Curve fitting

Curve fitting is the process of constructing a <a href="/facts/Curve/xBQ0pTBW">curve</a>, or <a href="/facts/Function_(mathematics)/CdReEKCh">mathematical function</a>, that has the best fit to a series of <a href="/facts/Data_points/IFEDysRP">data points</a>, possibly subject to constraints. Curve fitting can involve either <a href="/facts/Interpolation/8PyetX4f">interpolation</a>, where an exact fit to the data is required, or <a href="/facts/Smoothing/2svFjsbI">smoothing</a>, in which a "smooth" function is constructed that approximately fits the data. A related topic is <a href="/facts/Regression_analysis/n6z5Tf7K">regression analysis</a>, which focuses more on questions of <a href="/facts/Statistical_inference/sJLjubxm">statistical inference</a> 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, to infer values of a function where no data are available, and to summarize the relationships among two or more variables. <a href="/facts/Extrapolation/wggUrqjF">Extrapolation</a> refers to the use of a fitted curve beyond the <a href="/facts/Range_(statistics)/Yu0HgeRj">range</a> of the observed data, and is subject to a <a href="/facts/Uncertainty/VM9pnGvk">degree of uncertainty</a> 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., <a href="/facts/Ordinary_least_squares/q7H9k5vM">ordinary least squares</a>). However, for graphical and image applications, geometric fitting seeks to provide the best visual fit; which usually means trying to minimize the <a href="/facts/Orthogonal_distance/P0aEswE4">orthogonal distance</a> to the curve (e.g., <a href="/facts/Total_least_squares/1jRjpM8f">total least squares</a>), 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.

Curve fitting open-in-new

Curve fitting