非线性回归方法的应用与比较  

The Application and Comparison of Different Nonlinear Fit Methods

作　　者：谢兰[1] 高东红[2] 

机构地区：[1]清华大学医学院,北京100084 [2]北京大学医学部生物数学与生物统计学教研室,北京100083

出　　处：《数学的实践与认识》2009年第10期117-121,共5页Mathematics in Practice and Theory

基　　金：北京大学985-2

摘　　要：比较了非线性回归3种方法的数学原理:曲线直线化方法、非线性最小二乘方法、近似非线性法.说明了用方差分析确定回归模型的统计学意义、用决定系数R2描述曲线的拟合效果的理论依据.通过对同一问题用3种方法分析得出结论:非线性回归与近似非线性拟合方法决定系数相近(0.9966与0.9965),而曲线直线化决定系数为0.9738.因为近似非线性拟合方法无需选初值.建议应用近似非线性拟合方法.We used three different methods, that is, the curve linearization method, nonlinear least square method and the approximate nonlinear method, to analyze the same statistical problem and gave a comparison of these three methods. The regression model is proved of statistical significance by variance analysis, and the fitting effect is described quantitatively by determinant coefficient R^2. The results suggest that the nonlinear least square method and the approximate nonlinear method can fit the curve perfectly and possess the similar determinant coefficient while the curve linearization method leads to a relatively worse result.

关 键 词：非线性回归 决定系数 最小二乘法 曲线直线化 近似非线性 

分 类 号：O212.1[理学—概率论与数理统计] TQ221.211[理学—数学]