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The functions described in this section can be used to perform
least-squares fits to a straight line model without a constant term,
*Y = c_1 X*.

- Function:
*int***gsl_fit_mul***(const double **`x`, const size_t`xstride`, const double *`y`, const size_t`ystride`, size_t`n`, double *`c1`, double *`cov11`, double *`sumsq`) This function computes the best-fit linear regression coefficient

`c1`of the model*Y = c_1 X*for the datasets (`x`,`y`), two vectors of length`n`with strides`xstride`and`ystride`. The errors on`y`are assumed unknown so the variance of the parameter`c1`is estimated from the scatter of the points around the best-fit line and returned via the parameter`cov11`. The sum of squares of the residuals from the best-fit line is returned in`sumsq`.

- Function:
*int***gsl_fit_wmul***(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 *`c1`, double *`cov11`, double *`sumsq`) This function computes the best-fit linear regression coefficient

`c1`of the model*Y = c_1 X*for the weighted datasets (`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 variance of the parameter

`c1`is computed using the weights and returned via the parameter`cov11`. The weighted sum of squares of the residuals from the best-fit line,*\chi^2*, is returned in`chisq`.

- Function:
*int***gsl_fit_mul_est***(double*`x`, double`c1`, double`cov11`, double *`y`, double *`y_err`) This function uses the best-fit linear regression coefficient

`c1`and its covariance`cov11`to compute the fitted function`y`and its standard deviation`y_err`for the model*Y = c_1 X*at the point`x`.

Next: Multi-parameter fitting, Previous: Linear regression, Up: Least-Squares Fitting [Index]