Somebody requested me why we advocate plotting fact on the y-axis and predicted worth on the x-axis quite than the opposite method round.
At first thought it would make sense to plot fact on x-axis and predicted worth on the y-axis, as, underneath the generative mannequin, the reality comes first.
The rationale why we advocate plotting fact on the y-axis and predicted worth on the x-axis is that, when contemplating predictions, the related ordering shouldn’t be generative however inferential. And, inferentially, the information come first, as that’s what are noticed.
Right here’s how I responded to my correspondent: We focus on this in part 11.3 of Regression and Different Tales: “A complicated selection: plot residuals vs. predicted values, or residuals vs. noticed values?”
The short reply is that E(y|x) is sort of a regression. And, with a regression, x is the factor you realize and y is the factor you need to predict. With noticed and predicted information, the prediction is what you realize and the true worth is what you don’t know, therefore it is sensible to label y = true and x = predicted. One other method of placing it’s, if all goes properly, E(true | predicted) = predicted. So the slope of the fitted regression line ought to be 1. Equivalently, E(true – predicted | predicted) = 0, which is why we plot residuals vs. predicted, not residuals vs. true worth. We present that in part 11.3 with a simulation too.
P.S. I did a google search and located this paper from 2008 by Gervasio Piñeiro et al. that makes the identical level. It has over 1000 citations! That’s good.
