GNU Scientific Library Reference Manual - Third Edition (v1.12)by M. Galassi, J. Davies, J. Theiler, B. Gough, G. Jungman, P. Alken, M. Booth, F. Rossi Paperback (6"x9"), 592 pages, 60 figures ISBN 0954612078 RRP £24.95 ($39.95) |

## 36.2 Linear regression

The functions described in this section can be used to perform least-squares fits to a straight line model, Y(c,x) = c_0 + c_1 x.

__Function:__int**gsl_fit_linear***(const double **`x`, const size_t`xstride`, const double *`y`, const size_t`ystride`, size_t`n`, double *`c0`, double *`c1`, double *`cov00`, double *`cov01`, double *`cov11`, double *`sumsq`)- This function computes the best-fit linear regression coefficients
(
`c0`,`c1`) of the model Y = c_0 + c_1 X for the dataset (`x`,`y`), two vectors of length`n`with strides`xstride`and`ystride`. The errors on`y`are assumed unknown so the variance-covariance matrix for the parameters (`c0`,`c1`) is estimated from the scatter of the points around the best-fit line and returned via the parameters (`cov00`,`cov01`,`cov11`). The sum of squares of the residuals from the best-fit line is returned in`sumsq`. Note: the correlation coefficient of the data can be computed using`gsl_stats_correlation`

(see 20.6), it does not depend on the fit.

__Function:__int**gsl_fit_wlinear***(const double **`x`, const size_t`xstride`, const double *`w`, const size_t`wstride`, const double *`y`, const size_t`ystride`, size_t`n`, double *`c0`, double *`c1`, double *`cov00`, double *`cov01`, double *`cov11`, double *`chisq`)- This function computes the best-fit linear regression coefficients
(
`c0`,`c1`) of the model Y = c_0 + c_1 X for the weighted dataset (`x`,`y`), two vectors of length`n`with strides`xstride`and`ystride`. The vector`w`, of length`n`and stride`wstride`, specifies the weight of each datapoint. The weight is the reciprocal of the variance for each datapoint in`y`.The covariance matrix for the parameters (

`c0`,`c1`) is computed using the weights and returned via the parameters (`cov00`,`cov01`,`cov11`). The weighted sum of squares of the residuals from the best-fit line, \chi^2, is returned in`chisq`.

__Function:__int**gsl_fit_linear_est***(double*`x`, double`c0`, double`c1`, double`cov00`, double`cov01`, double`cov11`, double *`y`, double *`y_err`)- This function uses the best-fit linear regression coefficients
`c0`,`c1`and their covariance`cov00`,`cov01`,`cov11`to compute the fitted function`y`and its standard deviation`y_err`for the model Y = c_0 + c_1 X at the point`x`.

ISBN 0954612078 | GNU Scientific Library Reference Manual - Third Edition (v1.12) | See the print edition |