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Curve fitting
Curve fitting〔Sandra Lach Arlinghaus, PHB Practical Handbook of Curve Fitting. CRC Press, 1994.〕〔William M. Kolb. Curve Fitting for Programmable Calculators. Syntec, Incorporated, 1984.〕 is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points,〔S.S. Halli, K.V. Rao. 1992. Advanced Techniques of Population Analysis. ISBN 0306439972 Page 165 (''cf''. ... functions are fulfilled if we have a good to moderate fit for the observed data.)〕 possibly subject to constraints.〔(''The Signal and the Noise ): Why So Many Predictions Fail-but Some Don't.'' By Nate Silver〕〔(Data Preparation for Data Mining ): Text. By Dorian Pyle.〕 Curve fitting can involve either interpolation,〔Numerical Methods in Engineering with MATLAB®. By Jaan Kiusalaas. Page 24.〕〔Numerical Methods in Engineering with Python 3. By Jaan Kiusalaas. Page 21.〕 where an exact fit to the data is required, or smoothing,〔Numerical Methods of Curve Fitting. By P. G. Guest, Philip George Guest. Page 349.〕〔See also: Mollifier〕 in which a "smooth" function is constructed that approximately fits the data. A related topic is regression analysis,〔Fitting Models to Biological Data Using Linear and Nonlinear Regression. By Harvey Motulsky, Arthur Christopoulos.〕〔Regression Analysis By Rudolf J. Freund, William J. Wilson, Ping Sa. Page 269.〕 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,〔Visual Informatics. Edited by Halimah Badioze Zaman, Peter Robinson, Maria Petrou, Patrick Olivier, Heiko Schröder. Page 689.〕〔Numerical Methods for Nonlinear Engineering Models. By John R. Hauser. Page 227.〕 to infer values of a function where no data are available,〔Methods of Experimental Physics: Spectroscopy, Volume 13, Part 1. By Claire Marton. Page 150.〕 and to summarize the relationships among two or more variables.〔Encyclopedia of Research Design, Volume 1. Edited by Neil J. Salkind. Page 266.〕 Extrapolation refers to the use of a fitted curve beyond the range of the observed data,〔Community Analysis and Planning Techniques. By Richard E. Klosterman. Page 1.〕 and is subject to a degree of uncertainty〔An Introduction to Risk and Uncertainty in the Evaluation of Environmental Investments. DIANE Publishing. (Pg 69 )〕 since it may reflect the method used to construct the curve as much as it reflects the observed data.
== Different types of curve fitting ==
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