Linearity of regression of milk energy on fat percentage.

From the last line Gaines and Davidson (I9~3) derived the formula, F C M = M (.4q-.I5 f) or F C M = . 4 M-+-I5 F, in which FCM is milk energy in terms of pounds of natural whole cows' milk of 4 percent fat content, M is milk in pounds and F is milk fat in pounds. Recently, Bonnier, Hansson and Jarl (I946) report that the regression of milk energy per unit milk on fat percentage is not linear and present a table for computing milk energy in terms of 4 percent milk, based on a graphicallysmoothed regression line obtained from chemical analyses of uI5~ milk samples. The samples came from the identical twins, and other cows, at the Institute of Breeding, Wiad, Sweden, and represent short periods at various stages of lactation. Their smoothed curve showing the regression of milk energy on fat percentage is concave upward. Range of fat percentage was from ~. 11 to 7-~8. The .4 M + I 5 F formula for estimating milk energy is now in wide use and it seems desirable, therefore, to consider carefully the curvilinear modification advocated by Bonnier. The present paper considers three sets of observations from the linearity angle: Set i. These are data of Overman and Sanmann (r9~7) and consist of ~ 3-day samples from cows of several breeds at the Illinois Station, at various stages of lactation. Fat percentage was determined by chemical analysis. Milk energy was determined by direct calorimetry. Range of fat percentage was from ~.68 to 7-59.