多元线性回归模型案例.doc

我国农民收入影响因素的回归分析
本文力图应用适当的多元线性回归模型,对有关农民收入的历史数据和现状进行分析,探讨影响农民收入的主要因素,并在此基础上对如何增加农民收入提出相应的政策建议。 农民收入水平的度量常采用人均纯收入指标。影响农民收入增长的因素是多方面的，既有结构性矛盾因素，又有体制性障碍因素。但可以归纳为以下几个方面：一是农产品收购价格水平。二是农业剩余劳动力转移水平。三是城市化、工业化水平。四是农业产业结构状况。五是农业投入水平。考虑到复杂性和可行性，所以对农业投入与农民收入，本文暂不作讨论。因此，以全国为例，把农民收入与各影响因素关系进行线性回归分析，并建立数学模型。
一、计量经济模型分析
(一)、数据搜集
根据以上分析，我们在影响农民收入因素中引入7个解释变量。即： -财政用于农业的支出的比重， -第二、三产业从业人数占全社会从业人数的比重， -非农村人口比重， -乡村从业人员占农村人口的比重， -农业总产值占农林牧总产值的比重， -农作物播种面积，—农村用电量。

y
x2
x3
x4
x5
x6
x7
x8
年份
78年可比价
比重
%
%
比重
比重
千公顷
亿千瓦时
1986
133.60
13.43
29.50
17.92
36.01
79.99
150104.07
253.10
1987
137.63
12.20
31.30
19.39
38.62
75.63
146379.53
320.80
1988
147.86
7.66
37.60
23.71
45.90
69.25
143625.87
508.90
1989
196.76
9.42
39.90
26.21
49.23
62.75
146553.93
790.50
1990
220.53
9.98
39.90
26.41
49.93
64.66
148362.27
844.50
1991
223.25
10.26
40.30
26.94
50.92
63.09
149585.80
963.20
1992
233.19
10.05
41.50
27.46
51.53
61.51
149007.10
1106.90
1993
265.67
9.49
43.60
27.99
51.86
60.07
147740.70
1244.90
1994
335.16
9.20
45.70
28.51
52.12
58.22
148240.60
1473.90
1995
411.29
8.43
47.80
29.04
52.41
58.43
149879.30
1655.70
1996
460.68
8.82
49.50
30.48
53.23
60.57
152380.60
1812.70
1997
477.96
8.30
50.10
31.91
54.93
58.23
153969.20
1980.10
1998
474.02
10.69
50.20
33.35
55.84
58.03
155705.70
2042.20
1999
466.80
8.23
49.90
34.78
57.16
57.53
156372.81
2173.45
2000
466.16
7.75
50.00
36.22
59.33
55.68
156299.85
2421.30
2001
469.80
7.71
50.00
37.66
60.62
55.24
155707.86
2610.78
2002
468.95
7.17
50.00
39.09
62.02
54.51
154635.51
2993.40
2003
476.24
7.12
50.90
40.53
63.72
50.08
152414.96
3432.92
2004
499.39
9.67
53.10
41.76
65.64
50.05
153552.55
3933.03
2005
521.20
7.22
55.20
42.99
67.59
49.72
155487.73
4375.70
资料来源《中国统计年鉴2006》。
(二)、计量经济学模型建立
我们设定模型为下面所示的形式：

利用Eviews软件进行最小二乘估计，估计结果如下表所示：
Dependent Variable: Y
Method: Least Squares
Sample: 1986 2004
Included observations: 19
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
-1102.373
375.8283
-2.933184
0.0136
X1
-6.635393
3.781349
-1.754769
0.1071
X3
18.22942
2.066617
8.820899
0.0000
X4
2.430039
8.370337
0.290316
0.7770
X5
-16.23737
5.894109
-2.754847
0.0187
X6
-2.155208
2.770834
-0.777819
0.4531
X7
0.009962
0.002328
4.278810
0.0013
X8
0.063389
0.021276
2.979348
0.0125
R-squared
0.995823
Mean dependent var
345.5232
Adjusted R-squared
0.993165
S.D. dependent var
139.7117
S.E. of regression
11.55028
Akaike info criterion
8.026857
Sum squared resid
1467.498
Schwarz criterion
8.424516
Log likelihood
-68.25514
F-statistic
374.6600
Durbin-Watson stat
1.993270
Prob(F-statistic)
0.000000
表1 最小二乘估计结果
回归分析报告为：
二、计量经济学检验
(一)、多重共线性的检验及修正
①、检验多重共线性
(a)、直观法
从“表1 最小二乘估计结果”中可以看出，虽然模型的整体拟合的很好，但是x4 x6的t统计量并不显著，所以可能存在多重共线性。
(b)、相关系数矩阵

X2
X3
X4
X5
X6
X7
X8
X2
1.000000
-0.717662
-0.695257
-0.731326
0.737028
-0.332435
-0.594699
X3
-0.717662
1.000000
0.922286
0.935992
-0.945701
0.742251
0.883804
X4
-0.695257
0.922286
1.000000
0.986050
-0.937751
0.753928
0.974675
X5
-0.731326
0.935992
0.986050
1.000000
-0.974750
0.687439
0.940436
X6
0.737028
-0.945701
-0.937751
-0.974750
1.000000
-0.603539
-0.887428
X7
-0.332435
0.742251
0.753928
0.687439
-0.603539
1.000000
0.742781
X8
-0.594699
0.883804
0.974675
0.940436
-0.887428
0.742781
1.000000
表2 相关系数矩阵
从“表2 相关系数矩阵”中可以看出，个个解释变量之间的相关程度较高，所以应该存在多重共线性。
②、多重共线性的修正——逐步迭代法
A、 一元回归
Dependent Variable: Y
Method: Least Squares
Sample: 1986 2004
Included observations: 19
