目的:1、正确使用EVIEWS
2、能根据计算结果进行多重共线性检验和出现多重共线性时的补救。
3、数据为demo data2
实例:我国钢材供应量分析(多重共线性检验及补救)
通过分析我国改革开放以来(1978-1997)钢材供应量的历史资料,可以建立一个单一方程模型。根据理论及对现实情况的认识,影响我国钢材供应量Y(万吨)的主要因素有:原油产量X1(万吨),生铁产量X2(万吨),原煤产量X3(万吨),电力产量X4(亿千瓦小时),固定资产投资X5(亿元),国内生产总值X6(亿元),铁路运输量X7(万吨)。
设模型的函数形式为:
一、运用OLS估计法对上式中参数进行估计,EVIEWS操作步骤为:
1、 在FILE菜单中选择NEW-WORKFILE,输入起止时间。
2、 在主窗口菜单选QUICK-EMPTY GROUP,在编辑数据区输入Y X1 X2 X3 X4 X5 X6 X7所对应的数据。
3、 在主窗口菜单选在QUICK-ESTIMATE EQUATION,对参数做OSL估计,输出结果见下表:
Variable | Coefficient | Std. Error | t-Statistic | Prob. |
C | 139.2362 | 718.2493 | 0.193855 | 0.8495 |
X1 | -0.051954 | 0.090753 | -0.572483 | 0.5776 |
X2 | 0.127532 | 0.132466 | 0.962751 | 0.3547 |
X3 | -24.29427 | 97.48792 | -0.249203 | 0.8074 |
X4 | 0.863283 | 0.186798 | 4.621475 | 0.0006 |
X5 | 0.330914 | 0.105592 | 3.133889 | 0.0086 |
X6 | -0.070015 | 0.025490 | -2.746755 | 0.0177 |
X7 | 0.002305 | 0.019087 | 0.120780 | 0.9059 |
R-squared | 0.999222 | Mean dependent var | 5153.350 | |
Adjusted R-squared | 0.998768 | S.D. dependent var | 2511.950 | |
S.E. of regression | 88.17626 | Akaike info criterion | 12.08573 | |
Sum squared resid | 93300.63 | Schwarz criterion | 12.48402 | |
Log likelihood | -112.8573 | F-statistic | 2201.081 | |
Durbin-Watson stat | 1.703427 | Prob(F-statistic) | 0.000000 |
Y = 139.2361608 - 0.05195439459*X1 + 0.1275320853*X2 - 24.294272*X3 + 0.8632825292*X4 + 0.330913843*X5 - 0.07001518918*X6 + 0.002305379405*X7
二、分析
由F=2201.081>F0.05(7,12)=2.91(显著性水平a=0.05),表明模型从整体上看钢材供应量与解释变量之间线性关系显著。
三、检验
计算解释变量之间的简单相关系数。EVIEWS过程如下:
1、主菜单QUICK-GROUP STATISTICS-CORRRELATION,在对话框中输入X1 X2 X3 X4 X5 X6 X7,结果如下:
X1 | X2 | X3 | X4 | X5 | X6 | X7 | |
X1 | 1.000000 | 0.921956 | 0.975474 | 0.931882 | 0.826401 | 0.845837 | 0.986815 |
X2 | 0.921956 | 1.000000 | 0.964400 | 0.994921 | 0.969686 | 0.972530 | 0.931689 |
X3 | 0.975474 | 0.964400 | 1.000000 | 0.974809 | 0.894963 | 0.913344 | 0.982943 |
X4 | 0.931882 | 0.994921 | 0.974809 | 1.000000 | 0.959613 | 0.969105 | 0.945444 |
X5 | 0.826401 | 0.969686 | 0.894963 | 0.959613 | 1.000000 | 0.996169 | 0.827643 |
X6 | 0.845837 | 0.972530 | 0.913344 | 0.969105 | 0.996169 | 1.000000 | 0.846079 |
X7 | 0.986815 | 0.931689 | 0.982943 | 0.945444 | 0.827643 | 0.846079 | 1.000000 |
2、由上表可以看出,解释变量之间存在高度线性相关性。尽管方程整体线性回归拟合较好,但X1 X2 X3 X7变量的参数t值并不显著, X3 X6 系数的符号与经济意义相悖。表明模型确实存在严重的多重共线性。
四、修正
1、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。
Variable | Coefficient | Std. Error | t-Statistic | Prob. | |
C | -10123.78 | 1528.060 | -6.625250 | 0.0000 | |
X1 | 1.181784 | 0.116936 | 10.10629 | 0.0000 | |
R-squared | 0.850171 | Mean dependent var | 5153.350 | ||
