Regression to the mean math question
roundsquare: Don't do a least squares line.  That doesn't help.  In the first plot, you'll see that in general:x < mean => y > xx > mean => y < xIf the scores are normalized.  Regression to the mean is that most people move towards the mean in subsequent games/attempts/whatever.But I fail to see what has changed in the analysis -- a and b are both just supposed to be samples from the same distribution, right?Not at all.  b is not independent of a, thats the whole point of regression to the mean.  If you take ordered pairs where there is no connection between a and b, then you won't get any regression to the mean, you'll get points essentially randomly placed on the plane.