Volume 34 Issue 11
Nov.  2008
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Wang Huiwen, Guo Lijuan. Polynomial regression modeling based on Gram-Schmidt process[J]. Journal of Beijing University of Aeronautics and Astronautics, 2008, 34(11): 1349-1352. (in Chinese)
Citation: Wang Huiwen, Guo Lijuan. Polynomial regression modeling based on Gram-Schmidt process[J]. Journal of Beijing University of Aeronautics and Astronautics, 2008, 34(11): 1349-1352. (in Chinese)

Polynomial regression modeling based on Gram-Schmidt process

  • Received Date: 13 Nov 2007
  • Publish Date: 30 Nov 2008
  • 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 multicollinearity 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.

     

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  • [1] Wold S,Martens H,Wold H.The multivariate calibration problem in chemistry solved by the PLS method[M]. Heidelberg: Springer-Verlag, 1983 [2] Tenenhaus M. L’approche PLS[M]. Revue de Statistique Appliquée, 1998 [3] 王惠文.偏最小二乘回归方法及其应用[M].北京:国防工业出版社, 1999:93-107 Wang Huiwen. Partial least-squaresregression-method and applications[M]. Beijing: National Defense Industry Press,1997,93-107(in Chinese) [4] 付凌晖,王惠文.多项式回归的建模方法比较研究[J].数理统计与管理, 2004, 23(1): 48-52 Fu Linghui,Wang Huiwen. A comparative reseach of polynomial regression modelling methods[J].Application of Statistics and Management, 2004, 23(1): 48-52(in Chinese) [5] Jain S K,Gunawarddena A D.Linear algebra: an interactive approach[M]. Bejing:China Machine Press,2003 [6] 内特,沃塞曼,库特纳. 应用线性回归模型[M].张勇,王国明,赵秀珍译. 北京:中国统计出版社, 1990 Neter,Wasserman,Kutner. Applied linear regression model[M]. Translated by Zhang Yong, Wang Guoming,Zhao Xiuzhen.Beijing:China Statistics Press,1990(in Chinese) [7] 王惠文,陈梅玲,Gilbert Saporta. Gram-Schmidt回归及在刀具磨损预报中的应用[J].北京航空航天大学学报,2008,34(6): 729-733 Wang Huiwen,Chen Meiling,Gilbert Saporta.Gram-Schmidt regression and application in cutting tool abrasion prediction[J].Journal of Beijing University of Aeronautics and Astronautics,2008,34(6): 729-733(in Chinese)
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