ll 62, 63, and 76 inches tall. When we examine the actual
details of the resemblance we find, as a matter of fact, that neither
of these possibilities is actually realized. What we do find is that
fathers below or above the average height have sons whose average
height is also below or above the general average but not so far below
or above the general average as were the fathers. If we measured a
large number of pairs of fathers and sons with respect to stature we
should find each generation with a variability such as that
illustrated in Fig. 3 of the stature of mothers, the limits here,
however, being about 62 and 76 inches. But if we measured all the sons
of 62-inch fathers they would be found to vary say from 62 to only 69
inches, averaging about 66 inches. Similarly 63-inch fathers would
have sons from 62 to 70 inches tall, averaging about 66.5 inches, or
76-inch fathers might have sons from 69 to 76 inches in height,
averaging about 72 inches, and so on for fathers of all heights. In
general, then, we may say that fathers with a characteristic of a
certain plus or minus deviation from the average of the whole group
have sons who on the whole deviate in the same direction but less
widely than the fathers, although the fact of variability comes in so
that some few of the sons deviate as widely as, or even more widely
than, the fathers, others deviate less widely than the fathers from
the average of the whole group. This is the general and very important
statistical fact of _regression_.

The phenomenon of regression may be made somewhat clearer by the aid
of a simple diagram--Fig. 10. Here are plotted first the heights, by
inches, of a group of fathers, giving the series of dots joined by the
diagonal _AB_. Next are plotted the average heights of the sons of
each class of fathers: 62-inch fathers give 66-inch sons, 63-inch
fathers 66.5-inch sons, 64-inch fathers 67-inch sons, and so for all
the classes of fathers. These dots are then joined by the line _EF_.
This is the _regression line_. Had it been the case that there was no
regression in stature the different classes of fathers would have had
sons averaging just the same as themselves and the line representing
the heights of the sons would have coincided with the line _AB_. Or if
regression had been complete the fathers of any class would have had
sons averaging about 69 inches--just the same as the average of the
whole group--and the line representing their heig