squaring errors

[michalovadek]

A very minor idea: I teach OLS on a yearly basis (with much less mathematical sophistication) and the more inquisitive students sometimes ask: why are we squaring the errors in OLS? why not just take the absolute value? isn't that simpler? I was wondering if this is something you might want to add into a box in chapter 6 and I would have somewhere reliable to point the students towards :) perhaps the (non-)differentiability at zero of $x^2$ vs $|x|$ is a more generally useful lesson. Though I understand this is not necessarily a key issue for understanding OLS