Sir Francis Galton, in his 1885 Presidential address before the anthropology section of the British Association for the Advancement of Science (Stigler, 1986), described his study of how tall children are compared with the height of their parents. In this study, Galton defined ranges of parents’ heights, and then calculated the mean child height for each range. He drew a straight line that went through the means (as best as he could), and thought he had made a discovery when he found that the child heights tended to be more moderate than the parent heights. For example, if a parent was tall, the children similarly tended to be tall, but not as tall as the parent. If a parent was short, the child tended to be short, but not as short as the parent. This discovery he called regression to the mean, with the regression meaning “to come back to.”

Somehow, the term regression became associated with the technique of fitting the line, rather than the process describing inheritance. Galton’s data are covered later in this chapter.

This chapter covers the case where there is only one factor and one response—the kind of regression situation you can see on a scatterplot.