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

Illinois Agricultural Experiment Station, Urbana, Illinois

ABSTRACT

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, (= mean f), V_f (= _f/), V_M and r_fM, computed from the observations of f and M afford the only data needed for the computation of r_fF, r_fFCM, r_MF, r_MFCM and r_FFCM, 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 r_fFCM = 0 (as is characteristically the case among dairy cows) it follows as an algebraic corollary that

. Biologically the relation, r_fFCM = 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.