Curve fitting 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. Curve fitting can involve either interpolation, where an exact fit to the data is required, or smoothing, in which a "smooth" function is constructed that approximately fits the data. A related topic is regression analysis, 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, to infer values of a function where no data are available, and to summarize the relationships among two or more variables. Extrapolation refers to the use of a fitted curve beyond the range of the observed data, and is subject to a greater degree of uncertainty since it may reflect the method used to construct the curve as much as it reflects the observed data.
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Famous quotes containing the words curve and/or fitting:
“And out again I curve and flow
To join the brimming river,
For men may come and men may go,
But I go on forever.”
—Alfred Tennyson (1809–1892)
“Children’s view of the world and their capacity to understand keep expanding as they mature, and they need to ask the same questions over and over, fitting the information into their new level of understanding.”
—Joanna Cole (20th century)