X.—CORRELATION : ILLUSTRATIONS AND METHODS. 201 
tion of the marriage-rate in any one year with the deviation of 
the exports and imports of the year before, or two years before, 
instead of the same year; if a sufficient number of years be 
taken, an estimate may be made, by interpolation, of the time- 
difference that would make the correlation a maximum if it were 
possible to obtain the figures for exports and imports for periods 
other than calendar years. Thus Mr Hooker finds (ref. 5) that 
on an average of the years 1861-95 the correlation would be a 
maximum between the marriage-rate and the foreign trade of 
about one-third of a year earlier. The method is an extremely 
useful one, and is obviously applicable to any similar case. The 
2) 
| $ ‘ 
1860 65 os 7 Ce 85 90 95 
Fic. 43.—Fluctuations in (1) Marriage-rate and (2) Foreign Trade (Exports 
+ Imports per head) in England and Wales : the Curves show Deviations 
from 9-year means. Data of R. H. Hooker, Jour. Roy. Stat. Soc., 1901. 
student should refer to the paper by Mr Hooker, cited. Reference 
may also be made to ref. 10, in which several diagrams are given 
similar to fig. 43, and the nature of the relationship between the 
marriage-rate and such factors as trade, unemployment, ete., is 
discussed, it being suggested that the relation is even more 
complex than appears from the above. The same method of 
separating the short-period oscillations was used at an earlier 
date by Poynting in ref. 16, to which the student is referred 
for a discussion of the method. 
18. It was briefly mentioned in § 9 of the last chapter that 
the treatment of cases when the regression was non-linear was, 
in general, somewhat difficult. Such cases lie strictly outside 
the scope of the present volume, but it may be pointed out 
that if a relation between X and ¥ be suggested, either by