INCLAN Graphics: plot fit

Synopsis

plot fit x y σ f₁... (list mode)

Description

Performs a linear least-squares fit of the basis functions given by the vector expressions f₁,... to the data points with x-coordinates, y-coordinates and errors given by the vector expressions x, y and σ, respectively. For m basis functions, f₁,... ,f_m, the optimal linear combination,

y(x) = a₁f₁(x) + ... + a_mf_m(x)

is determined by minimizing

χ²(a₁, ..., a_m) = \sum_{i} ((y_i - y(x_i)) / σ_i)²

where i runs over the list data points. The optimal fit function y(x) is added as another column to the list data. This command does not draw anything. The fit parameters, a₁,...,a_m, their standard deviations, χ², and the probability that this value of χ² would be exceeded by chance are available through the intrinsic functions fitpar, fiterr, fitchisq and fitprob, respectively. If the errors σ_i of the data points are unknown, this can be indicated by setting σ to zero in the fit command.

dot x y1	        # plot original data points
fit x log(y1) 0 1 x	# logarithmic fit of y = a1 exp(-a2x)
spline x exp(y2)	# plot fitted curve