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

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 .0 84 82 6 + 0 .2 3179X3- 0 .0 5 0 2 86 X3X3+ 0 .0 2 84 2 2 X1 X3- 0 .0 0 1396 2 X2 X3;( 2 ) Y =0 .0 6 2 32 0 + 0 .2 5 11X3- 0 .0 6 0 0 X3X3+ 0 .0 2 347X1 X3。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 。

The two multivariate second degree polynomial models, (1)Y=0.084 826+0.231 79X 3-0.050 286X 3X 3+0.028 422X 1X 3-0.001 396 2X 2X 3,(2)Y=0.062 320+0.251 1X 3-0.060 0X 3X 3+0.023 47X 1X 3,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.