Tall parents have shorter children, on average

Sir Francis Galton (1822-1911) was the first to note that tall parents have
shorter children, on average.
dad and son walking

His protege and colleague Karl Pearson (1857-1936) studied 1078 father-and-son pairs. He found that the fathers' average height was 68 inches and the sons' average 69 inches. However, the tall fathers (say, of height 72 inches, within the vertical strip on the graph below) had sons averaging 71 inches. They were one inch shorter, on average. On the other hand, the sons of short fathers (say, 64 inches in height) averaged 67 inches in height.
They were three inches taller, on average.

Galton termed this phenomenon "regression to mediocrity".

Ever since, the method of studying how one variable relates to another variable has been called regression analysis.


The figure shows the heights of 1078 fathers and their sons at maturity. Each father is paired with only one of his sons. Fathers and sons of equal height lie along the solid line on the figure (x=y).

The figure is based on a graph from Statistics by Freedman, Pisani, Purves and Adhikari.