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 Propor- 
tion 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 devia- 
tions 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.