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Linearity of Regression of Milk Energy on Fat Percentage

Illinois Agricultural Experiment Station¹

Abstract

This article considers the contention of Bonnier, Hansson and Jarl (1946)that the regression of kcal/kg. milk () on fat percentage (f) is significantly not linear, and that the estimation of milk energy in terms of 4 percent milk should be made on the basis of their graphically-smoothed regression line, which is concave upward. Three sets of observations on and f are examined in the present article, from the linearity angle.

Two sets agree with their results in being significantly not linear, but in each set the fitted regression line is concave downward, the opposite of their results. It seems unsafe and unwise to generalize the estimate of milk energy on the basis of either a concave-upward or a concave-downward regression line. A compromise between the two seems to offer a safer genralization, namely, a fitted linear regression. The quantitative difference between the linear and curvilinear regression lines is very small.

¹ Department of Dairy Husbandry, University of Illinois, Urbana, Illinois.