An elementary proof independence of least squares estimators of regression coefficients and of variance in linear regression - De Leon, Alexander R.; Punzalan, Joyce Raymond B. (2013)
This pedagogical note extends to the linear regression context an elementary proof of independence of the sample mean and sample variance when sampling from a normal population. The proof is simple enough for classroom demonstration in an elementary statistical inference course as an interesting execise in multivariable transformation; it can be used as well to highlight the link between classical random sample and non-iid (i.e., independent and identical distribution) regression settings.
Keywords: Multivariate analysis; Regression analysis