多重共线性的识别与补救

S.E. of regression
3.215617
Akaike info criterion
5.417240
Sum squared resid
72.38134
Schwarz criterion
5.508016
Log likelihood
-24.08620
F-statistic
801.6108
Durbin-Watson stat
Log likelihood
-34.22191
F-statistic
234.3827
Durbin-Watson stat
0.468380
Prob(F-statistic)
0.000000
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。经分析在四个一元线性回归模型中食品需求量Y对可支配收入x1的线性关系强，拟合程度好，即
-24.29012
F-statistic
1758.713
Durbin-Watson stat
2.627059
Prob(F-statistic)
0.000000
Ls y c x2
Dependent Variable: Y
Method: Least Squares
Date: 12/06/10 Time: 09:34
收集到1995——2004年食品需求函数有关统计资料。
针对该问题，检验模型是否存在多重共线性。若存在，给出消除多重共线性的方法并重新对模型进行估计。
实验
步骤
1、启动Eviews3.1
2、建立新工作文档，输入时间范围数据1995——2004
3、单击file→import调入数据
4、用OLS估计方法求模型的参数估计：
0.994906
S.D. dependent var
43.01163
S.E. of regression
3.069899
Akaike info criterion
5.258023
Sum squared resid
75.39426
Schwarz criterion
5.318540
Log likelihood
0.305330
0.7724
R-squared
0.998009
Mean dependent var
140.0000
Adjusted R-squared
0.996416
S.D. de. of regression
2.575114
Akaike info criterion
Sum squared resid
806.4989
Schwarz criterion
7.688511
Log likelihood
-36.13997
F-statistic
157.1583
Durbin-Watson stat
2.401329
Prob(F-statistic)
0.000002
Ls y c x3
43.01163
S.E. of regression
6.837496
Akaike info criterion
6.859577
Sum squared resid
374.0108
Schwarz criterion
6.920094
Log likelihood
-32.29788
F-statistic
348.1394
Sample: 1995 2004
Included observations: 10
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
-385.1904
42.01379
-9.168190
0.0000
X2
5.164114
0.411934
12.53628
0.0000
统计学实验报告单（实验五）
姓名
班级
学号
实验地点
E322
指导老师
实验时间
2010年12月2日
报告上交时间
2010年12月9日
实验
名称
多重共线性的识别与补救
实验
目的
要求
1、掌握多重共线性的识别方法
2、能针对具体问题提出解决多重共线性问题的措施
实验
内容
下表是某地区1995-2004年食品需求量Y，可支配收入X1,食品类价格指数X2，物价总指数X3和流动资产拥有量X4的数据资料。根据理论分析，食品需求量受四个因素的影响，建立回归方程：
Sum squared resid
33.77426
Schwarz criterion
4.976025
Log likelihood
-20.27495
F-statistic
983.9580
Durbin-Watson stat
3.524120
Prob(F-statistic)
0.000000
Y=--127.5926+0.103606X1-1.881785x2+3.185637x3
Coefficient
Std. Error
t-Statistic
Prob.
C
-12.45554
3.762734
-3.310238
0.0107
X1
0.117845
0.002810
41.93701
0.0000
R-squared
0.995472
Mean dependent var
140.0000
Adjusted R-squared
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
21.18167
8.191658
2.585761
0.0323
X4
0.326873
0.021351
15.30956
0.0000
R-squared
0.966994
Mean dependent var
140.0000
Std. Error
t-Statistic
Prob.
