多重线性回归分析的核心内容与关键技术概述

Overview of the core concepts and key techniques in the multiple linear regression analysis

目的本文目的是概述多重线性回归分析的核心内容与关键技术。其核心内容有以下四点:第一,构建多重线性回归模型的方法和求解参数的方法;第二,进行回归诊断的意义和方法;第三,筛选自变量的意义和方法;第四,评价模型拟合效果的方法。其关键技术是如何基于经典统计思想、贝叶斯统计思想和机器学习统计思想实现多重线性回归分析。

The paper aims at summarizing the core concepts and key techniques in the multiple linear regression analysis. The core concepts include the follow four points:(1)The methods of constructing a multiple linear regression model and finding the solution of the parameters in the model.(2)The meanings of implementing regression diagnosis and its methods.(3)The meanings and methods of screening the independent variables.(4)The methods of appraising the fitting effect of the regression models. The key techniques of the multiple linear regression analysis are involved in three kinds of statistical thoughts which are classical statistical thought,Bayesian statistical thought and the statistical thought of the machine learning.