. . . .
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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 计量经济学实验
项 目 类 型 多重共线性模型的检验与处理
实验(实训)日期 2011
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、实验（实训）概述：
【目的及要求】
(1)建立对数线性多元回归模型
(2)如果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)如果有多重共线性，你准备怎样解决这个问题？试写出整个分析和解决过程。
【基本原理】
Klein判别法，逐步回归法,OLS
【实施环境】（使用的材料、设备、软件）
1、电脑1人一台。2、Eviews3.1学生版
二、实验（实训）容：
【项目容】
建立并检验影响影响能源消费需求总量的因素模型
【方案设计】
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1985-2002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
2001
134914
95727.9
97314.8
42374.6
6375.4
5968.3
144.6
70.41
2002
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》2004、2000年版，中国统计。
【实验（实训）过程】（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
Dependent Variable: Y
Method: Least Squares
Date: 06/14/11 Time: 10:20
Sample: 1985 2002
Included observations: 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
Mean dependent var
114898.3
Adjusted R-squared
0.939758
S.D. dependent var
22162.37
S.E. of regression
5439.605
Akaike info criterion
20.34190
Sum squared resid
2.96E+08
Schwarz criterion
20.73762
Log likelihood
-175.0771
F-statistic
38.88476
Durbin-Watson stat
1.842204
Prob(F-statistic)
0.000002
Estimation Command:
=====================
LS Y C X1 X2 X3 X4 X5 X6 X7
Estimation Equation:
=====================
Y = C(1) + C(2)*X1 + C(3)*X2 + C(4)*X3 + C(5)*X4 + C(6)*X5 + C(7)*X6 + C(8)*X7
Substituted Coefficients:
=====================
Y = -80155.51982 + 36X1 - 28X2 - 10X3 - 17.526428*X4 - 34X5 + 336.4865768*X6 + 1952.572512*X7
二、如果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，这表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，证实确实存在严重多重共线性。
三、消除多重共线性
采用逐步回归的办法，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，
Dependent Variable: Y
Method: Least Squares
Date: 06/14/11 Time: 10:46
Sample: 1985 2002
Included observations: 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
Mean dependent var
114898.3
Adjusted R-squared
0.857287
S.D. dependent var
22162.37
S.E. of regression
8372.365
Akaike info criterion
21.00770
Sum squared resid
1.12E+09
Schwarz criterion
21.10663
Log likelihood
-187.0693
F-statistic
103.1201
Durbin-Watson stat
0.253364
Prob(F-statistic)
0.000000
Dependent Variable: Y
Method: Least Squares
Date: 06/14/11 Time: 10:46
Sample: 1985 2002
Included observations: 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
Mean dependent var
114898.3
Adjusted R-squared
0.855985
S.D. dependent var
22162.37
S.E. of regression
8410.478
Akaike info criterion
21.01678
Sum squared resid
1.13E+09
Schwarz criterion
21.11571
Log likelihood
-187.1511
F-statistic
102.0429
Durbin-Watson stat
0.254758
Prob(F-statistic)
0.000000
Dependent Variable: Y
Method: Least Squares
Date: 06/14/11 Time: 10:47
Sample: 1985 2002
Included observations: 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
Mean dependent var
Adjusted R-squared
0.844984
S.D. dependent var
S.E. of regression
8725.793
Akaike info criterion
Sum squared resid
1.22E+09
Schwarz criterion
Log likelihood
-187.8135
F-statistic
Durbin-Watson stat
0.238854
Prob(F-statistic)
Dependent Variable: Y
Method: Least Squares
Date: 06/14/11 Time: 10:48
Sample: 1985 2002
Included observations: 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
Mean dependent var
Adjusted R-squared
0.850698
S.D. dependent var
S.E. of regression
8563.442
Akaike info criterion
Sum squared resid
1.17E+09
Schwarz criterion
Log likelihood
-187.4755
F-statistic
Durbin-Watson stat
0.244443
Prob(F-statistic)
Dependent Variable: Y
Method: Least Squares
Date: 06/14/11 Time: 10:48
Sample: 1985 2002
Included observations: 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
Mean dependent var
Adjusted R-squared
0.816026
S.D. dependent var
S.E. of regression
9505.923
Akaike info criterion
Sum squared resid
1.45E+09
Schwarz criterion
Log likelihood
-189.3549
F-statistic
Durbin-Watson stat
0.291497
Prob(F-statistic)
Dependent Variable: Y
Method: Least Squares
Date: 06/14/11 Time: 10:49
Sample: 1985 2002
Included observations: 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
Mean dependent var
114898.3
Adjusted R-squared
0.834631
S.D. dependent var
22162.37
S.E. of regression
9012.457
Akaike info criterion
21.15504
Sum squared resid
1.30E+09
Schwarz criterion
21.25397
