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 greater
degree of uncertainty since it may reflect the method used to
construct the curve as much as it reflects the observed
data.
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