Theory-driven nonlinear regression

While opinions vary as to how theory-driven data analysis should be in science, nearly all scientists agree that a well thought out theoretical model applied to real data is typically ideal. The clearest use for nonlinear regression is when you know how two or more variables relate to one another theoretically, and your theory tells you that they are not linearly related. An example of this is a classical model of gas adsorption, known as the Langmuir adsorption model (other adsorption models also exist).

Adsorption is the phenomenon in which gases tend to concentrate near the surface of a material. Practically speaking, this has applications in engineering for gas separations. We will not delve into the theory of how the Langmuir model was derived but will give its equation, which is as follows:

In the preceding formula, is a proportion of the surface covered by gas. is a constant for a given gas interacting with a given solid at a given temperature and...