Common empirical functions are polynomial regression, spline fits, and Pade approximants. For data with two or more independent variable, the multivariate regression may be used. If there is a good theoretical model, then that model will provide a fitting function. Often the parameters of a theoretical model are the desired physical descriptors of the measurements. Then you will want to fit the data to this model and report the parameter values.
Least squares fitting is based on minimizing the residuals between the data and fitting function.
In general it is not possible to achieve perfect agreement. Instead we strive for a minimum of D . At the minimum of D , these derivatives vanish. Mathcad has tools to find such minima for various choices of the fitting function. Here is a summary of some of the most common and popular fitting functions that are built into Mathcad.