ir 



290 HARRIS, KIRKPATRICK, BLAKESLEE, WARNER AND CARD 



Third, the mathematical theory of multiple correlation shows that L 

 dealing with correlated characters the gain in accuracy of prediction rapidlj 

 decreases with the number of characters employed. In our first detailed 

 treatment of the problem of the correlation between the egg records ol 

 the individual months we showed by the constants for a series of selected 

 months that the egg records of the individual months are correlated among 

 themselves. This has since been demonstrated for the entire series oi 

 | n(n - 1) = 66 different combinations of the 12 months of the pullet 

 year. It is evident, therefore, that very large gains in accuracy of pre 

 diction cannot be expected to result from an increase in the number of 

 periods, except in so far as the gain is due directly to the contribution of 

 the months included. 



We now turn to the results of the test of equations for the prediction 

 of annual record from two-consecutive-months production. The equa 

 tions are as follows : 



Months from which prediction is made Prediction equation 



November and December E = + 132 .887 + 2 . 160 (ei + c 2 ) 



December and January E = +130.822 + 2 . 176 (e 2 + e 3 ) 



January and February E = +146.040 + 2 .579 (e 3 + e t ) 



February and March E = + 78 .008 + 2 .915 (e t + e b ) 



March and April E = +48.374 + 3.029 (e- 3 + et) 



April and May E = +39 . 955 + 3 . 005 (et + e 7 ) 



May and June E = +32 . 783 + 3 . 065 (e 7 + e) 



June and July E = +44 . 650 + 2 . 864 (e t + ,) 



July and August E = +62 . 861 + 2 . 625 (e t + do) 



August and September E = +91 .865 + 2 .302 (e :0 + e u ) 



September and October E =* + 122 . 597 + 2 . 140 (en + e K ) 



Since a primary object of the present analyses is a comparison of equa 

 tions based on two-months production with those based on a single month s 

 record as a means of predicting the annual egg record of a bird, it is advan 

 tageous to place the results for the two methods side by side in the same 

 tables. The results are given in tables 2 to 4. 6 



Table 2 shows the average errors with regard to sign of the egg records 

 of the 415 White Leghorns studied at Storrs in 1917-1918, when prediction 

 is made from two-months production using equations based on the Storrs 

 experience of the preceding six years. 



The average deviations with regard to sign are small. In 7 cases the 

 equations have predicted values which are too large, whereas in 4 cases 

 they have predicted values which are too small. The individual errors 



6 It has seemed conducive to clearness to duplicate entries in order to secure the 22 differ 

 ences which serve as a basis of comparison. 



