174 
PROFESSOR KARL PEARSOR, MATHEMATICAL 
A/B or B/A as a method of prediction. We may, in fact, at once dismiss all 
reconstruction formulae as insufficieiit which are not based on the theory of corre¬ 
lation. The theory as here applied, he it noted, depends on the linearity of the 
proposed formula and not on any special form of the distribution of variations. 
(ii.) The accuracy of a prediction will not be indefinitely increased by increasing- 
the number of organs upon which the prediction is based. This fundamental fact of 
the application of the theory of correlation to prediction has already been noticed by 
Miss Alice Lee and mj^-'self in the case of barometric prediction." The choice of 
organs upon which to base the prediction is far more important. Thus, to illustrate 
this from stature I may remark that the probable error of a prediction of male stature 
from radius is to a prediction from femur in the ratio of 2’723 to 2T74 ; that if one 
takes both femur and tibia for the prediction, the probable error is only reduced to 
2’030, and further, if one takes femur, tibia, humerus, and radius, we only reach 
1‘961. This latter reduction is so small as to be well within the errors of the 
determination of our means, variations, and correlations, and accordingly scarcelv 
worth making. To pass from the radius to the femur is a real gain ; to pass from 
femur and humerus, say, to femur, humerus, tibia, and radlns, is no sensible gain. 
Hence, one or two organs well selected are worth much more for prediction than a 
much larger number selected less carefully. 
(iii.) It is the custom of French writers, when determining stature, to predict it 
from several single types of bones, say from femur, tibia, humerus, and radius, and 
then to take the mean of these results for the true stature. This is not the best 
theoretical procedure. Suppose the regression formulge for the prediction of B from 
Ai, Ao, A 3 . A 4 sejiarately to be 
^ — Co T " <^1 
B = Co" + c/A.3, 
c "'A 
B = Co'" 
B = Co"" -b c/"'A4. 
Then the mean of all these results would give 
B - J (Cq + Co + Co' -f- Co" ') -f- + i^/'Ao + ^Ci"'A3 -+■ 5Ci""A4, 
that is to say, B has been really found from a linear relationship between B and the 
four organs in question. But the best linear relationship for the four organs is 
B — Cq CjAi -f- fvAo "F C 3 A 3 F C 4 A 4 , 
where the c’s are the true regression coefficients. But the slightest acquaintance 
with the theory of regression shows that the partial regression coefficient is as a 
* “ On tlie Distribution of Frequency (Yariation and Correlation) of tbe Barometric Heiglit at 
Divers Stations,” ‘Phil. Trans.,’ A, vol. 190, p. 45G et seq. 
