多重线性回归模型及其应用

An overview of multiple linear regression model and its application

多重线性回归(MLR)是简单线性回归的推广,是多变量统计分析中的常用方法之一。本文从实际应用的角度出发,介绍多重线性回归分析方法。内容重点包括多重线性回归基本原理、应用实例拟合及结果解释、模型应用条件及模型诊断、MLR的扩展应用四大部分。特别是在第四部分方法扩展应用中,简要介绍了对于多重现性回归条件不满足的时候可以用哪些方法进行替代。以期读者对多重线性回归分析有所了解,在科研工作中能正确使用多变量回归模型分析,提高数据使用效率和统计分析水平。

Multiple Linear Regression (MLR) is a generalization of simple linear regression and is one of the commonly used models in multivariate statistical analysis. This article introduces the MLR model from the perspective of practical application. Four parts, including basic principle, application examples, the application condition and diagnosis, and the extension of the model, are sequentially illustrated in this article. Particularly, in the last part, alternative methods of the model are introduced when the application condition of the model is not met. We sincerely hope that this article could make our audiences have a better understanding of the MLR model in order to improve the efficiency of data utilization and statistical analysis by correctly performing this model in their research.