Nonexistence in reciprocal and logarithmic regression

Abstract

Fitting logarithmic bln(c+x), a+bln (c+x) or reciprocal b/(c+x), a+b/(c+x) regression models to data by the least squares method asks for the determination of the closure of the set of each type of these functions defined on a finite domain. It follows that a minimal solution may not exist. But it does exist when the closure is considered.