/* From: "COMPUTATIONAL PHYSICS, 2nd Ed" 
   by RH Landau, MJ Paez, and CC Bordeianu 
   Copyright Wiley-VCH, 2007.
   Electronic Materials copyright: R Landau, Oregon State Univ, 2007;
   MJ Paez, Univ Antioquia, 2007; & CC Bordeianu, Univ Bucharest, 2007
   Support by National Science Foundation
*/
//   fit.c:    Least square fit    

#include <stdio.h>
#include <math.h>
#define data 12       // number of data points 

main() {
	
  int i, j;
  double s, sx, sy, sxx, sxy, delta, inter, slope;
  double x[data], y[data], d[data];
	                                                      // input data
  for (i = 0; i<data; i++) x[i] = i*10+5;                  
  y[0] = 382; y[1] = 187;  y[2] = 281; y[3] = 87;           
  y[4] = 8;  y[5] = 6;   y[6] = 5;  y[7] = 28;         
  y[8] = 2;  y[9] = 80.1; y[10] = 4; y[11] = 18; 
	                                                     // reset sums
  for (i = 0; i<data; i++) d[i] = 1.;   
  s = sx = sy = sxx = sxy = 0;    
	                                                // calculating sums
  for (i = 0;i<data;i++)  {                            
    s   +=         1 / (d[i]*d[i]);
    sx  +=      x[i] / (d[i]*d[i]);
    sy  +=      y[i] / (d[i]*d[i]); 
    sxx += x[i]*x[i] / (d[i]*d[i]); 
    sxy += x[i]*y[i] / (d[i]*d[i]);
  } 
  delta= s*sxx-sx*sx;
  slope=  (s*sxy-sx*sy) / delta;                   // calculating all
  inter = (sxx*sy-sx*sxy) / delta;                    // coefficients
  printf("intercept = %f\t +/- %f\n", inter, sqrt(sxx/delta) );
  printf("slope = %f\t +/- %f\n", slope, sqrt(s/delta) );
  printf("correlation = %f\n", -sx/sqrt(sxx*s));
}