Analysis of families of curves

A systematic approach is presented for fitting empirical expressions to data depending on two variables. The problem can also be described as the simultaneous fitting of a family of curves depending on a parameter. The proposed method reduces a surface fitting problem to that of fitting a few functions of one variable each. First, the surface is expressed in terms of these one-variable functions, and using an extension of two-way analysis of variance, the accuracy of this fit is assessed without having to determine, at this point, the nature of the one-variable functions. Then, the one-variable functions are fitted by customary curve-fitting procedures. For illustration, the method is applied to two sets of experimental data.