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In the philosophy of science, and science generally, and in statistics, the curve fitting problem is how to choose among an infinite number of curves that fit the graphically-represented data points, normally by finding a mathmatical expresion to créate the curve.
The simplest curve is said to be preferable. This is thought to be related to Occam's Razor in so far as there is a preference for simplicity among a family of curves just as there is a preference of simplicity among competing théories.
Commonly used procedures are least squares fitting, linear regression, and nonlinéar regression. One of the difficulties in curve fitting is to choose the functional form of the data for paraméter optimization. Computers are often used to perform curve fitting procedures. Computers do this by solving a system of equations to find the paraméters of the function that minimize the squared error. The gradient descent algorithm is often used for this purpose.
Audi, R., Ed. (1996) The Cambridge Dictionary of Philosophy. Cambridge, Cambridge University Press. curve fitting problem p. 172-173.
- LAB Fit Curve Fitting Software 2D and 3D fitting with Finder
- Curve Expert (shareware) fits functions to data (limited to one dependant and one independent variable.)
- Online curve and surface fitting
- TableCurve2D and TableCurve3D by Systat automates curve fitting
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