Useful procedure in least squares, and tests of some equations for thermistors

Hoge, Harold J.
June 1988
Review of Scientific Instruments;Jun88, Vol. 59 Issue 6, p975
Academic Journal
When an equation is to be fitted to a set of data by least squares, it is often much more difficult to minimize the sum of squares of the residuals of the independent variable than those of the dependent variable. This article presents a procedure that greatly simplifies the fitting of the independent variable. Given y=f(x) it permits not only y and x, but also y2 , x2 , ln y, ln x, and similar simple functions to be fitted almost as easily as y. It is shown that the residuals change significantly when the quantity fitted is changed. Five different equations representing the R(T) relations of thermistors are examined and their ΔT residuals for the same set of experimental data are shown; three of these fit the data more closely than the often-used cubic equation in ln R.


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