多重共线性的检验与修正.docx
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多重共线性的检验与修正.docx
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多重共线性的检验与修正
附件二:
实验报告格式(首页)
山东轻工业学院实验报告成绩
课程名称计量经济学指导教师实验日期2013-5-25
院(系)商学院专业班级实验地点二机房
学生姓名学号同组人无
实验项目名称多重共线性的检验与修正
一、实验目的和要求
掌握Eviews软件的操作和多重共线性的检验与修正
二、实验原理
Eviews软件的操作和多重共线性的检验修正方法
三、主要仪器设备、试剂或材料
Eviews软件,计算机
四、实验方法与步骤
(1)准备工作:
建立工作文件,并输入数据:
CREATEEX-7-1A19741981;
TATAYX1X2X3X4X5;
(2)OLS估计:
LSYCX1X2X3X4X5;
(3)计算简单相关系数
CORX1X2X3X4X5;
(4)多重共线性的解决
LSYCX1;
LSYCX2;
LSYCX3;
LSYCX4;
LSYCX5;
LSYCX1X3;
LSYCX1X3X2;
LSYCX1X3X4;
LSYCX1X3X5;
五、实验数据记录、处理及结果分析
(1)建立工作组,输入以下数据:
98.45
560.20
153.20
6.53
1.23
1.89
100.70
603.11
190.00
9.12
1.30
2.03
102.80
668.05
240.30
8.10
1.80
2.71
133.95
715.47
301.12
10.10
2.09
3.00
140.13
724.27
361.00
10.93
2.39
3.29
143.11
736.13
420.00
11.85
3.90
5.24
146.15
748.91
491.76
12.28
5.13
6.83
144.60
760.32
501.00
13.50
5.47
8.36
148.94
774.92
529.20
15.29
6.09
10.07
158.55
785.30
552.72
18.10
7.97
12.57
169.68
795.50
771.16
19.61
10.18
15.12
162.14
804.80
811.80
17.22
11.79
18.25
170.09
814.94
988.43
18.60
11.54
20.59
178.69
828.73
1094.65
23.53
11.68
23.37
(2)OLS估计
DependentVariable:
Y
Method:
LeastSquares
Date:
05/25/13Time:
11:
10
Sample:
19741987
Includedobservations:
14
Variable
Coefficient
Std.Error
t-Statistic
Prob.
C
-3.496563
30.00659
-0.116526
0.9101
X1
0.125330
0.059139
2.119245
0.0669
X2
0.073667
0.037877
1.944897
0.0877
X3
2.677589
1.257293
2.129646
0.0658
X4
3.453448
2.450850
1.409082
0.1965
X5
-4.491117
2.214862
-2.027719
0.0771
R-squared
0.970442
Meandependentvar
142.7129
AdjustedR-squared
0.951968
S.D.dependentvar
26.09805
S.E.ofregression
5.719686
Akaikeinfocriterion
6.623232
Sumsquaredresid
261.7185
Schwarzcriterion
6.897114
Loglikelihood
-40.36262
F-statistic
52.53086
Durbin-Watsonstat
1.972755
Prob(F-statistic)
0.000007
用Eviews进行最小二乘估计得,
=-3.497+0.125X1+0.074X2+2.678X3+3.453X4-4.491X5
(-0.1)(2.1)(1.9)(2.1)(1.4)(-2.0)
R
=0.970,
=0.952,DW=1.97,F=52.53
其中括号内的数字是t值。
给定显著水平α=0.05,回归系数估计值都没有显著性。
查F分布表,得临界值为F0.05(5,8)=3.69,故F=52.53>3.69,回归方程显著。
(3)计算简单相关系数
CORX1X2X3X4X5;
X1
X2
X3
X4
X5
X1
1
0.86655186727917
0.882293108606499
.852*********
0.821305444858646
X2
0.86655186727917
1
0.945895698320027
0.964773022012192
0.98253206329193
X3
0.882293108606499
0.945895698320027
1
0.940505820823996
0.948361346495427
X4
.852*********
0.964773022012192
0.940505820823996
1
0.98197917741363
X5
0.821305444858646
0.98253206329193
0.948361346495427
0.98197917741363
1
r12=0.867,r13=0.882,
r14=0.852,r15=0.821,
r23=0.946,r24=0.965,
r25=0.983,r34=0.941,
r35=0.948,r45=0.982
可见解释变量之间是高度相关的。
(4)多重共线性的解决,采用Frisch法。
&1.对Y关于X1,X2,X3,X4,X5作最小二乘回归:
1)LSYCX1
DependentVariable:
Y
Method:
LeastSquares
Date:
05/25/13Time:
11:
12
Sample:
19741987
Includedobservations:
14
Variable
Coefficient
Std.Error
t-Statistic
Prob.
