多元线性回归模型中无量纲化方法比较  

Comparison of Dimensionless Methods in Multiple Linear Regression Models

作　　者：高晓红[1] 李兴奇[2] Gao Xiaohong;Li Xingqi(School of Mathematics and Computer Science,Chuxiong Normal University,Chuxiong Yunnan 675000,China;School of Management and Economics,Chuxiong Normal University,Chuxiong Yunnan 675000,China)

机构地区：[1]楚雄师范学院数学与计算机科学学院,云南楚雄675000 [2]楚雄师范学院管理与经济学院,云南楚雄675000

出　　处：《统计与决策》2022年第6期5-9,共5页Statistics & Decision

基　　金：国家自然科学基金资助项目(11261001);云南省应用基础研究计划青年项目(2017FD152);楚雄师范学院校级一般项目(XJYB2007)。

摘　　要：构建多元线性回归模型前通常需要对原始数据进行无量纲化处理,以减小各变量间的量纲差异,从而能真实地反映解释变量与被解释变量之间的依存关系。现有的无量纲化方法众多,但经不同无量纲化方法处理后所得的多元线性回归结果不同,甚至差异较大,因此选取合理的无量纲化方法是多元线性回归结果可靠与否的关键。文章首先从理论上对多元线性回归模型和无量纲化方法进行剖析;然后建立无量纲化方法优劣的评价指标体系;最后通过数值模拟实验来分析不同无量纲化方法的优劣,并探究方法的稳定性。结果发现,不同的无量纲化方法对多元线性回归模型的影响不同,归一化是一种既能消除变量间量纲差异,又能保留变量内差异信息,还能增强模型拟合效果的最优方法。Before building multiple linear regression models, it is usually necessary to conduct dimensionless processing on the original data to reduce the dimensional difference between variables, so as to truly reflect the interdependence between explanatory variables and explained variables. There are many dimensionless methods available, but the results of multiple linear regression are different or even greatly different after being processed by different dimensionless methods. Therefore, the selection of reasonable dimensionless methods is the key to the reliability of multiple linear regression results. This paper firstly analyzes the multiple linear regression model and dimensionless methods theoretically, then constructs the evaluation index system of dimensionless methods, and finally analyzes the advantages and disadvantages of different dimensionless methods by numerical simulation,also exploring the stability of the method. The results show that different dimensionless methods have different effects on multiple linear regression models, and that normalization is the optimal method that can not only eliminate dimensional differences among variables, but also retain the difference information within variables, and at the same time enhance the fitting effect of the model.

关 键 词：多元线性回归模型 无量纲化方法 评价指标体系 数值模拟 

分 类 号：C812[社会学—统计学] O213.9[理学—概率论与数理统计]