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
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.