I was reminded by the posts in, New variable programmatically; also: Solving under/over defined system of linear eqautions, that I'd recently used an algorithm for overdetermined systems that I'd unearthed in Wikipedia: I've documented it's use very simply so that even I'll know how to use it next time it's needed. (memory gets a lot worse with age ) Perhaps others will find it useful.
The β snippet represents the 'Cholesky' solver, used directly for fitting polynomials to noisy data set. It is also the basic solver in association with the "Conjugate Gradient".