Adjusted R-squared | 0.841847 | S.D. dependent var | 2511.950 | ||
S.E. of regression | 998.9623 | Akaike info criterion | 16.74595 | ||
Sum squared resid | 17962663 | Schwarz criterion | 16.84552 | ||
Log likelihood | -165.4595 | F-statistic | 102.1371 | ||
Durbin-Watson stat | 0.217842 | Prob(F-statistic) | 0.000000 |
Variable | Coefficient | Std. Error | t-Statistic | Prob. |
C | -618.7199 | 108.3930 | -5.708116 | 0.0000 |
X2 | 0.926212 | 0.016019 | 57.82017 | 0.0000 |
R-squared | 0.994645 | Mean dependent var | 5153.350 | |
Adjusted R-squared | 0.994347 | S.D. dependent var | 2511.950 | |
S.E. of regression | 188.8610 | Akaike info criterion | 13.41454 | |
Sum squared resid | 642032.9 | Schwarz criterion | 13.51411 | |
Log likelihood | -132.1454 | F-statistic | 3343.172 | |
Durbin-Watson stat | 0.962290 | Prob(F-statistic) | 0.000000 |
Variable | Coefficient | Std. Error | t-Statistic | Prob. |
C | -3770.942 | 581.6642 | -6.483023 | 0.0000 |
X3 | 926.7178 | 58.38537 | 15.87243 | 0.0000 |
R-squared | 0.933317 | Mean dependent var | 5153.350 | |
Adjusted R-squared | 0.929612 | S.D. dependent var | 2511.950 | |
S.E. of regression | 666.4367 | Akaike info criterion | 15.93641 | |
Sum squared resid | 7994483. | Schwarz criterion | 16.03598 | |
Log likelihood | -157.3641 | F-statistic | 251.9341 | |
Durbin-Watson stat | 0.477559 | Prob(F-statistic) | 0.000000 |
Variable | Coefficient | Std. Error | t-Statistic | Prob. | |
C | -34.32474 | 91.75324 | -0.374098 | 0.7127 | |
X4 | 0.884047 | 0.014146 | 62.49381 | 0.0000 | |
R-squared | 0.995412 | Mean dependent var | 5153.350 | ||
Adjusted R-squared | 0.995157 | S.D. dependent var | 2511.950 | ||
S.E. of regression | 174.8044 | Akaike info criterion | 13.25985 | ||
Sum squared resid | 550018.2 | Schwarz criterion | 13.35942 | ||
Log likelihood | -130.5985 | F-statistic | 3905.476 | ||
Durbin-Watson stat | 0.824221 | Prob(F-statistic) | 0.000000 | ||
Variable | Coefficient | Std. Error | t-Statistic | Prob. | |
C | 2896.350 | 211.0245 | 13.72518 | 0.0000 | |
X5 | 0.572451 | 0.036983 | 15.47892 | 0.0000 | |
R-squared | 0.930123 | Mean dependent var | 5153.350 | ||
Adjusted R-squared | 0.926241 | S.D. dependent var | 2511.950 | ||
S.E. of regression | 682.2088 | Akaike info criterion | 15.98319 | ||
Sum squared resid | 8377359. | Schwarz criterion | 16.08276 | ||
Log likelihood | -157.8319 | F-statistic | 239.5971 | ||
Durbin-Watson stat | 0.181794 | Prob(F-statistic) | 0.000000 |
Variable | Coefficient | Std. Error | t-Statistic | Prob. |
C | 2720.664 | 205.3405 | 13.24952 | 0.0000 |
