回归模型在统计分析中的应用

回归模型在统计分析中的应用

摘要

在人们研究对象的内在特性和个因素间的关系时，通常会建立数学模型。在无法分析实际对象内在的因果关系时，往往会基于对数据的统计分析去建立模型。回归分析作为统计数据寻求变量间关系的近似表达式的一种方法，其广泛用途使得回归模型成为了数据统计分析中的一种常见模型。

本论文分别从数学模型，回归分析，统计分析等的基本概念出发，进一步阐述了数学建模的基本方法和一般步骤，回归分析的基本模型、步骤和分类，以及统计分析的步骤。最后借用MATLAB软件，以一个关于人们对某种品牌食品的评价的实例，用合理的步骤详细描述了在解决回归模型在统计分析中的应用的问题中该如何具体去做。

关键词：数学模型；统计分析；回归分析；回归模型；MATLAB软件

APPLICATION OF REGRESSION MODEL IN

STATISTICAL ANALYSIS

ABSTRACT

In the process of researching the relationship between the inner characteristics and factors of the object，people usually build mathematical model. In the case of the inner causality that people can not analyse of actual object，we often to build model based on statistical analysis of data. As a method for seeking a approximate expressions of the statistical data,the wide applications of regression analysis made regression model become a common model in statistical analysis of data.

This paper starts from the the basic concept such as the mathematical

model,regression analysis and statistical analysis.Then further elaborated the basic methods and general steps of mathematical modeling, the basic model, steps and classification of regression analysis, and the steps of statistical analysis. Finally, applying MATLAB software,using reasonable steps to describe how to solve the problem that the application of regression models in statistical analysis in detail,by using a example about people's evaluation towards a certain brand of food.

Key words: mathematical model; statistical analysis; regression analysis;

regression model; MATLAB software

目录

1 问题的提出-------------------------------------------------------- 1

2 数学模型与数学建模------------------------------------------------ 2

2.1 基本概念---------------------------------------------------- 2

2.2 数学建模的基本方法------------------------------------------ 2

2.2 数学建模的一般步骤------------------------------------------ 2

3 回归分析与回归模型------------------------------------------------ 4

3.1 基本概念---------------------------------------------------- 4

3.2 刻画回归模型------------------------------------------------ 4

3.3 回归分析的步骤---------------------------------------------- 4

3.4 回归分析的分类---------------------------------------------- 5

4 统计分析---------------------------------------------------------- 6

4.1 基本概念---------------------------------------------------- 6

4.2 统计分析的步骤---------------------------------------------- 6

5 一个线性回归模型实例---------------------------------------------- 7

5.1 问题的提出-------------------------------------------------- 7

5.2 分析与假设-------------------------------------------------- 7

5.3 模型建立---------------------------------------------------- 8

5.4 模型求解---------------------------------------------------- 8

5.5 结果分析---------------------------------------------------- 8

5.5.1 输出数据结果------------------------------------------- 9

5.5.2 模型检验----------------------------------------------- 9

5.5.3 解决提出的三个问题------------------------------------- 9

6 结论------------------------------------------------------------- 14 参考文献----------------------------------------------------------- 15附录--------------------------------------------------------------- 16