90 



Journal of Agricultural Research voi. xvi, no. 3 



cient in this case is r = 0.8991 ±0.0071 and the correlation ratio r? = 

 0.9023 ±0.0069. As in the previous tables, the cell which contained 

 the doubtful observation is indicated by parentheses. Where this 

 doubtful observation is left out of consideration, the correlation rises 

 slightly to r = 0.9095 ±0.0063, and the correlation ratio is 7^ = 0.9064 

 ±0.0066. 



Table IX. — Correlation surf ace for pounds of solids-not-fat and pounds of butter fat as 

 deduced from individual year records 



These constituents of cow's milk are shown by these correlations to 

 be highly correlated variates. This correlation can not be accounted 

 for by the regression of solids-not-fat on butter fat, not being a linear 

 regression, as even a glance at the values of the correlation coefficient 

 and the correlation ratio will convince anyone that they are so nearly 

 the same in value as to make it certain that the regressions are linear. 

 Consequently it does not seem necessary to calculate the customary 

 constants for this linearity, as both Zm and 17^ — r^ would be negligible 

 quantities. This establishes the conclusion finally that butter fat and 

 solids-not-fat contained in cow's milk are correlated variates. This 

 correlation being positive, a rise in the amount of either constituent 

 also means a rise in the other. 



Part of the correlation between the butter fat and solids-not-fat may 

 be due to the rise in the amount of milk of the different individual cows. 

 For the problem of the mechanism of the secretion of these constituents 

 this is of especial importance. Tables X and XI give the correlation 

 surfaces for the variables. 



