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

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...

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Published in:Journal of dairy science 1941-02, Vol.24 (2), p.159-164
Main Author: Gaines, W.L.
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Language:English
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description 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.
doi_str_mv 10.3168/jds.S0022-0302(41)95398-5
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title A Supplemental Note on the Correlation Between Fat Percentage and Yield of Milk, Milk Fat, Milk Energy
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