Regression to the Mean

Regression to the mean (RTM) is a widespread statistical phenomenon that occurs when [Page 1236]a nonrandom sample is selected from a population and the two variables of interest measured are imperfectly correlated. The smaller the correlation between these two variables, the more extreme the obtained value is from the population mean, and the larger the effect of RTM (that is, there is more opportunity or room for RTM).

If variables X and Y have standard deviations SDx and SDy, and correlation = r, the slope of the familiar least squares regression line can be written rSDy/SDx. Thus a change of one standard deviation in X is associated with a change of r standard deviations in Y. Unless X and Y are perfectly linearly related, so that ...