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
820.3133
151.8712
5.401374
0.0000
X2
-51.37836
16.18923
-3.173614
0.0056
R-squared
0.372041
Mean dependent var
345.5232
Adjusted R-squared
0.335102
S.D. dependent var
139.7117
S.E. of regression
113.9227
Akaike info criterion
12.40822
Sum squared resid
220632.4
Schwarz criterion
12.50763
Log likelihood
-115.8781
F-statistic
10.07183
Durbin-Watson stat
0.644400
Prob(F-statistic)
0.005554
表3 y对x2的回归结果
Dependent Variable: Y
Method: Least Squares
Sample: 1986 2004
Included observations: 19
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
-525.8891
64.11333
-8.202492
0.0000
X3
19.46031
1.416043
13.74274
0.0000
R-squared
0.917421
Mean dependent var
345.5232
Adjusted R-squared
0.912563
S.D. dependent var
139.7117
S.E. of regression
41.31236
Akaike info criterion
10.37950
Sum squared resid
29014.09
Schwarz criterion
10.47892
Log likelihood
-96.60526
F-statistic
188.8628
Durbin-Watson stat
0.598139
Prob(F-statistic)
0.000000
表4 y对x3的回归结果
Dependent Variable: Y
Method: Least Squares
Sample: 1986 2004
Included observations: 19
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
-223.1905
69.92322
-3.191937
0.0053
X4
18.65086
2.242240
8.317956
0.0000
R-squared
0.802758
Mean dependent var
345.5232
Adjusted R-squared
0.791155
S.D. dependent var
139.7117
S.E. of regression
63.84760
Akaike info criterion
11.25018
Sum squared resid
69300.77
Schwarz criterion
11.34959
Log likelihood
-104.8767
F-statistic
69.18839
Durbin-Watson stat
0.282182
Prob(F-statistic)
0.000000
表5 y对x4的回归结果
Dependent Variable: Y
Method: Least Squares
Sample: 1986 2004
Included observations: 19
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
-494.1440
118.1449
-4.182526
0.0006
X5
15.77978
2.198711
7.176832
0.0000
R-squared
0.751850
Mean dependent var
345.5232
Adjusted R-squared
0.737253
S.D. dependent var
139.7117
S.E. of regression
71.61463
Akaike info criterion
11.47978
Sum squared resid
87187.14
Schwarz criterion
11.57919
Log likelihood
-107.0579
F-statistic
51.50691
Durbin-Watson stat
0.318959
Prob(F-statistic)
0.000002
表6 y对x5的回归结果
Dependent Variable: Y
Method: Least Squares
Sample: 1986 2004
Included observations: 19
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
1288.009
143.8088
8.956395
0.0000
X6
-15.52398
2.351180
-6.602635
0.0000
R-squared
0.719448
Mean dependent var
345.5232
Adjusted R-squared
0.702945
S.D. dependent var
139.7117
S.E. of regression
76.14674
Akaike info criterion
11.60250
Sum squared resid
98571.54
Schwarz criterion
11.70192
Log likelihood
-108.2238
F-statistic
43.59479
Durbin-Watson stat
0.395893
Prob(F-statistic)
0.000004
表7 y对x6的回归结果
Dependent Variable: Y
Method: Least Squares
Sample: 1986 2004
Included observations: 19
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
-4417.766
681.1678
-6.485577
0.0000
X7
0.031528
0.004507
6.994943
0.0000
R-squared
0.742148
Mean dependent var
345.5232
Adjusted R-squared
0.726980
S.D. dependent var
139.7117
S.E. of regression
73.00119
Akaike info criterion
11.51813
Sum squared resid
90595.96
Schwarz criterion
11.61754
Log likelihood
-107.4222
F-statistic
48.92923
Durbin-Watson stat
0.572651
Prob(F-statistic)
0.000002
表8 y对x7的回归结果
Dependent Variable: Y
Method: Least Squares
Sample: 1986 2004
Included observations: 19
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
140.1625
28.96616
