Weierstrass逼近定理在回归分析建模中的应用

Applications of Weierstrass Theorem in Regression Analysis and Mathematical Modeling

摘要: 基于Weierstrass逼近定理，阐释了将一般非线性回归模型近似为多项式模型来处理的数学原理，从而引入了把多元非线性回归分析转化为多元线性回归分析的一般方法，并且通过实际应用案例分析表明该方法的实用性和有效性。

Abstract: Based on Weierstrass’ approximation theorem, the mathematical principle of a nonlinear regres-sion model which can be approximated by a polynomial regression model is interpreted, and then the general method of converting the multivariate nonlinear regression analysis into the multiva-riate linear regression analysis is introduced. To show the practicability and validity, a practical application example is given.