Q-Q Plot Comparison 

Hello these are both Q-Q plots I have created for my models. The top is a Q-Q plot for an old model, and the bottom is a Q-Q plot for an improved new model. What is the difference between the two graphs? What can be tell from the differences? Thanks.
 A: This appears to be a qq plot of the residuals.  The top model seems to have fatter tails than the normal assumption would result in.
Adding additional covariates to the model (bottom plot) rectifies this slightly.  The right tail is much closer to a normal distribution, but the left tail is still considerably fatter.
A: It is easier to make some broad-brush comments on these kinds of plots than to tell you what best to do with your data, as we have no idea on what the variables are, whether a plain linear regression is a good idea for the data, or whether a quite different model would make more sense.
I hold various views that I don't think are contradictory:

*

*It is generally a good idea to look at these plots if only because in many fields people don't look at enough graphs in doing regressions or similar analyses, including before a model fit as well as after. (The culture or psychology can run: no graph can tell me everything when there are several variables, so no graph will be useful; or: interpreting graphs is subjective and completely lacking in rigour, so every decision should be based on a formal test.)


*Sometimes a strongly nonlinear configuration can point up that you need to do something very different such as transform a variable or use a generalized linear model.


*But mild deviations from normality are common in practice -- more common than many texts or courses appear to teach -- and it's usually hard, if not impossible, to tell from mild deviations how or even whether you can improve on the model. It's salutary to remember, as the better texts all explain, that normality of residuals (strictly, of errors) is the least important assumption.
In this case a distribution that is close to normal in the middle (sometimes called "Winsor's principle")  but deviant in the tails could mean many things, including some degree of heterogeneity in the data not captured by predictors so far. But to say that is merely to give the problem a name.
I find that a scatter plot of observed versus predicted -- one of the simplest plots to fire up and to explain -- is often neglected but helpful. A plot of residuals versus fitted, which carries the same information, is often preferred in principle, but can be a bit harder to think about for people fairly new to the game.
