# Curve fitting

## Process of constructing a curve that has the best fit to a series of data points / From Wikipedia, the free encyclopedia

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**Curve fitting**^{[1]}^{[2]} is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points,^{[3]} possibly subject to constraints.^{[4]}^{[5]} Curve fitting can involve either interpolation,^{[6]}^{[7]} where an exact fit to the data is required, or smoothing,^{[8]}^{[9]} in which a "smooth" function is constructed that approximately fits the data. A related topic is regression analysis,^{[10]}^{[11]} which focuses more on questions of statistical inference such as how much uncertainty is present in a curve that is fitted to data observed with random errors. Fitted curves can be used as an aid for data visualization,^{[12]}^{[13]} to infer values of a function where no data are available,^{[14]} and to summarize the relationships among two or more variables.^{[15]} Extrapolation refers to the use of a fitted curve beyond the range of the observed data,^{[16]} and is subject to a degree of uncertainty^{[17]} since it may reflect the method used to construct the curve as much as it reflects the observed data.

For linear-algebraic analysis of data, "fitting" usually means trying to find the curve that minimizes the vertical (*y*-axis) displacement of a point from the curve (e.g., ordinary least squares). However, for graphical and image applications, geometric fitting seeks to provide the best visual fit; which usually means trying to minimize the orthogonal distance to the curve (e.g., total least squares), or to otherwise include both axes of displacement of a point from the curve. Geometric fits are not popular because they usually require non-linear and/or iterative calculations, although they have the advantage of a more aesthetic and geometrically accurate result.^{[18]}^{[19]}^{[20]}