A Supplemental Note on the Correlation Between Fat Percentage and Yield of Milk, Milk Fat, Milk Energy

• Published in: Journal of dairy science 1941-02, Vol.24 (2), p.159-164
• Main Author: Gaines, W.L.
• Format: Article
• Language: English
• ISSN: 0022-0302; 1525-3198
• DOI: 10.3168/jds.S0022-0302(41)95398-5

Formulas are derived expressing the coefficient of correlation (r) between any two of the variables, fat per cent (f), milk yield (M), milk-fat yield (F) and milk-energy yield (FCM), entirely in terms of f and M. The 4 statistics, f¯(=mean   f),Vf(=σf/f¯), VM and rfM, computed from the observations of f and M afford the only data needed for the computation of rfF, rfFCM, rMF, rMFCM and rFFCM, by use of the formulas. It is presupposed that n is large and the frequency distributions normal, or fairly so. A previous result is confirmed: if rfFCM = 0 (as is characteristically the case among dairy cows) it follows as an algebraic corollary that −rfM=f¯8/3+f¯VfVM. Biologically the relation, rfFCM = 0, is regarded as primary, and interpreted to mean that the amount of lactation metabolism is proportional to FCM and is a common denominator as between cows differing in f, but otherwise comparable.