共线性在多元二次多项式回归模型中的危害及其处理方法

Problems Caused by Collinearity and Solution in the Multivariate Second-degree Polynomial Models

关键词:  多元二次多项式回归模型  共线性  回归分析

Key words:  multivariate second-degree polynomial model  collinearity  regression analyse

摘要:

以1个均匀设计应用的实例为对象,回归分析得到2个多元二次多项式方程:(1)Y=0.084826+0.23179X₃-0.050286X₃X₃+0.028422X₁X₃-0.0013962X₂X₃;(2)Y=0.062320+0.2511X₃-0.0600X₃X₃+0.02347X₁X₃。对这2个方程进行线性变换处理后,用SPSS软件包进行共线性诊断分析,得出方程(1)第4项和第2项存在强烈的共线性关系,共线性的存在使方程的预测变得不可靠;方程(2)没有共线性存在,可以正确指导科研工作。

Abstract:

The two multivariate second degree polynomial models, Y=0.084826+0.23179X₃-0.050286X₃X₃+0.028422X₁X₃-0.0013962X₂X₃;(2)Y=0.062320+0.2511X₃-0.0600X₃X₃+0.02347X₁X₃,are obtained from an application of uniform design.These two models transformed by linear method,are analyzed by SPSS Kit to solve collinearity problems.The strong collinearity relation between the fourth item and the second item in Equation(1) is found,which leads to fallibility prognosis.There is no collinearity found in Equation(2) which could be employed in scientific researches.