#include <stdio.h>
#include <gsl/gsl_fit.h>

int
main (void)
{
  int i, n = 4;
  double x[4] = { 1970, 1980, 1990, 2000 };
  double y[4] = {   12,   11,   14,   13 };
  double w[4] = {  0.1,  0.2,  0.3,  0.4 };

  double c0, c1, cov00, cov01, cov11, chisq;

  gsl_fit_wlinear (x, 1, w, 1, y, 1, n, 
                   &c0, &c1, &cov00, &cov01, &cov11, 
                   &chisq);

  printf ("# best fit: Y = %g + %g X\n", c0, c1);
  printf ("# covariance matrix:\n");
  printf ("# [ %g, %g\n#   %g, %g]\n", 
          cov00, cov01, cov01, cov11);
  printf ("# chisq = %g\n", chisq);

  for (i = 0; i < n; i++)
    printf ("data: %g %g %g\n", 
                   x[i], y[i], 1/sqrt(w[i]));

  printf ("\n");

  for (i = -30; i < 130; i++)
    {
      double xf = x[0] + (i/100.0) * (x[n-1] - x[0]);
      double yf, yf_err;

      gsl_fit_linear_est (xf, 
                          c0, c1, 
                          cov00, cov01, cov11, 
                          &yf, &yf_err);

      printf ("fit: %g %g\n", xf, yf);
      printf ("hi : %g %g\n", xf, yf + yf_err);
      printf ("lo : %g %g\n", xf, yf - yf_err);
    }
  return 0;
}

$ ./demo > tmp
$ more tmp
# best fit: Y = -106.6 + 0.06 X
# covariance matrix:
# [ 39602, -19.9
#   -19.9, 0.01]
# chisq = 0.8

$ for n in data fit hi lo ; 
   do 
     grep "^$n" tmp | cut -d: -f2 > $n ; 
   done
$ graph -T X -X x -Y y -y 0 20 -m 0 -S 2 -Ie data 
     -S 0 -I a -m 1 fit -m 2 hi -m 2 lo