平、收入水平、產(chǎn)業(yè)發(fā)展、人民生活水平提高、能源轉(zhuǎn)換技術(shù)等因素。為此，收集了中國能源消費總量Y(萬噸標準煤)、國生產(chǎn)總值(億元)X1(代表經(jīng)濟發(fā)展水平)、國民總收入(億元)X2(代表收入水平)、工業(yè)增加值(億元)X3、建筑業(yè)增加值(億元)X4、交通運輸郵電業(yè)增加值(億元)X5(代表產(chǎn)業(yè)發(fā)展水平及產(chǎn)業(yè)結(jié)構(gòu))、人均生活電力消費(千瓦小時)X6(代表人民生活水平提高)、能源加工轉(zhuǎn)換效率(%)X7(代表能源轉(zhuǎn)換技術(shù))等在1985-2022年期間的統(tǒng)計數(shù)據(jù)，具體如下：

年份

能源消費

國民

總收入

ＧＤＰ

工業(yè)

建筑業(yè)

交通運輸郵電

人均生活

電力消費

能源加工

轉(zhuǎn)換效率

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

資料來源：《中國統(tǒng)計年鑒》2022、2000年版，中國統(tǒng)計。

（步驟、記錄、數(shù)據(jù)、程序等）

一、建立對數(shù)線性多元回歸模型

利用Eviews軟件，輸入Y、X1、X2、X3、X4、X5、X6、X7等數(shù)據(jù)，采用這些數(shù)據(jù)對模型進行OLS回歸，結(jié)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、假如決定用表中全部變量作為解釋變量，你預(yù)料會遇到多重共線性的問題嗎？為什么？

由表1.1可見，該模型R2=0.964563，可決系數(shù)很高，F(xiàn)檢驗值38.88476,明顯顯著。但是當(dāng)時,2.228，不僅X1、X2、X3、X4、X5、X6、X7的t檢驗不顯著，而且X2、X3、X4、X5系數(shù)的符號與預(yù)期的相反，這說明很可能存在嚴重的多重共線性。

計算各解釋變量的相關(guān)系數(shù)，選擇X1、X2、X3、X4、X5、X6、X7數(shù)據(jù)，點〞view/correlations〞得相關(guān)系數(shù)矩陣（如表1.2）：

表1.2

由相關(guān)系數(shù)矩陣可以看出：各解釋變量相互之間的相關(guān)系數(shù)較高，證明確實存在嚴重多重共線性。

三、消除多重共線性

采用逐步回歸的方法，去檢驗和解決多重共線性問題。分別作Y對X1、X2、X3、X4、X5、X6、X7的一元回歸，

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

結(jié)果如表1.3所示：

表1.3

變量

X1

X2

X3

X4

X5

X6

X7

參數(shù)估計值

0.624974

0.612846

1.370007

8.805949

10.14708

464.9711

6689.491

t統(tǒng)計量

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

按的大小排序為：X1、X2、X4、X3、X6、X5、X7。

以X1為基礎(chǔ)，順次參與其他變量逐步回歸。首先參與X2回歸結(jié)果為：

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

當(dāng)取時，，X2參數(shù)的t檢驗不顯著，故剔除X2，

再參與X3回歸得

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

當(dāng)取時，，X3參數(shù)通過t檢驗，

再參與X4回歸得

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

當(dāng)取時，，X4參數(shù)的t檢驗不顯著，故剔除X4，

再參與X5回歸得

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

當(dāng)取時，，X5參數(shù)通過t檢驗，

再參與X6回歸得

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