When plotting predictions over linear predictors, what's a "informative" range for linear predictor values? When plotting predictions over linear predictors, what's a "informative" range for linear predictor values?
The reason to ask is this:

This is a very common plot in logistic regression, but isn't the range of -4 to 4 a bit uninformative? Like what does e.g. lin. predictor == -4 mean?
So is this the only way to plot this?
Is the x-axis inferable in some "informative" way?
 A: I'm not sure that multiple logistic regression models are 'usually' presented like that.  I think when we teach logistic regression, we might present a plot like that, but not necessarily as a way to present a real model to some audience.  
Perhaps there are a couple of things I can say that might help you:  


*

*When presenting logistic regression generically, as in an introductory class setting, I might show a plot ranging from $-4$ to $4$ because that's where the 'action' is.  There isn't much to see beyond those limits.  When the linear predictor is $<-4$, the probability is $\approx 0$, and when it's $>4$, it's $\approx 1$.  In truth, it will not exactly equal $0$ or $1$, and will always be getting closer to those values, but it will be hard for students to see.  

*It also might help to think about what the 'linear predictor' is.  Modeling the probability of a binary outcome is tricky, because $X$-variables are not necessarily bounded, but probabilities must lie within $[0, 1]$.  The way this is dealt with in logistic regression is that we don't quite model the probability of 'success' (i.e., $Pr(Y=1)$) in a straightforward sense, but instead model the log odds of success (i.e., $\ln(^{\text{odds}(Y=1)}/_{1+\text{odds}(Y=1)})$).  With that in mind, the linear predictor is the result of multiplying your coefficients by the $X$-values and summing them.  It is the log odds of success.  


It may help you to read a little more about logistic regression.  Although written in a different context, you could try my answers here and here.  