C
-127.5926
65.15987
-1.958147
0.0979
X1
0.103606
0.013881
7.463972
0.0003
X2
-1.881785
0.762063
-2.469329
0.0485
X3
3.185637
1.216410
2.618884
(7.463972 ) (-2.469329) (2.618884)
R2=0.9979723 S.E.= 2.372560 F=983.9580
Durbin-Watson stat
2.172010
Prob(F-statistic)
0.000000
Ls y c x4
Dependent Variable: Y
Method: Least Squares
Date: 12/06/10 Time: 09:36
Sample: 1995 2004
Included observations: 10
R-squared
0.951562
Mean dependent var
140.0000
Adjusted R-squared
0.945507
S.D. dependent var
43.01163
S.E. of regression
10.04054
Akaike info criterion
7.627994
引入X3: Ls y c x1 x2 x3
Dependent Variable: Y
Method: Least Squares
Date: 12/06/10 Time: 09:42
Sample: 1995 2004
Included observations: 10
Variable
Coefficient
4、修正：
（1）运用OLS方法逐一求Y对各个解释变量的回归。
Ls y c x1
Dependent Variable: Y
Method: Least Squares
Date: 12/06/10 Time: 09:15
Sample: 1995 2004
Included observations: 10
Variable
Prob.
C
-536.5081
36.32179
-14.77097
0.0000
X3
6.632432
0.355464
18.65850
0.0000
R-squared
0.977537
Mean dependent var
140.0000
Adjusted R-squared
0.974729
S.D. dependent var
5.036517
Sum squared resid
33.15605
Schwarz criterion
5.187810
Log likelihood
-20.18259
F-statistic
626.4634
Durbin-Watson stat
3.382618
Prob(F-statistic)
0.000001
Date: 12/06/10 Time: 09:23
Sample: 1995 2004
Included observations: 10
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
14.04708
49.25543
0.285188
0.7838
X1
0.125742
Y=--12.45554+0.117845X1
(-3.310238 ) (41.93701)
R2=0.995472 S.E.= 3.069899 F=1758.713
(2)逐步回归。
引入x2:Ls y c x1 x2
Dependent Variable: Y
Method: Least Squares
1.000000
0.991796
0.969962
X3
0.987666
0.991796
1.000000
0.969477
X4
0.988315
0.969962
0.969477
1.000000
有相关系数矩阵可知解释变量之间存在高度线性相关。同时由回归结果可以看出，尽管整体上线性回归拟合较好，但x1,x2,x3,x4变量的参数t值都不显著，表明模型中存在严重的多重共线性。
0.0396
R-squared
0.997972
Mean dependent var
140.0000
Adjusted R-squared
0.996957
S.D. dependent var
43.01163
S.E. of regression
2.372560
Akaike info criterion
4.854991
Dependent Variable: Y
Method: Least Squares
Date: 12/06/10 Time: 09:30
Sample: 1995 2004
Included observations: 10
Variable
Coefficient
Std. Error
t-Statistic
5、分析：由F=626.4634>F0.05(5,4)=5.19,表明模型从整体上看食品需求量与解释变量之间线性关系显著。
6、检验：
1）图示法：
从图中看出x1、x2存在较强的线性关系。
2）相关系数法：
X1
X2
X3
X4
X1
1.000000
0.980356
0.987666
0.988315
X2
0.980356
Adjusted R-squared
0.962869
S.D. dependent var
43.01163
S.E. of regression
8.288125
Akaike info criterion
7.244381
Sum squared resid
549.5442
Schwarz criterion
7.304898
Prob.
C
-135.3352
75.13155
-1.801310
0.1315
X1
0.096954
0.026488
3.660278
0.0146
X2
-1.991343
0.901601
-2.208675
0.0782
X3
3.401405
1.497488
2.271407
0.0723
X4
0.015081
0.049393
2.533515
Prob(F-statistic)
0.000000
Y=-14.04708+0.125742X1-0.361055x2
(8.425943 ) (-0.539796)
R2=0.995653 S.E.= 3.215617 F=801.6108
由回归结果知可绝系数高，符合经济意义，符号正确。F值显著，Tx2值不显著，则X2暂留。
0.014923
8.425943
0.0001
X2
-0.361055
0.668873
-0.539796
0.6061
R-squared
0.995653
Mean dependent var
140.0000
Adjusted R-squared
0.994411
S.D. dependent var
43.01163
Dependent Variable: Y
Method: Least Squares
Date: 12/06/10 Time: 09:35
Sample: 1995 2004
Included observations: 10
Variable
Coefficient
Std. Error
t-Statistic