176 THEORY OF STATISTICS,
similarly the regression of » on x. Whilst the coefficient of
correlation is always a pure number, the regressions are only
pure numbers if the two variables have the same dimensions, as
in Tables I.-IV. : their magnitudes depend on the ratio of o,/o,, and
consequently on the units in which «# and y are measured. They
are both necessarily of the same sign (the sign of 7). Since r is
Proportion of Male births per 1000 births.
~ = 3
10,
5
2
3 20,
< 10
S
Fre. 39. Correlation between births in a Registration District and Proportion
 of Male Births per thousand of all births (England and Wales,
1881-90, Table VI.): means of rows shown by circles and means
of columns by crosses : r= — 0014.
not greater than unity, one at least of the regressions must be
not greater than unity, but the other may be considerably greater
if the ratio a,/o, or o,/o, be great. The name regression arose
from the term being first introduced in the case of inheritance of
stature (Galton, refs. 2, 3). In this case the two standard deviations
 are very nearly equal, so that both 5, and &, are less than
unity, say (using the more recent data of Table III.) 0-50 and 0-52.