带交互作用的双因素方差分析的线性回归建模

Linear Regression Modeling of Two-factor ANOVA With Interaction

文章引入虚拟变量,将带交互作用的双因素方差分析进行了线性回归模型重构,给出了模型的参数估计,证明了回归分析的误差分解与方差分析的离差分解是一致的,得出方差分析的因素显著性F检验与回归模型的显著性检验的等价性。同时对方差分析的多重比较t检验和线性模型的回归系数检验做了比较,指出了他们之间的联系和差异性,分析了差异来源是由于样本的选择差异,最后通过实例给出了两种方法的具体实现。

This paper introduces dummy variables and reconstructs linear regression model for two-factor analysis of variance(ANOVA)with interaction,gives parameter estimation of the model,proves the consistency of error decomposition of regression analysis and deviation decomposition of ANOVA,and concludes the equivalence of the factor significance F test of ANOVA and sig⁃nificance test of regression model.At the same time,the paper compares the multiple comparison t test of ANOVA and the regres⁃sion coefficient test of linear model,pointing out the connection and differences between them,and analyzing the source of differenc⁃es due to the selection differences of samples.Finally,the paper presents specific implementation of the two methods by examples.