Eviews多重共线性检验及补救 |
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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)。 2014-3-28 10:01:13 上传 下载附件 (106.61 KB) 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 |
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