David Hogg on linear regression:
… in almost all cases in which scientists fit a straight line to their data, they are doing something that is simultaneously wrong and unnecessary. It is wrong because … linear relationship is exceedingly rare.
Even if the investigator doesn’t care that the fit is wrong, it is likely to be unnecessary. Why? Because it is rare that … the important result … is the slope and intercept of a best-fit line! Usually the full distribution of data is much more rich, informative, and important than any simple metrics made by fitting an overly simple model.
That said, it must be admitted that one of the most effective ways to communicate scientific results is with catchy punchlines and compact, approximate representations, even when those are unjustified and unnecessary.