290 Maine Agricultural Experiment Station. 1919. 



The linearity of all the regressions is established by the 

 calculation of the correlation ratios and their comparison with 

 the corresponding correlation coefficient. 



From the means, standard deviations and correlation coef- 

 ficients are formed the straight line equations for the prediction 

 of the amount of milk production of any given lactation at any 

 age from these known variables at another age. These equa- 

 tions are tabled. Examination of these equations seems to 

 show that most stress is laid on the milk production at two 

 years old by the coefficients, indicating that the milk production 

 at this age represents most accurately of all others the future 

 possibilities of the cow. Similar analysis reveals the fact that 

 correction of the milk records to the age about the time of maxi- 

 mum productivity of the cow gives the nearest approach to the 

 correct milk production for that cow. 



The correlation coefficients of milk production at a given 

 age with the total milk production of two lactations are pre- 

 sented. These correlations prove to be very high ranging from 

 -f- 0.7324Hz. 0286 to -7-0.943 ±.0116. Such high values make it 

 appear that the milk production of one lactation is the deter- 

 mining factor for total milk production of two lactations when 

 the given lactation is one of the components. 



This conclusion is confirmed by a study of a smaller series 

 of data where the first five lactation records are known, the 

 first commencing at two years old and the other four commenc- 

 ing approximately at one year apart. These correlation coef- 

 ficients for milk production of a lactation at a given age with 

 the total milk production over the five lactations range from 

 -j-0.7416zb.0323 to -fo.8613ziz.0186. Each regression is linear 

 as is shown by a comparison of the correlation coefficients and 

 correlation ratios. 



A means of measuring the effect of environmental changes 

 on the coefficient of correlation of the milk production of a 

 lactation at a given age with the milk production of a lactation 

 at another age is given. This measure depends on the differ- 

 ence in the correlation coefficients of the milk production of a 

 given age correlated with the milk productions of several suc- 

 cessive lactations and the correlation of the milk production of 

 the given lactation and the total milk production of the other 

 lactations. In the first case the environmental changes of the 