Log likelihood
-188.3954
F-statistic
86.80043
Durbin-Watson stat
0.270852
Prob(F-statistic)
0.000000
Dependent Variable: Y
Method: Least Squares
Date: 06/14/11 Time: 10:49
Sample: 1985 2002
Included observations: 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
Mean dependent var
114898.3
Adjusted R-squared
0.323844
S.D. dependent var
22162.37
S.E. of regression
18223.83
Akaike info criterion
22.56329
Sum squared resid
5.31E+09
Schwarz criterion
22.66222
Log likelihood
-201.0696
F-statistic
9.142136
Durbin-Watson stat
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，顺次加入其他变量逐步回归。首先加入X2回归结果为：
Dependent Variable: Y
Method: Least Squares
Date: 06/14/11 Time: 11:06
Sample: 1985 2002
Included observations: 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
Mean dependent var
Adjusted R-squared
0.858172
S.D. dependent var
S.E. of regression
8346.365
Akaike info criterion
Sum squared resid
1.04E+09
Schwarz criterion
Log likelihood
-186.4325
F-statistic
Durbin-Watson stat
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，
再加入X3回归得
Dependent Variable: Y
Method: Least Squares
Date: 01/03/10 Time: 13:44
Sample: 1985 2002
Included observations: 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
Mean dependent var
114898.3
Adjusted R-squared
0.908496
S.D. dependent var
22162.37
S.E. of regression
6704.025
Akaike info criterion
20.60982
Sum squared resid
6.74E+08
Schwarz criterion
20.75821
Log likelihood
-182.4883
F-statistic
85.39239
Durbin-Watson stat
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，
再加入X4回归得
Dependent Variable: Y
Method: Least Squares
Date: 01/03/10 Time: 13:48
Sample: 1985 2002
Included observations: 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
Mean dependent var
114898.3
Adjusted R-squared
0.903792
S.D. dependent var
22162.37
S.E. of regression
6874.191
Akaike info criterion
20.70207
Sum squared resid
6.62E+08
Schwarz criterion
20.89993
Log likelihood
-182.3186
F-statistic
54.23356
Durbin-Watson stat
0.920113
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，
再加入X5回归得
Dependent Variable: Y
Method: Least Squares
Date: 01/03/10 Time: 13:53
Sample: 1985 2002
Included observations: 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
Mean dependent var
114898.3
Adjusted R-squared
0.928821
S.D. dependent var
22162.37
S.E. of regression
5912.807
Akaike info criterion
20.40076
Sum squared resid
4.89E+08
Schwarz criterion
20.59862
Log likelihood
-179.6068
F-statistic
74.94427
Durbin-Watson stat
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，
再加入X6回归得
Dependent Variable: Y
Method: Least Squares
Date: 01/03/10 Time: 13:57
Sample: 1985 2002
Included observations: 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
Mean dependent var
114898.3
Adjusted R-squared
0.923410
S.D. dependent var
22162.37
S.E. of regression
6133.405
Akaike info criterion
20.51102
Sum squared resid
4.89E+08
Schwarz criterion
20.75835
Log likelihood
-179.5992
F-statistic
52.24043
Durbin-Watson stat
1.150509
Prob(F-statistic)
0.000000
Y = 64354.22244 + 8.030361821*X1 - 14X3 - 14X5 + 95X6
t=(3.539131) (-3.226767) （-0.872916） （0.105081） R2=0.941431
当取 时，，X6参数的t检验不显著，予以剔除，
再加入X7回归得
Dependent Variable: Y
Method: Least Squares
Date: 01/03/10 Time: 14:03
Sample: 1985 2002
Included observations: 18
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
89268.75
95105.65
0.938627
0.3650
X1
7.922042
2.110078
3.754384
0.0024
X3
-14.25917
4.690771
-3.039834
0.0095
X5
-13.78204
6.359577
-2.167131
0.0494
X7
-347.9448
1388.709
-0.250553
0.8061
R-squared
0.941663
Mean dependent var
114898.3
Adjusted R-squared
0.923714
S.D. dependent var
22162.37
S.E. of regression
6121.248
Akaike info criterion
20.50705
Sum squared resid
4.87E+08
Schwarz criterion
20.75438
Log likelihood
-179.5635
F-statistic
52.46107
Durbin-Watson stat
1.176599
Prob(F-statistic)
0.000000
Y = 89268.74629 + 7.922042434*X1 - 14X3 - 13X5 - 347.9448125*X7
t=(3.754384) (-3.039834) （-2.167131） （-0.250553） R2=0.941663
当取 时，，X7参数的t检验不显著，予以剔除。
所以，最后消除多重共线性的结果是：
Y = 65480.88431 + 8.163829785*X1 - 14X3 - 13X5
t=(4.503980) (-3.923403) （-2.298483） R2=0.941382
=0.928821 F=
这说明，在其他因素不变的情况下，当国民总收入X1增长1亿元时，能源消费Y将增长8.16万吨标准煤；在其他因素不变的情况下，当工业增加值X3增长1亿元时，能源消费Y将减少14.9万吨标准煤；在其他因素不变的情况下，当交通运输邮电增加值X5增加1单位时，能源消费Y减少13.22万吨标准煤。
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