- Function File:
`p`=**polyfit***(*`x`,`y`,`n`) - Function File:
*[*`p`,`s`] =**polyfit***(*`x`,`y`,`n`) - Function File:
*[*`p`,`s`,`mu`] =**polyfit***(*`x`,`y`,`n`) Return the coefficients of a polynomial

`p`(`x`) of degree`n`that minimizes the least-squares-error of the fit to the points`[`

.`x`,`y`]If

`n`is a logical vector, it is used as a mask to selectively force the corresponding polynomial coefficients to be used or ignored.The polynomial coefficients are returned in a row vector.

The optional output

`s`is a structure containing the following fields:- ‘
`R`’ Triangular factor R from the QR decomposition.

- ‘
`X`’ The Vandermonde matrix used to compute the polynomial coefficients.

- ‘
`C`’ The unscaled covariance matrix, formally equal to the inverse of

`x’`*`x`, but computed in a way minimizing roundoff error propagation.- ‘
`df`’ The degrees of freedom.

- ‘
`normr`’ The norm of the residuals.

- ‘
`yf`’ The values of the polynomial for each value of

`x`.

The second output may be used by

`polyval`

to calculate the statistical error limits of the predicted values. In particular, the standard deviation of`p`coefficients is given by`sqrt (diag (s.C)/s.df)*s.normr`

.When the third output,

`mu`, is present the coefficients,`p`, are associated with a polynomial in

where`xhat`= (`x`-`mu`(1)) /`mu`(2)`mu`(1) = mean (`x`), and`mu`(2) = std (`x`).This linear transformation of

`x`improves the numerical stability of the fit.**See also:**polyval, polyaffine, roots, vander, zscore.- ‘

Package: octave