多重共线性报告
分析背景与意义：农产品的产量及其分布构成在国民生产生活中具
有重要意义，它能真切反应国名的日常生活需求什么，因此本次研究就是对于2000年---2008年人均主要工农业产品产量进行分析，主要考虑各解释变量之间是否存在多重共线性，并对其进行修正处理降低多重共线性对结果的影响，从而使结果模型更具代表性，更真切的展示结果，进而有利于国家对农业产品的生产组成的了解以及监控，才能更好的对其，促进其稳定、科学的发展。
一、数据选择
主要人均主要工农业产品产量
年 份
2000 2001 2002 2003 2004 2005 2006 2007 2008
工农业
产品产量
536.78 536.81 552.77 583.12 618.47 632.99 652.91 670.29 710.21
粮 食
366.04 355. 356.96 334.29 362.22 371.26 379. 380.61 399.13
油 料
23.4 22.53 22.63 21.82 23.66 23.6 20.14 19.49 22.29
糖 料
60.47 68.05 80.39 74.83 73.84 72.5 79.78 92.48 101.31
水 果
49.3 52.35 54.3 112.68 118.36 123.65 130.45 137.62 145.1
猪牛羊肉
37.57 37.99 38.49 39.5 40.39 41.98 42.65 40.09 42.38
（来源与中国统计网）
二、实验步骤：
1、 参数估计，过程如下：
（1）先录入数据至eviews，得到下表：
（2）在命令窗口输入LS y c x1 x2 x3 x4 x5,出现下列结果：
2、 分析
从结果看判断系数R^2很高，说明方程很显著，但四个参数t检验值中有三个较显著，有一个不显著，不符合经济理论，显然认为出现了多重线性回归。
三、 检验
计算解释变量之间的简单相关系数。Eviews过程如下：
（1） 在Quick菜单中选Group Statistics项中的Correlation命令。在
出现Series List对话框时，直接输入x1 X2 X3 X4，出现解释变量x1 x2 x3 x4 之间的相关系数为：
可以看出四个解释变量x1 x2 x3 x4之间的高度相关，必然存在严重的多重共线性。
辅助回归检验：解释变量x1 x2 x3 x4之间的辅助回归分别为： 在命令窗口分别输入：ls x1 c x2;ls x1 c x3;ls x1 c x4;ls x2 c x3;ls x2 c x4;ls x3 c x4;结果分别为：
Dependent Variable: X1 Method: Least Squares Date: 11/24/11 Time: 08:46 Sample(adjusted): 1978 1998
Included observations: 21 after adjusting endpoints
Variable C X2 R-squared
Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat Dependent Variable: X1 Method: Least Squares Date: 11/24/11 Time: 08:53 Sample(adjusted): 1978 1998
Included observations: 21 after adjusting endpoints
Variable C X3
R-squared
Coefficient 2337.206 1.453973
Std. Error 525.8878 0.0674
t-Statistic 4.444305 21.55187
Prob. 0.0003 0.0000
Coefficient 1077.333 13.18376 Std. Error 543.4594 0.577598 t-Statistic 1.982362 22.82514 Prob. 0.0621 0.0000 6638.021 17.23360 17.33307 520.9871 0.000000 0.9814 Mean dependent var 11725.53 0.962962 S.D. dependent var 1277.503 Akaike info criterion 310082 Schwarz criterion -178.9527 F-statistic 0.611662 Prob(F-statistic) 0.960702 Mean dependent var 11725.53
Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat Dependent Variable: X1 Method: Least Squares
0.958634 S.D. dependent var 1350.091 Akaike info criterion 34632150 Schwarz criterion -180.1133 F-statistic 0.865011 Prob(F-statistic)
6638.021 17.34412 17.44360 4.4832 0.000000
Date: 11/24/11 Time: 09:05 Sample(adjusted): 1978 1998
Included observations: 21 after adjusting endpoints Variable C
Coefficient
9042
X4
R-squared
Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat
Std. Error
387
t-Statistic
Prob.
