The fitting algorithm in Mathematica is powerful enough to solve many problems without needing good starting guesses, but even so, there are inevitably some problems where they are necessary. Mathematica 's algorithm also eliminates the need to consider effects such as parameter scaling by handling a number of these issues invisibly. Whether you need to perform a complex nonlinear fit or can make do with a simple interpolation, Mathematica provides the functionality and reliability to tackle any fitting task. This flow chart shows the four main approaches and the Mathematica functions that are most appropriate. If you are simply trying to obtain a standard curve for comparison or for baseline subtraction, and you have plenty of data to describe the line or curve, it is simplest to use Mathematica 's Interpolation function.
Interpolation constructs a curve that gives a good approximation to the data.
The InterpolatingFunction will give the exact value of y at the x values used to construct the approximation. Linear Fitting Linear fitting is performed in Mathematica with the Fit and Regress commands. As an example consider fitting the square root data to a quadratic. This output is the default. In short the TStat should be high, the PValue should be below 0.05, the RSquared should be close to 1, and the lower the EstimatedVariance the better.