曲线回归的拟合优度指标的探讨

Approach on the Fitting Optimization Index of Curve Regression

目的 解决用线性回归的拟合优度指标的计算方法求曲线回归的拟合优度指标时所发生的问题 ;寻找计算简单、分辨率与灵敏度较高的曲线拟合优度指标 ,便于实际应用时合理选用。方法 通过从相关系数r到复相关系数R的推导过程的讨论以及对曲线回归拟合优度指标rNL的定义的讨论 ,找出所发生问题的原因 ,寻求解决问题的方法。结果 给出一个几何意义清晰、计算简单且分辨率与灵敏度较高的曲线拟合优度指标。结论 几何意义清晰且计算简单、分辨率与灵敏度较高的统一的曲线拟合优度指标 (或曲线拟合优度指标对 ) 。

Objective To finding a highly distinguishable and highly sensitive curve fitting optimization index for the convenient and rational application.Methods By discussing correlation coefficient r and R as well as fitting optimization index r NL ,finding united curve fitting optimization index.Results Finding a highly distinguishable and highly sensitive curve fitting optimization index(R NL ,FR).Conclusion The highly distinguishable and highly sensitive curve fitting optimization index (R NL ,FR) is not only suitable for curve regression but also suitable for linear regression.