Fit[data, funs, vars] finds a least-squares fit to a list of data as a linear combination of the functions funs of variables vars.
The data can have the form , , ... , , , , ... , , ... , where the number of coordinates x, y, ... is equal to the number of variables in the list vars.
The data can also be of the form , , ... , with a single coordinate assumed to take values 1, 2, ... .
The argument funs can be any list of functions that depend only on the objects vars.
Fit[, , ... , 1, x, x^2, x] gives a quadratic fit to a sequence of values . The result is of the form + x + x^2, where the are real numbers. The successive values of x needed to obtain the are assumed to be 1, 2, ... .
Fit[, , , , ... , 1, x, x^2, x] does a quadratic fit, assuming a sequence of x values .
Fit[, , , ... , 1, x, y, x, y] finds a fit of the form + x + y.
Fit always finds the linear combination of the functions in the list funs that minimizes the sum of the squares of deviations from the values .
Exact numbers given as input to Fit are converted to approximate numbers with machine precision.
See The Mathematica Book: Section 1.6.6 and Section 3.8.1.
Implementation Notes: see section A.9.4.
See also: Interpolation, InterpolatingPolynomial, Solve, PseudoInverse, QRDecomposition, FindMinimum.
Related packages: Statistics`NonlinearFit`, Statistics`LinearRegression`.