﻿ 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

Modeling and Simulation
Vol.05 No.04(2016), Article ID:18919,5 pages
10.12677/MOS.2016.54016

Applications of Weierstrass Theorem in Regression Analysis and Mathematical Modeling

Xiao Yu*, Zhan Li

School of Communication and Information Engineering, University of Electronic Science and Technology of China, Chengdu Sichuan

Received: Oct. 19th, 2016; accepted: Nov. 8th, 2016; published: Nov. 11th, 2016

ABSTRACT

Based on Weierstrass’ approximation theorem, the mathematical principle of a nonlinear regression 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 multivariate linear regression analysis is introduced. To show the practicability and validity, a practical application example is given.

Keywords:Weierstrass’ Approximation Theorem, Regression Analysis, Mathematical Model

Weierstrass逼近定理在回归分析建模中的应用

1. 引言

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2. Weierstrass逼近定理

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3. 多元多项式回归模型

4. 应用案例分析

4.1. 问题：农作物施肥效果分析

4.2. 失败的尝试：线性回归模型

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4.3. 有效的模型：多项式回归模型

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4.4. 完善的模型：含交叉项的多项式回归模型

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5. 结束语

Applications of Weierstrass Theorem in Regression Analysis and Mathematical Modeling[J]. 建模与仿真, 2016, 05(04): 118-122. http://dx.doi.org/10.12677/MOS.2016.54016

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