Dear Professor Mean,
When you look at a plot of predicted values versus an independent variable in linear regression, you might see evidence non-linearity. When should you act on this and try a more complex model?
Loyal Reader
Dear Reader,
There’s a saying “The good is the enemy of the great.” This applies here. A linear fit might be good and a more complex non-linear fit might be great. If you settle for the good linear fit, are you missing out on a chance to do better? If you insist on the great non-linear fit, are you doing wasting time when the simple answer is good enough?
It depends on how extreme the non-linearity, and how important it is to produce the best possible predictions. That is something that you should bring to the attention of the research team, as the answer is not always obvious.