“Lots of things in nature are squared relationships.”

Very true. One major problem with polynomial fits is that using them effectively separates the data from any resemblance to a physical model. I touched on this in Graphical Approach to a Simple Physics Problem, pointing out that the relationship to hole diameter squared was probably a linear first order relationship to hole area.

In follow-up discussions I will assume powers of 2 and 0.5 and show how to optimize the pre-exponential coefficient.

Looking at the results, I want to jump to

y = 13.508x^.5 and y = 161.77x^-2

Lots of things in nature are squared relationships.

…mrt