## Linear fitting without a constant term

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. For weighted data the best-fit is found by minimizing the weighted sum of squared residuals, \chi^2,

    \chi^2 = \sum_i w_i (y_i - c_1 x_i)^2

for the parameter c_1. For unweighted data the sum is computed with w_i = 1.

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 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 estimated from the weighted data and returned via the parameters 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 c11, double *y, double *y_err)
  This function uses the best-fit linear regression coefficient c1 and its estimated 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.