Non-linear curve fitting and the true method of least squares

This paper is concerned with the fitting of non-linear relationships such as the logistic and Gompertz functions. Although Gauss had proposed the now standard Gauss-Newton procedure for this purpose in 1809, and it was strongly championed by Schultz in 1930, this procedure did not come into common use until modern computing equipment was introduced in the 1960s. In its stead a variety of virtually arbitrary procedures were employed. These arbitrary procedures are still used when the practitioner requires preliminary estimates of the parameters of a given non-linear function.