基于Gram-Schmidt过程的多项式回归建模方法  

Polynomial regression modeling based on Gram-Schmidt process

作　　者：王惠文[1] 郭丽娟[1] 

机构地区：[1]北京航空航天大学经济管理学院,北京100191

出　　处：《北京航空航天大学学报》2008年第11期1349-1352,共4页Journal of Beijing University of Aeronautics and Astronautics

基　　金：国家自然科学基金资助项目(70371007;70521001;70531010);北京市自然科学基金资助项目(9052006)

摘　　要：多项式回归模型是一种常用的非线性回归方法.由于在多项式回归模型中,自变量之间往往存在较强的相关关系,采用普通最小二乘回归方法来估计回归系数会存在较大的计算误差.为了提高多项式回归模型的预测准确性和可靠性,提出一种基于Gram-Schmidt过程进行多项式回归的建模方法,可以实现自变量集合的正交化,克服自变量集合多重共线对回归建模的不良影响,从而有效地运用最小二乘建立回归模型.同时可以进行信息筛选有效选取对因变量有显著解释作用的自变量,排除自变量中的冗余信息.采用仿真数据分析,检验了该方法的有效性.The polynomial regression model is a widely applied nonlinear regression method. Since the high correlation exists among independent variables in the polynomial regression model, it will induce excessive computational error to estimate coefficients with the ordinary least square regression. A method of polynomial regression modeling based on Gram-Schmidt process which can achieve the orthogonalization of the independent variables and overcome the adverse effects of muhicollinearity to regression modeling was proposed, so as to apply ordinary least square to regression modeling effectively. The independent variables including notable explaining information can be selected effectively, at the same time redundant information is deleted. Simulation data analysis was adopted to test the effectiveness of the method.

关 键 词：Gram—Schmidt过程 多项式回归 多重相关性 

分 类 号：O212[理学—概率论与数理统计]