hts would have had
the position of _CD_ in the diagram. As a matter of fact, however,
neither of these possibilities is actually realized and the regression
line _EF_ is approximated in an actual series of data. A similar
relation has been found for many characters other than stature.

[Illustration: FIG. 10.--Diagram illustrating the phenomenon
of regression. Explanation in text.]

The fact of regression is of considerable importance for the theory of
evolution as well as for the subject of Eugenics when describing the
phenomena of heredity in this statistical manner in whole groups
without paying attention to particular individuals. Regression is
found in all characteristics observed in this way, psychic as well as
purely physical. "The father [i. e., fathers] with a great excess of
the character contributes [contribute] sons with an excess, but a less
excess of it; the father [fathers] with a great defect of the
character contributes [contribute] sons with a defect, but less defect
of it."

Now, whatever the actual extent of this regression is in a group we
need to know how uniformly it occurs for all the classes of different
deviations from the general average, that is, we need to know whether
the extreme groups regress to the same relative extent as do those
nearer the general average; and, further, we need to know how nearly
the sons of fathers of any certain height are grouped about their own
average. In other words, we should know, first, whether the regression
of the sons of 62 and 76 or 67 and 71 inch fathers is proportionately
the same in each case, and, second, to what extent the sons of 62-inch
fathers vary, whether they vary as do the fathers of 62-inch sons, and
so for each group. This kind of information we get by calculating what
is called the _coefficient of heredity_. The calculation of this
coefficient is a complicated process which it is unnecessary to
describe here. It must suffice to say that a numerical coefficient can
readily be determined, which will express the average closeness and
regularity of the relationship between all the plus and minus
deviations from the group average in fathers and the corresponding
plus and minus deviations from the group average of their sons with
respect to a given characteristic. This coefficient of heredity may
vary between 0.0 and 1.0. When it is 0.0 there is, on the whole, no
regularity in the relationship, i. e., no heredity; when it is 1.0
there