regression towards the mean

An expression of the observation that, when we take pairs of related measurements, the more extreme values of one variable will, on average, be paired with less extreme values of the other variable. In his early work on inheritance Galton included a study of the heights of successive generations of people. Some of his data are summarized below.

Mean height of parents (inches)	72.5	70.5	68.5	66.5	64.5
Mean height of their adult children (inches)	72.2	69.5	68.2	67.2	65.8

Galton noted that, on average, the children of tall parents are shorter than their parents (72.2 < 72.5, etc.), whereas the children of short parents are taller than their parents (65.8>64.5, etc.): there is a regression towards the mean. These findings led Galton (in a talk entitled 'Regression towards Mediocrity in Hereditary Stature' given in 1885 to the British Association for the Advancement of Science) to refer to the summary line as a line of regression.


Regression towards the mean. The diagram illustrates Galton's data. The dotted line is the regression line.

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