Process of constructing a curve that has the best fit to a series of data points
"Best fit" redirects here. For placing ("fitting") variable-sized objects in storage, see Fragmentation (computing).
Fitting of a noisy curve by an asymmetrical peak model, with an iterative process (Gauss–Newton algorithm with variable damping factor α).
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]
^William M. Kolb. Curve Fitting for Programmable Calculators. Syntec, Incorporated, 1984.
^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.)
^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.
^Numerical Methods in Engineering with MATLAB®. By Jaan Kiusalaas. Page 24.
^Numerical Methods in Engineering with Python 3. By Jaan Kiusalaas. Page 21.
^Numerical Methods of Curve Fitting. By P. G. Guest, Philip George Guest. Page 349.
^See also: Mollifier
^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.
^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.
^Methods of Experimental Physics: Spectroscopy, Volume 13, Part 1. By Claire Marton. Page 150.
^Encyclopedia of Research Design, Volume 1. Edited by Neil J. Salkind. Page 266.
^Community Analysis and Planning Techniques. By Richard E. Klosterman. Page 1.
^An Introduction to Risk and Uncertainty in the Evaluation of Environmental Investments. DIANE Publishing. Pg 69
^Ahn, Sung-Joon (December 2008), "Geometric Fitting of Parametric Curves and Surfaces" (PDF), Journal of Information Processing Systems, 4 (4): 153–158, doi:10.3745/JIPS.2008.4.4.153, archived from the original (PDF) on 2014-03-13
^Chernov, N.; Ma, H. (2011), "Least squares fitting of quadratic curves and surfaces", in Yoshida, Sota R. (ed.), Computer Vision, Nova Science Publishers, pp. 285–302, ISBN 9781612093994
^Liu, Yang; Wang, Wenping (2008), "A Revisit to Least Squares Orthogonal Distance Fitting of Parametric Curves and Surfaces", in Chen, F.; Juttler, B. (eds.), Advances in Geometric Modeling and Processing, Lecture Notes in Computer Science, vol. 4975, pp. 384–397, CiteSeerX 10.1.1.306.6085, doi:10.1007/978-3-540-79246-8_29, ISBN 978-3-540-79245-1
Curvefitting 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...
Look up fitting in Wiktionary, the free dictionary. Fitting can refer to: Curvefitting, the process of constructing a curve, or mathematical function...
Practical Handbook of CurveFitting. CRC Press. ISBN 978-0-8493-0143-8.[page needed] Kolb, William M. (1984). CurveFitting for Programmable Calculators...
and phase. A knowledge of shape function is needed for spectroscopic curvefitting and deconvolution. A spectral line corresponds to an electron transition...
is affected negatively. Mathematics portal Non-linear least squares Curvefitting Generalized linear model Local regression Response modeling methodology...
otherwise. Safeguarded curve-fitting methods simultaneously execute a linear-convergence method in parallel to the curve-fitting method. They check in each...
In analytical chemistry, a calibration curve, also known as a standard curve, is a general method for determining the concentration of a substance in...
is to use curvefitting. A minimum of N values are calculated evenly spaced along the range of the desired calculations. Using a curvefitting technique...
In mathematics, linear interpolation is a method of curvefitting using linear polynomials to construct new data points within the range of a discrete...
Crinkled arc CurvefittingCurve orientation Curve sketching Differential geometry of curves Gallery of curves Index of the curve List of curves topics List...
a weighted least squares estimator may be used to account for that. Curvefitting Line regression Local polynomial regression Polynomial and rational...
a parabola to the resulting data set. While this provides a simple curvefitting procedure, the resulting algorithm may be biased by excessively weighting...
Beta regression is a form of regression which is used when the response variable, y{\displaystyle y}, takes values within (0,1){\displaystyle (0,1)} and...
In statistics, the term linear model refers to any model which assumes linearity in the system. The most common occurrence is in connection with regression...
California. Its products include the 2D scientific graphing, biostatistics, curvefitting software GraphPad Prism and the free, web-based statistical calculation...
1029/WR002i004p00709. Seki, K. (2007). "SWRC fit - a nonlinear fitting program with a water retention curve for soils having unimodal and bimodal pore structure"...
to a model that attempts to fit the outliers more than the data. Line fitting is the process of constructing a straight line that has the best fit to...
the related and partially overlapping concept of curvefitting in the following ways: curvefitting often involves the use of an explicit function form...
Global Information