Some further results concerning regression to the mean

Algebraic formulae are derived for the regression to the mean effect for a measurement whose population mean and variance change over time and for subpopulations selected according to initial value in any defined range. The distribution of values for the whole population is assumed to be normal. The results are applied to plasma cholesterol levels of participants in a dietary intervention study, some of whom were selected as having high initial levels. The formulae enable the effects of intervention to be separated from secular change and regression to the mean in studies for which this was not previously possible.