Key concepts: Polynomial

Usefulness of polynomial models

There are two situations where you might want to choose a polynomial model:

•	Your scientific model is described by a polynomial equation. This is rare in biology. Few chemical or pharmacological models are described by polynomial equations.

•	You don't have a scientific model, but want to fit a curve to interpolate unknown values. With this goal, you often don't care much about the details of the model. Instead, you care only about finding a model that goes near the data points. Polynomial models often work well.

Which polynomial model?

The order of a polynomial model expresses how many terms it has. Prism offers up to a sixth order equation (and it would be easier to enter higher order equations). The higher order equations have more inflection points.

Choosing the best polynomial model is often a matter of trial and error. If the curve doesn't follow the trend of your data, pick a higher order equation. If it wiggles too much, pick a lower order equation.

How are polynomial models special?

To a mathematician, polynomial models are very special. Strictly speaking, polynomial models are not 'nonlinear'. Even though a graph of X vs. Y is curved (in all but some special cases), the derivative of Y with respect to the parameters is linear.

Because polynomial models are not nonlinear, it is possible (but not with Prism) to fit polynomial models without fussing with initial values. And the fit can be in one step, rather than the iterative approach used for nonlinear models.

Since Prism treats polynomial models the same way it treats nonlinear models, it does require initial values (it chooses 1.0 for each parameter automatically). It doesn't matter what values are used -- polynomial regression cannot encounter false minima.