C
-90.92074
19.32929
-4.703781
0.0005
X1
0.316925
0.026081
12.15161
0.0000
R-squared
0.924841
Meandependentvar
142.7129
AdjustedR-squared
0.918578
S.D.dependentvar
26.09805
S.E.ofregression
7.446964
Akaikeinfocriterion
6.985054
Sumsquaredresid
665.4873
Schwarzcriterion
7.076347
Loglikelihood
-46.89537
F-statistic
147.6617
Durbin-Watsonstat
1.536885
Prob(F-statistic)
0.000000
得回归方程为:
=-90.921+0.317X1
(-4.7)(12.2)
R
=0.925,
=0.919,DW=1.537,F=147.619
2)LSYCX2
DependentVariable:
Y
Method:
LeastSquares
Date:
05/25/13Time:
11:
14
Sample:
19741987
Includedobservations:
14
Variable
Coefficient
Std.Error
t-Statistic
Prob.
C
99.61349
6.431242
15.48900
0.0000
X2
0.081470
0.010738
7.587119
0.0000
R-squared
0.827498
Meandependentvar
142.7129
AdjustedR-squared
0.813123
S.D.dependentvar
26.09805
S.E.ofregression
11.28200
Akaikeinfocriterion
7.815858
Sumsquaredresid
1527.403
Schwarzcriterion
7.907152
Loglikelihood
-52.71101
F-statistic
57.56437
Durbin-Watsonstat
0.638969
Prob(F-statistic)
0.000006
得回归方程为:
=99.614+0.0815X2
(15.5)(7.6)
R
=0.828,
=0.813,DW=0.639,F=57.564
3)LSYCX3
DependentVariable:
Y
Method:
LeastSquares
Date:
05/25/13Time:
11:
14
Sample:
19741987
Includedobservations:
14
Variable
Coefficient
Std.Error
t-Statistic
Prob.
C
74.64824
8.288989
9.005711
0.0000
X3
4.892712
0.563578
8.681514
0.0000
R-squared
0.862651
Meandependentvar
142.7129
AdjustedR-squared
0.851205
S.D.dependentvar
26.09805
S.E.ofregression
10.06704
Akaikeinfocriterion
7.587974
Sumsquaredresid
1216.144
Schwarzcriterion
7.679268
Loglikelihood
-51.11582
F-statistic
75.36868
Durbin-Watsonstat
0.813884
Prob(F-statistic)
0.000002
得回归方程为:
=74.648+4.893X3
(9.0)(8.7)
R
=0.863,
=0.851,DW=0.814,F=75.369
4)LSYCX4
DependentVariable:
Y
Method:
LeastSquares
Date:
05/25/13Time:
11:
15
Sample:
19741987
Includedobservations:
14
Variable
Coefficient
Std.Error
t-Statistic
Prob.
C
108.8647
5.934330
18.34490
0.0000
X4
5.739752
0.838756
6.843175
0.0000
R-squared
0.796019
Meandependentvar
142.7129
AdjustedR-squared
0.779021
S.D.dependentvar
26.09805
S.E.ofregression
12.26828
Akaikeinfocriterion
7.983475
Sumsquaredresid
1806.129
Schwarzcriterion
8.074769
Loglikelihood
-53.88433
F-statistic
46.82904
Durbin-Watsonstat
0.769006
Prob(F-statistic)
0.000018
得回归方程为:
=108.865+5.740X4
(18.3)(6.8)
R
=0.796,
=0.779,DW=0.769,F=46.829
5)LSYCX5
DependentVariable:
Y
Method:
LeastSquares
Date:
05/25/13Time:
11:
16
Sample:
19741987
Includedobservations:
14
Variable
Coefficient
Std.Error
t-Statistic
Prob.
