Curve fitting is an art as well as
a science. While the science of curve fitting is primarily focused on the numerical
algorithms and methods used for determining the parameters for the best curve
fit, the "art" of curve fitting places an emphasis on three items that
aren’t discussed often. They are:
Understanding the underlying
limitations of the curve fitting process. Some examples include numerical
accuracy issues, residual examination, and graphical inspection.
Some models, which are may
fit the data set just fine, are sometimes unsuitable for interpolation, extrapolation,
invalid for all X values below a certain point, or fail because of variable
constraints. You need to understand which models will be valid for your data
set and under what conditions.
When working with “real
world” data, the most important thing to remember is that it usually
takes a lot of experimentation via “trial and error” to find the
best fit. This is a very important step to determine if the intended model
will appropriately describe the data, especially for research purposes. It
can mean using a different equation, better parameter estimates, robust minimization
(for reducing the effect of outliners), etc.