4.838835
0.0002
X8
0.119827
0.014543
8.239503
0.0000
R-squared
0.799739
Mean dependent var
345.5232
Adjusted R-squared
0.787959
S.D. dependent var
139.7117
S.E. of regression
64.33424
Akaike info criterion
11.26536
Sum squared resid
70361.21
Schwarz criterion
11.36478
Log likelihood
-105.0209
F-statistic
67.88941
Durbin-Watson stat
0.203711
Prob(F-statistic)
0.000000
表9 y对x8的回归结果
综合比较表3~9的回归结果，发现加入x3的回归结果最好。以x3为基础顺次加入其他解释变量，进行二元回归，具体的回归结果如下表10~15所示：
Dependent Variable: Y
Method: Least Squares
Sample: 1986 2004
Included observations: 19
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
-754.4481
149.1701
-5.057637
0.0001
X3
21.78865
1.932689
11.27375
0.0000
X2
13.45070
8.012745
1.678663
0.1126
R-squared
0.929787
Mean dependent var
345.5232
Adjusted R-squared
0.921010
S.D. dependent var
139.7117
S.E. of regression
39.26619
Akaike info criterion
10.32254
Sum squared resid
24669.34
Schwarz criterion
10.47167
Log likelihood
-95.06417
F-statistic
105.9385
Durbin-Watson stat
0.595954
Prob(F-statistic)
0.000000
表10 加入x2的回归结果
Dependent Variable: Y
Method: Least Squares
Sample: 1986 2004
Included observations: 19
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
-508.6781
75.73220
-6.716802
0.0000
X3
17.88200
3.752121
4.765837
0.0002
X4
1.753351
3.844305
0.456090
0.6545
R-squared
0.918481
Mean dependent var
345.5232
Adjusted R-squared
0.908291
S.D. dependent var
139.7117
S.E. of regression
42.30965
Akaike info criterion
10.47185
Sum squared resid
28641.71
Schwarz criterion
10.62097
Log likelihood
-96.48254
F-statistic
90.13613
Durbin-Watson stat
0.596359
Prob(F-statistic)
0.000000
表11 加入x4的回归结果
Dependent Variable: Y
Method: Least Squares
Sample: 1986 2004
Included observations: 19
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
-498.1550
67.21844
-7.410986
0.0000
X3
23.97516
3.967183
6.043370
0.0000
X5
-4.320566
3.553466
-1.215874
0.2417
R-squared
0.924405
Mean dependent var
345.5232
Adjusted R-squared
0.914956
S.D. dependent var
139.7117
S.E. of regression
40.74312
Akaike info criterion
10.39639
Sum squared resid
26560.02
Schwarz criterion
10.54551
Log likelihood
-95.76570
F-statistic
97.82772
Durbin-Watson stat
0.607882
Prob(F-statistic)
0.000000
表12 加入x5的回归结果
Dependent Variable: Y
Method: Least Squares
Sample: 1986 2004
Included observations: 19
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
-1600.965
346.9265
-4.614709
0.0003
X3
29.93768
3.534753
8.469528
0.0000
X6
9.980135
3.184176
3.134291
0.0064
R-squared
0.948835
Mean dependent var
345.5232
Adjusted R-squared
0.942440
S.D. dependent var
139.7117
S.E. of regression
33.51927
Akaike info criterion
10.00606
Sum squared resid
17976.66
Schwarz criterion
10.15518
Log likelihood
-92.05754
F-statistic
148.3576
Durbin-Watson stat
1.125188
Prob(F-statistic)
0.000000
表13 加入x6的回归结果
Dependent Variable: Y
Method: Least Squares
Sample: 1986 2004
Included observations: 19
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
-2153.028
327.1248
-6.581673
0.0000
X3
14.40497
1.358355
10.60472
0.0000
X7
0.012268
0.002447
5.014015
0.0001
R-squared
0.967884
Mean dependent var
345.5232
Adjusted R-squared
0.963869
S.D. dependent var
139.7117
S.E. of regression
26.55648
Akaike info criterion
9.540364
Sum squared resid
11283.94
Schwarz criterion
9.689485
Log likelihood
-87.63345
F-statistic
241.0961
Durbin-Watson stat
0.690413
Prob(F-statistic)
0.000000