X6 | 0.108665 | 0.006568 | 16.54535 | 0.0000 |
R-squared | 0.938303 | Mean dependent var | 5153.350 | |
Adjusted R-squared | 0.934875 | S.D. dependent var | 2511.950 | |
S.E. of regression | 641.0376 | Akaike info criterion | 15.85869 | |
Sum squared resid | 7396725. | Schwarz criterion | 15.95827 | |
Log likelihood | -156.5869 | F-statistic | 273.7485 | |
Durbin-Watson stat | 0.259927 | Prob(F-statistic) | 0.000000 |
Variable | Coefficient | Std. Error | t-Statistic | Prob. | |
C | -9760.099 | 1317.227 | -7.409582 | 0.0000 | |
X7 | 0.106826 | 0.009326 | 11.45524 | 0.0000 | |
R-squared | 0.879375 | Mean dependent var | 5153.350 | ||
Adjusted R-squared | 0.872673 | S.D. dependent var | 2511.950 | ||
S.E. of regression | 896.3356 | Akaike info criterion | 16.52915 | ||
Sum squared resid | 14461517 | Schwarz criterion | 16.62872 | ||
Log likelihood | -163.2915 | F-statistic | 131.2225 | ||
Durbin-Watson stat | 0.183657 | Prob(F-statistic) | 0.000000 |
经分析在7个一元回归模型中钢材供应量Y对电力产量X4的线性关系强,拟合度好,即:
Y = -34.32474492 + 0.8840472792*X4
(-0.374098) (62.49381)
R2= 0.995412 S.E.=174.8044,F=3905.476
截距项不显著,去掉,重新估计:
Y = 0.8792594492*X4
2、逐步回归。
将其余解释变量逐一代入上式,得如下模型:
Y = -0.005935225118*X1 + 0.8906555628*X4
(-0.604681) (45.03888)
R2= 0.995469 S.E.=173.7270, F=3954.290
式中X1不显著,删去,继续:
Y = 0.1741981867*X2 + 0.6978252624*X4
(1.879546) (7.217200)
R2= 0.996135 S.E.=160.4431, F=4639.290
Y = 0.2753793175*X2 + 0.5595511241*X4 + 0.04060861466*X5
(3.082485) (5.637333) (2.615818)
R2= 0.997244 S.E.=139.4060, F=3075.985
Y = 0.466836912*X2 + 0.5219953469*X4 - 0.03080496295*X5 - 0.004998894793*X7
(3.245804) (5.366654) (-0.674009) (-1.651391)
R2= 0.997646 S.E.=132.8222, F=2259.899
X7不符合经济意义,应去掉。
所以:
Y = 0.2753793175*X2 + 0.5595511241*X4 + 0.04060861466*X5
(3.082485) (5.637333) (2.615818)
R2= 0.997244 S.E.=139.4060, F=3075.985
即为最优模型。
Dependent Variable: Y | ||||
Method: Least Squares | ||||
Date: 10/17/05 Time: 22:53 | ||||
Sample: 1978 1997 | ||||
Included observations: 20 | ||||
Variable | Coefficient | Std. Error | t-Statistic | Prob. |
X2 | 0.275379 | 0.089337 | 3.082485 | 0.0068 |
X4 | 0.559551 | 0.099258 | 5.637333 | 0.0000 |
X5 | 0.040609 | 0.015524 | 2.615818 | 0.0181 |
R-squared | 0.997244 | Mean dependent var | 5153.350 | |
Adjusted R-squared | 0.996920 | S.D. dependent var | 2511.950 | |
S.E. of regression | 139.4060 | Akaike info criterion | 12.85014 | |
Sum squared resid | 330378.5 | Schwarz criterion | 12.99950 | |
Log likelihood | -125.5014 | F-statistic | 3075.985 | |
Durbin-Watson stat | 0.790639 | Prob(F-statistic) | 0.000000 |