多项式回归的建模方法比较研究

A comparative reseach of polynomial regression modelling methods

在实际工作中,人们在采用回归模型解释因果变量间的相关关系时,经常会遇到自变量之间存在幂乘关系的情况。在这种情况下,多项式回归模型成为一个合理的选择。由于多项式回归模型中自变量之间存在较强的相关关系,采用普通最小二乘回归方法来估计变量的回归系数,则会存在较大的误差。在本文中,为了提高多项式回归模型的预测准确性和可靠性,提出使用主成分分析、偏最小二乘回归建模,并采用仿真数据来比较它们的异同。

In practical work,it is frequent that there is power relation among independent variables when the correlation between dependent variable and independent variables is explained by regression model.Then,the polynomial regression model becomes a reasonable choice.Since the high correlation among independent variables exist,it will produce excessive error to estimate coefficient with the ordinary least square regression.In this paper,in order to improve the accuracy and reliability of polynomial regression prediction,Principal Component Analysis,Partial Least-Squares Regression,Sliced Inverse Regression are proposed.Simulation data is adopted to compare the difference among them.