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Fun with Residual Plots

Nina Zumel explains why, when plotting residuals, you always put predictions on the X axis and residuals on the Y axis:

One reason that the proper residual graph (for a well fit model) should smooth out to the line y=0 is known as reversion to mediocrity, or regression to the mean.

Imagine that you have an ideal process that always produces a single value y. You don’t actually observe this “true value”; instead, what you observe is y plus (IID, zero mean) noise. You can build a “model” for this process that predicts the mean of the observations, in this case the value 0.1033149. Then you can calculate the residuals of your “model” in the usual way.

This post went in a direction I wasn’t expecting, and it was all the better for it.