Predicting Body Fat Using Data on the BMI

A data set contained in the Journal of Statistical Education's data archive provides a way of exploring regression analysis at a variety of teaching levels. An appropriate functional form for the relationship between percentage body fat and the BMI is shown to be the semi-logarithmic, with variation in the BMI accounting for a little over half of the variation in body fat. The fairly modest strength of the relationship implies that confidence intervals for body fat, and tolerance intervals for BMI, can be quite wide, so that strict reliance on the BMI as a measure of body fat, and hence obesity, is unwarranted. Nevertheless, when fitting percentage body fat as a function of the class of "power weight for height indices", i.e., indices of the form weight/heightP, the BMI, with a height exponent of p = 2, is an appropriate choice to make.