It’s not too difficult to check to see if adding the extra terms improves the regression. In my original comment, I listed AIC and BIC among others. On the other hand, different diagnostics will give different answers, so there’s the question of which diagnostic to trust if they disagree. I haven’t learned much about regression diagnostics yet, but at the moment they all seem ad hoc (maybe because I haven’t seen the theory behind them yet).
It’s not too difficult to check to see if adding the extra terms improves the regression. In my original comment, I listed AIC and BIC among others. On the other hand, different diagnostics will give different answers, so there’s the question of which diagnostic to trust if they disagree. I haven’t learned much about regression diagnostics yet, but at the moment they all seem ad hoc (maybe because I haven’t seen the theory behind them yet).