214 
GENETICS: J. A. HARRIS ET AL, ' 
Proc. N. A. S. 
In a population the straight line relating the egg production of a period 
E$ with that of a period used as a basis of prediction, e, is 
where the bars denote means, the sigmas represent standard deviations, 
and r indicates the correlation of the two variables in the standard popu- 
lation. 
The value of E P given by the equation is the theoretical mean produc- 
tion for the array of individuals of any class with respect to e. The as- 
sumption to be tested is that we may write E p and e' instead of E p and 
e, where E/ is the theoretical mean production for a period p of the array 
of birds of any grade of production e in the period used as a basis of pre- 
diction in a series of birds which are not involved in the data upon which 
the equations were based, but to which the equations are to be applied for 
practical purposes. 
The essential practical requisites for such prediction equations are: (1) 
That the errors of prediction shall be distributed about the true numbers 
in such a manner that estimation will not in the long run be either too 
high or too low. (2) That the magnitude of the deviation of the predicted 
from the observed egg production shall be as small as possible. 
Let E p " be the actual and E p the predicted egg production of an in- 
dividual bird for any period, p, in a flock to which the equation is being 
applied. The error of prediction is then E P — E P ." The average of these 
errors, with regard to sign 
furnishes a measure of the success with which the first requirement, (1) 
above, is met. The average of these errors without regard to sign fur- 
nishes a measure of the average error above or below the true production 
of the individual birds of a flock. The square root of mean square devia- 
tion 
furnishes a measure of this error which weights larger errors. 
The errors may be expressed in actual numbers of eggs, or, in relative 
terms, as percentages of the mean production of the period and flock for 
which prediction is made. Both methods have been used in testing the 
equations. 
In testing the efficiency of such equations for purposes of prediction 
we have proceeded in a purely objective manner. Working on the as- 
sumption that the crucial test of any theory is its capacity for predicting 
