IX.—CORRELATION. 173 
as to make the sum of the squares of the errors of estimate the 
least possible ; or (8) equations for estimating the mean of the 2's 
associated with a given type of ¥ (and the mean of the ¥’s associated 
with a given type of 2) in such a way as to make the sum of the 
squares of the errors of estimate the least possible, when every 
mean is counted once for each observation on which it is based. 
a. ES 
Fie. 36.— Correlation between Age of Husband and Age of Wife in England 
and Wales (Table IL): means of rows shown by circles and means of 
columns by crosses: r= + 0-91. 
The lines represented by the two equations are thus, in a certain 
natural sense, “lines of best fit ” to the two actual lines of means. 
12. The constant » is of very great importance. It is evi- 
dently a pure number, and its magnitude is unaffected by the 
scales in which 2 and y are measured, for these scales will 
affect the numerator and denominator of (4) to the same 
extent. If the two variables are independent, r is zero, for b, 
and b, are zero (cf. § 8). The sign is the sign of the mean 
product p, and accordingly » is positive if large values of # 
£0 
on 
27