Growth curves and other nonlinear relationships

Abstract

The words linear and nonlinear have special technical meanings in statistics. Thus, on the one hand, a relationship (also called a model) Y= f(A,B, C,…; X) is said to be linear if the partial derivative of the function f (A, B, C,…; X) with respect to each of its coefficients (parameters) A, B, C,… etc. does not involve either the same coefficient or another coefficient. On the other hand, the relationship Y= f (A, B, C,…; X) is said to be nonlinear if the partial derivative of the function f (A, B,C,…; X) with respect to any of its coefficients involves either the same or another coefficient. Let us consider for instance the relationship between the oxygen consumption Y of guinea pigs in g per kg of body weight per hour and the environmental temperature X= T in °C(figure 35.1.1).