C
113.3747
6.077133
18.65596
0.0000
X5
3.080811
0.512300
6.013688
0.0001
R-squared
0.750854
Meandependentvar
142.7129
AdjustedR-squared
0.730091
S.D.dependentvar
26.09805
S.E.ofregression
13.55865
Akaikeinfocriterion
8.183490
Sumsquaredresid
2206.044
Schwarzcriterion
8.274784
Loglikelihood
-55.28443
F-statistic
36.16444
Durbin-Watsonstat
0.593639
Prob(F-statistic)
0.000061
得回归方程为:
=113.375+3.081X5
(18.7)(6.0)
R
=0.75,
=0.73,DW=0.59,F=36.16
选第一个方程为基本回归方程。
&2.加入肉销售量X3,对Y关于X1,X3作最小二乘回归
1)LSYCX1X3
DependentVariable:
Y
Method:
LeastSquares
Date:
05/25/13Time:
11:
17
Sample:
19741987
Includedobservations:
14
Variable
Coefficient
Std.Error
t-Statistic
Prob.
C
-39.79479
25.01570
-1.590793
0.1400
X1
0.211543
0.045302
4.669581
0.0007
X3
1.909246
0.724153
2.636523
0.0231
R-squared
0.953945
Meandependentvar
142.7129
AdjustedR-squared
0.945571
S.D.dependentvar
26.09805
S.E.ofregression
6.088671
Akaikeinfocriterion
6.638146
Sumsquaredresid
407.7910
Schwarzcriterion
6.775087
Loglikelihood
-43.46702
F-statistic
113.9220
Durbin-Watsonstat
1.655554
Prob(F-statistic)
0.000000
得回归方程为:
=-39.795+0.212X1+1.909X3
(-1.6)(4.7)(2.6)
R
=0.954,
=0.946,DW=1.656,F=113.922
可以看出,加入X3后,拟合优度R
和
均有所增加,参数估计值的符号也正确,并且没有影响X1系数的显著性,所以在模型中保留X3.
2)加入人均收入X2,对Y关于X1,X2,X3作最小二乘回归
LSYCX1X3X2
DependentVariable:
Y
Method:
LeastSquares
Date:
05/25/13Time:
11:
18
Sample:
19741987
Includedobservations:
14
Variable
Coefficient
Std.Error
t-Statistic
Prob.
C
-34.77683
27.80679
-1.250660
0.2395
X1
0.206535
0.048000
4.302810
0.0016
X3
1.455520
1.180189
1.233294
0.2457
X2
0.009425
0.018923
0.498037
0.6292
R-squared
0.955060
Meandependentvar
142.7129
AdjustedR-squared
0.941577
S.D.dependentvar
26.09805
S.E.ofregression
6.308098
Akaikeinfocriterion
6.756502
Sumsquaredresid
397.9210
Schwarzcriterion
6.939090
Loglikelihood
-43.29551
F-statistic
70.83889
Durbin-Watsonstat
1.682584
Prob(F-statistic)
0.000000
得回归方程为:
=-34.777+0.207X1+0.009X2+1.456X3
(-1.3)(4.3)(0.5)(1.2)
R
=0.955,
=0.942,DW=1.683,F=70.839
可以看出,再加入X2后,拟合优度R
增加不显著,
有所减小,并且X2和X3系数均不显著,说明存在严重的共线性。
比较X2和X3,肉销售量比人均收入对粮食销售量的影响大,所以在模型中保留X3,略去X2。
3)加入蛋销售量X4,对Y关于X1,X3,X4作最小二乘估计
LSYCX1X3X4
DependentVariable:
Y
Method:
LeastSquares
Date:
05/25/13Time:
11:
19
Sample:
19741987
Includedobservations:
14
Variable
Coefficient
Std.Error
t-Statistic
Prob.
C
-37.99884
28.00654
-1.356785
0.2047
X1
0.210314
0.047919
4.388978
0.0014
X3
1.745767
1.178590
1.481234
0.1694
X4
0.234789
1.295874
0.181182
0.8598
R-squared
0.954096
Meandependentvar
142.7129
AdjustedR-squared
0.940324
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