PREDICTING EGG PRODUCTION IN WHITE LEGHORNS 271 



where E represents the annual egg production or the production of any 

 period of months, and e p denotes the production of any period used as a 

 basis for prediction. 



The reader may quite legitimately suggest that in certain cases better 

 prediction might have been secured by the use of regression curves of a 

 higher order. This may be true. Our plan has been to test not merely 

 the linear equations but others as well. Considerable progress has been 

 made toward this end. Comprehensive tests will, we hope, eventually be 

 published. Since, however, a relatively high degree of accuracy of pre 

 diction may be attained in most cases by the use of the linear equation, 

 it does not seem proper to withhold useful results until it is possible to 

 determine whether additional refinement can be attained. 



The essential characteristics of equations for the prediction of egg yield 

 are two : 



1. That the errors of prediction be distributed about the true numbers 

 in such a manner that estimations will not in the long run be either too 

 high or too low. 



2. That the magnitude of the deviations of the predicted from the 

 observed egg productions be as small as possible. 



Thus in testing formulae by determining how efficiently they predict 

 the production of birds whose record is actually known, we shall consider 

 that formula the best which (a) shows the least error in the direction of 

 consistently too high or too low prediction, and (b) gives the lowest devi 

 ation of the predicted from the observed record. 



To test the first of these essentials we have merely to determine the 

 average deviation with regard to sign of the predicted from the actually 

 measured egg production. This is given by 



N 



where E p is the actual egg production of a bird, E p the theoretical egg 

 record of an individual bird for a period p, and N the number of birds 

 considered. Here a negative sign indicates that the equation has predicted 

 records which are on the average too low, whereas a positive sign indicates 

 that it has predicted records which are on the average too high. 



But, as noted above, a formula must do more than fail to consistently 

 overestimate or underestimate. It must give predicted values which 

 show the lowest possible deviation from those determined by trap-nesting. 

 We have, therefore, to consider the test which shall be applied to deter- 



GENETICS 6: My 1921 



