I recently graduated graduate school and am looking for a proof on R squared. Specifically when to not use it. I really remember a professor impressing upon me multiple times not to report R squared due to the fact it is unreliable. I did a proof on the matter, I just do not remember it. I've looked all over the internet, and can not seem to remember the solution.
Of course do not use R square when the data is non-linear. And do not add variables in order to increase R square.
Here are some links to back me up:
http://jackman.stanford.edu/classes/ssmart/2011/rsquared.pdf Specifically section 3.1 #6
http://blog.minitab.com/blog/adventures-in-statistics/why-is-there-no-r-squared-for-nonlinear-regression Do not use R sq for non-linear regression