Curve fitting

Curve fitting is constructing a mathematical function which best fits a set of data points.^[1][2][3]

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 may involve either interpolation^[4] or smoothing.^[5] 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,^[6][7] 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,^[8][9] to guess values of a function where no data is available,^[10] and to summarize the relationships among two or more variables.^[11] Extrapolation refers to the use of a fitted curve beyond the range of the observed data.^[12] This is subject to a degree of uncertainty,^[13] since it may reflect the method used to construct the curve as much as it reflects the observed data.