表14 加入x7的回归结果
Dependent Variable: Y
Method: Least Squares
Sample: 1986 2004
Included observations: 19
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
-400.5635
103.0301
-3.887832
0.0013
X3
15.54271
2.916358
5.329493
0.0001
X8
0.029233
0.019233
1.519929
0.1480
R-squared
0.927840
Mean dependent var
345.5232
Adjusted R-squared
0.918820
S.D. dependent var
139.7117
S.E. of regression
39.80687
Akaike info criterion
10.34990
Sum squared resid
25353.40
Schwarz criterion
10.49902
Log likelihood
-95.32401
F-statistic
102.8643
Durbin-Watson stat
0.559772
Prob(F-statistic)
0.000000
表15 加入x8的回归结果
综合表10~15所示，加入x7的模型的R最大,以x3、x7为基础顺次加入其他解释变量，进行三元回归，具体回归结果如下表16~20所示：
Dependent Variable: Y
Method: Least Squares
Sample: 1986 2004
Included observations: 19
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
-2133.921
340.6965
-6.263406
0.0000
X3
14.96023
2.094645
7.142134
0.0000
X7
0.011843
0.002786
4.250908
0.0007
X2
2.195243
6.170403
0.355770
0.7270
R-squared
0.968153
Mean dependent var
345.5232
Adjusted R-squared
0.961783
S.D. dependent var
139.7117
S.E. of regression
27.31242
Akaike info criterion
9.637224
Sum squared resid
11189.52
Schwarz criterion
9.836053
Log likelihood
-87.55363
F-statistic
151.9988
Durbin-Watson stat
0.712258
Prob(F-statistic)
0.000000
表16 加入x2的回归结果
Dependent Variable: Y
Method: Least Squares
Sample: 1986 2004
Included observations: 19
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
-2226.420
353.4425
-6.299243
0.0000
X3
15.66729
2.443113
6.412839
0.0000
X7
0.012703
0.002589
4.906373
0.0002
X4
-1.601362
2.553294
-0.627175
0.5400
R-squared
0.968705
Mean dependent var
345.5232
Adjusted R-squared
0.962445
S.D. dependent var
139.7117
S.E. of regression
27.07472
Akaike info criterion
9.619741
Sum squared resid
10995.60
Schwarz criterion
9.818571
Log likelihood
-87.38754
F-statistic
154.7677
Durbin-Watson stat
0.704178
Prob(F-statistic)
0.000000
表17 加入x4的回归结果
Dependent Variable: Y
Method: Least Squares
Sample: 1986 2004
Included observations: 19
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
-2110.381
306.2690
-6.890613
0.0000
X3
18.60156
2.617381
7.106937
0.0000
X7
0.012139
0.002285
5.311665
0.0001
X5
-3.964878
2.163262
-1.832823
0.0868
R-squared
0.973760
Mean dependent var
345.5232
Adjusted R-squared
0.968512
S.D. dependent var
139.7117
S.E. of regression
24.79152
Akaike info criterion
9.443544
Sum squared resid
9219.289
Schwarz criterion
9.642373
Log likelihood
-85.71367
F-statistic
185.5507
Durbin-Watson stat
0.733972
Prob(F-statistic)
0.000000
表18 加入x5的回归结果
Dependent Variable: Y
Method: Least Squares
Sample: 1986 2004
Included observations: 19
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
-2418.859
323.7240
-7.471979
0.0000
X3
20.99887
3.397120
6.181374
0.0000
X7
0.009920
0.002495
3.976660
0.0012
X6
5.359184
2.571950
2.083705
0.0547
R-squared
0.975093
Mean dependent var
345.5232
Adjusted R-squared
0.970112
S.D. dependent var
139.7117
S.E. of regression
24.15359
Akaike info criterion
9.391407
Sum squared resid
8750.940
Schwarz criterion
9.590236
Log likelihood
-85.21837
F-statistic
195.7489
Durbin-Watson stat
1.084023
Prob(F-statistic)
0.000000
表19 加入x6的回归结果
Dependent Variable: Y
Method: Least Squares
Sample: 1986 2004
Included observations: 19
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
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