On normality and the linear regression model
这篇笔记讨论了线性同方差回归模型中正态性的作用，证明若线性、同方差和反向回归线性三个假设同时成立，则等价于解释变量和被解释变量联合正态分布。
The purpose of this note is to discuss the role of normality in the context of linear[zddot]homoskedastic regression models. A new characterization result, relating the joint normal distribution and the linear, homoskedastic regression, sheds some light on the role of normality in this context. It is shown that if the assumptions of (a) linearity and (b) homoskedasticity, are supplemented with the assumption of (c) linearity of the reverse regression, assumptions (a)-(c) are tantamount to assuming joint normality of the regressors and regressands, not just conditional normality.