多重共线性行情形及处理习题.doc

第六章 多重共线性行情形及处理习题

Coefficientsa
Model
Unstandardized Coefficients
Standardized Coefficients
t
Sig.
Collinearity Statistics
B
Std. Error
Beta
Tolerance
VIF
1
(Constant)
1348.338
2211.463

.610
.552

农业x1
-.641
.167
-1.125
-3.840
.002
.003
319.484
工业x2
-.317
.204
-1.306
-1.551
.143
.000
2.637E3
建筑业x3
-.413
.548
-.270
-.752
.464
.002
479.288
人口x4
-.002
.024
-.007
-.087
.932
.037
27.177
最终消费x5
.671
.128
3.706
5.241
.000
.001
1.861E3
受灾面积x6
-.008
.008
-.020
-.928
.369
.574
1.743
a. Dependent Variable: 财政收入y

书

Coefficientsa
Model
Unstandardized Coefficients
Standardized Coefficients
t
Sig.
Collinearity Statistics
B
Std. Error
Beta
Tolerance
VIF
1
(Constant)
1348.338
2211.463

.610
.552

农业x1
-.641
.167
-1.125
-3.840
.002
.003
319.484
工业x2
-.317
.204
-1.306
-1.551
.143
.000
2.637E3
建筑业x3
-.413
.548
-.270
-.752
.464
.002
479.288
人口x4
-.002
.024
-.007
-.087
.932
.037
27.177
最终消费x5
.671
.128
3.706
5.241
.000
.001
1.861E3
受灾面积x6
-.008
.008
-.020
-.928
.369
.574
1.743
a. Dependent Variable: 财政收入y

6.6解：将5.9数据录入spss ，在线性回归对话框里选择Statistics选择Collinear Diagnostic 做共线性判断然后做回归得到输出结果如下表：

从输出结果来看的扩大因子最大，=2637，远大于10，所以存在严重共线线性。因此剔除,继续建立变量y,关于的回归方程，有关结果输出如下：

Coefficientsa
Model
Unstandardized Coefficients
Standardized Coefficients
t
Sig.
Collinearity Statistics
B
Std. Error
Beta
Tolerance
VIF
1
(Constant)
-1252.832
1507.836

-.831
.419

农业x1
-.735
.163
-1.291
-4.524
.000
.004
276.969
建筑业x3
-.923
.459
-.604
-2.012
.063
.003
306.617
人口x4
.026
.017
.093
1.591
.132
.086
11.605
最终消费x5
.510
.078
2.815
6.527
.000
.002
632.896
受灾面积x6
-.011
.008
-.028
-1.274
.222
.608
1.645
a. Dependent Variable: 财政收入y

Coefficientsa
Model
Unstandardized Coefficients
Standardized Coefficients
t
Sig.
Collinearity Statistics
B
Std. Error
Beta
Tolerance
VIF
1
(Constant)
-2715.046
2829.351

-.960
.352

农业x1
-.047
.235
-.083
-.202
.843
.006
160.513
建筑业x3
1.463
.526
.957
2.781
.013
.009
111.949
人口x4
.036
.031
.128
1.160
.263
.087
11.507
受灾面积x6
.003
.015
.008
.206
.839
.649
1.540
a. Dependent Variable: 财政收入y

从输出结果看，的方差扩大因子=632.896依然远大于10，所以存在多重共线性性剔除，继续建立变量y关于做回归，输出如下：

Coefficientsa
Model
Unstandardized Coefficients
Standardized Coefficients
t
Sig.
Collinearity Statistics
B
Std. Error
Beta
Tolerance
VIF
1
(Constant)
-2296.322
1869.710

-1.228
.236

建筑业x3
1.359
.097
.889
14.036
.000
.249
4.018
人口x4
.031
.019
.111
1.649
.117
.222
4.509
受灾面积x6
.004
.014
.010
.256
.801
.673
1.485
a. Dependent Variable: 财政收入y

从输出结果看，的方差扩大因子=160.513依然远大于10，所以存在多重共线性性剔除，继续建立变量y关于做回归，输出如下：

从输出结果看到，3个方差扩大因子都小于10，回归系数也有合理的解释，说明回归模型不存在强多重共线性。可以作为最终回归模型。回归方程为：

标准化的回归方程为:

Coefficientsa
Model
Unstandardized Coefficients
Standardized Coefficients
t
Sig.
Collinearity Statistics
B
Std. Error
Beta
Tolerance
VIF
1
(Constant)
-1252.832
1507.836

-.831
.419

农业x1
-.735
.163
-1.291
-4.524
.000
.004
276.969
建筑业x3
-.923
.459
-.604
-2.012
.063
.003
306.617
人口x4
.026
.017
.093
1.591
.132
.086
11.605
最终消费x5
.510
.078
2.815
6.527
.000
.002
632.896
受灾面积x6
-.011
.008
-.028
-1.274
.222
.608
1.645
a. Dependent Variable: 财政收入y