2405.3699446.9817305.381360863.416340
31 591e-0
5
4.60403150.1821678425.27356814.356762
16 87706
0.9695934 S.D. dependent var
60743
1157.5030 Akaike info criterion
1152
254551. Schwarz criterion
2118
-176.88126 F-statistic
1024
0.5080094 Prob(F-statistic)
03722 9359 974 62e-16 85714 6638.02116668 17.0363105737 17.13578011 638.753249431 4.35676262e-16 0.9711137 Mean dependent var 11725.52
Dependent Variable: X2 Method: Least Squares Date: 11/24/11 Time: 09:05 Sample(adjusted): 1978 1998
Included observations: 21 after adjusting endpoints
Variable C X3
R-squared
Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat Dependent Variable: X2
Coefficient 101.1216 0.109424
Std. Error 27.77474 0.003563
t-Statistic 3.0776 30.71038
Prob. 0.0017 0.0000 494.5626 11.46220 11.56168 943.1276 0.000000 0.980252 Mean dependent var 807.6753 0.979213 S.D. dependent var 71.30498 Akaike info criterion 96603.61 Schwarz criterion -118.3531 F-statistic 2.211553 Prob(F-statistic) Method: Least Squares Date: 11/24/11 Time: 09:05 Sample(adjusted): 1978 1998
Included observations: 21 after adjusting endpoints Variable C X4 R-squared
Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat Dependent Variable: X3 Method: Least Squares Date: 11/24/11 Time: 09:06 Sample(adjusted): 1978 1998
Included observations: 21 after adjusting endpoints Variable C X4 R-squared
Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat Coefficient 179.7667 3.100874 Std. Error 310.3227 0.1272 t-Statistic 0.579290 24.51820 Prob. 0.5692 0.0000 4474.829 16.30650 16.40598 601.1422 0.000000 Coefficient 116.1081 0.341625 Std. Error 37.57614 0.015314 t-Statistic 3.0943 22.30772 Prob. 0.0060 0.0000 494.5626 12.08401 12.18349 497.6345 0.000000
0.963224 Mean dependent var 807.6753 0.961288 S.D. dependent var 97.30710 Akaike info criterion 179904.8 Schwarz criterion -124.8821 F-statistic 0.530959 Prob(F-statistic)
0.969362 Mean dependent var 57.012 0.967749 S.D. dependent var 803.6109 Akaike info criterion 12270021 Schwarz criterion -169.2183 F-statistic 0.6788 Prob(F-statistic) 六个回归方程均存在高度显著，拟合优度高，具有共线性。 四、 修正
运用OLS方法逐一求Y对各个解释变量的回归。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。
分别输入“ls y c x1”、
Dependent Variable: Y Method: Least Squares Date: 11/24/11 Time: 09:25 Sample(adjusted): 1978 1998
Included observations: 21 after adjusting endpoints Variable Coefficient Std. Error t-Statistic Prob.
C X1 R-squared
Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat -2241.475 2.009354 8.0392 0.048376 -3.458857 41.53657 0.0026 0.0000 13411.38 17.46762 17.56710 1725.286 0.000000 0.9107 Mean dependent var 21319.26 0.988534 S.D. dependent var 1436.083 Akaike info criterion 39184332 Schwarz criterion -181.4100 F-statistic 0.520820 Prob(F-statistic)
“ls y c x2”、
Dependent Variable: Y Method: Least Squares Date: 11/24/11 Time: 09:13 Sample(adjusted): 1978 1998
Included observations: 21 after adjusting endpoints Variable C X2 R-squared
Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat Coefficient -436.7055 26.93652 Std. Error 675.4209 0.717849 t-Statistic -0.6568 37.52394 Prob. 0.5256 0.0000 13411.38 17.66836 17.76784 1408.046 0.000000 0.986686 Mean dependent var 21319.26 0.985985 S.D. dependent var 1587.703 Akaike info criterion 475234 Schwarz criterion -183.5178 F-statistic 1.194877 Prob(F-statistic)
“ls y c x3”
Dependent Variable: Y Method: Least Squares Date: 11/24/11 Time: 09:18 Sample(adjusted): 1978 1998
Included observations: 21 after adjusting endpoints
Variable C X3
R-squared
Adjusted R-squared S.E. of regression Sum squared resid Log likelihood
Coefficient 2065.912 2.981774
Std. Error 540.80 0.069378
t-Statistic 3.820059 42.97882
Prob. 0.0012 0.0000 13411.38 17.40007 17.49955 1847.179
0.9819 Mean dependent var 21319.26 0.9283 S.D. dependent var 1388.391 Akaike info criterion 36624947 Schwarz criterion -180.7007 F-statistic
Durbin-Watson stat 1.384069 Prob(F-statistic) 0.000000
ls y c x4 :
Dependent Variable: Y Method: Least Squares Date: 11/24/11 Time: 09:23 Sample(adjusted): 1978 1998
Included observations: 21 after adjusting endpoints Variable C X4
R-squared
Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat
Coefficient 2391.344 9.350133
Std. Error 728.4526 0.296882
t-Statistic 3.282772 31.49449
Prob. 0.0039 0.0000 13411.38 18.01312 18.11260 991.9027 0.000000
0.981205 Mean dependent var 21319.26 0.980216 S.D. dependent var 1886.399 Akaike info criterion 67611550 Schwarz criterion -187.1378 F-statistic 0.461310 Prob(F-statistic)
得到Mean dependent var的值分别为21319.26；21319.26；21319.26；21319.26，具有共线性。
所以其回归方程为：y=x1+x2+x3+x4
