294 . Maine Agricultural Experiment Station. 1919. 



elusions drawn from these studies on the ground that the data 

 was subject to selection. 



The correlation coefficients for the butter-fat percentage 

 of one lactation with the butter-fat percentage of another lac- 

 tation range from 0.2470=!=. 0640 to. +0.6781 ±. 03 10. The sign 

 of these correlation coefficients are all plus. The grafts of 

 these correlations are approximately linear. Very little or no 

 difference occurs in the values of the correlations of the butter- 

 fat percentage at a given age with the butter-fat percentage for 

 another age. 



Comparison of these correlation coefficients with those for 

 milk production shows that the average coefficient of correla- 

 tion for the butter-fat 'percentage of one lactation with that of 

 another lactation is +0.5215 and the average correlation coeffi- 

 cient for milk production of one lactation with another lacta- 

 tion is -I-0.5352. The correlations for milk production are 

 higher, although not significantly so, than those for butter-fat 

 percentage. Such being, the case it follows -that the relative 

 accuracy in the use of one lactation record to predict the ex- 

 pected record of another lactation is approximately the same 

 for the butter- fat percentage and for milk yield. 



These correlation coefficients are high for data of economic 

 importance. The mean coefficient of correlation for monthly 

 egg production with the yearly egg production is -[-0.446. The 

 range is also lower than these correlations for butter-fat per- 

 centage. In terms of physiology this difference in the correla- 

 tion coefficients for ovulation and butter-fat percentage means 

 that the mechanism controlling the mammary gland has greater 

 precision in its action than has the mechanism controlling the 

 action of the ovary. 



The correlation ratios were calculated. Comparison of 

 these correlation ratios with the correlation coefficient show all 

 of the regressions to be linear regressions. 



The means, standard deviations and correlation coefficients 

 give the necessary constants to form the straight line equations 

 for the prediction of the butter-fat percentage of any given lac- 

 tation at any age from these known variables at another age. 

 The equations are given. Examination of these equations shows 

 that the age at which the butter-fat percentage determined for 

 the milk most nearly represents the cow's potentialities is five 



