Curve fitting

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Fitting of a noisy curve by an asymmetrical peak model, with an iterative process (Gauss-Newton algorithm with variable damping factor α).
Top: raw data and model.
Bottom: evolution of the normalised sum of the squares of the errors.

Curve fitting is the idea to construct a mathematical function which best fits a set of data points.[1] possibly subject to constraints.[2][3] Curve fitting can involve either interpolation[4][5] or smoothing.[6][7] Using interpolation requires an exact fit to the data. With smoothing, a "smooth" function is constructed, that fit the data approximately. A related topic is regression analysis,[8][9] 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 to help data visualization,[10][11] to guess values of a function where no data is available,[12] and to summarize the relationships among two or more variables.[13] Extrapolation refers to the use of a fitted curve beyond the range of the observed data.[14] This is subject to a degree of uncertainty[15] since it may reflect the method used to construct the curve as much as it reflects the observed data.

References[change | change source]

  1. 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.)
  2. The Signal and the Noise: Why So Many Predictions Fail-but Some Don't. By Nate Silver
  3. Data Preparation for Data Mining: Text. By Dorian Pyle.
  4. Numerical Methods in Engineering with MATLAB®. By Jaan Kiusalaas. Page 24.
  5. Numerical Methods in Engineering with Python 3. By Jaan Kiusalaas. Page 21.
  6. Numerical Methods of Curve Fitting. By P. G. Guest, Philip George Guest. Page 349.
  7. See also: Mollifier
  8. Fitting Models to Biological Data Using Linear and Nonlinear Regression. By Harvey Motulsky, Arthur Christopoulos.
  9. Regression Analysis By Rudolf J. Freund, William J. Wilson, Ping Sa. Page 269.
  10. Visual Informatics. Edited by Halimah Badioze Zaman, Peter Robinson, Maria Petrou, Patrick Olivier, Heiko Schröder. Page 689.
  11. Numerical Methods for Nonlinear Engineering Models. By John R. Hauser. Page 227.
  12. Methods of Experimental Physics: Spectroscopy, Volume 13, Part 1. By Claire Marton. Page 150.
  13. Encyclopedia of Research Design, Volume 1. Edited by Neil J. Salkind. Page 266.
  14. Community Analysis and Planning Techniques. By Richard E. Klosterman. Page 1.
  15. An Introduction to Risk and Uncertainty in the Evaluation of Environmental Investments. DIANE Publishing. Pg 69