Regression to the mean math question
mbrubeck: Regression to the mean does not imply that the first slope should be less than one.If for some reason only the above-average students regressed, then the slope would be <1.  But regression to the mean also affects the scores of students who started below average; as a group we should expect them to regress upward toward the mean.  Combine the two groups, and the effects exactly cancel out, leaving a slope of 1.(Since you say the slope "should be" one, I assume the scores are normalized somehow so that the mean score for exam A is the same as the mean for exam B.)