Curve fitting is the process of constructing a
curve, or
mathematical function, that has the best fit to a series of
data points, possibly subject to constraints. Curve fitting can involve either
interpolation, where an exact fit to the data is required, or
smoothing, in which a "smooth" function is constructed that approximately fits the data. A related topic is
regression analysis, which focuses more on questions of
statistical inference such as how much uncertainty is present in a curve that is fit to data observed with random errors. Fitted curves can be used as an aid for data visualization, to infer values of a function where no data are available, and to summarize the relationships among two or more variables.
Extrapolation refers to the use of a fitted curve beyond the
range of the observed data, and is subject to a
degree of uncertainty since it may reflect the method used to construct the curve as much as it reflects the observed data.
