/* Simple program to compute Covariance on (x,y) data */
/* Assumes a two-column data file with N rows of data */
/*                                                    */
/* Written by Carey Williamson, November 2017         */
/*                                                    */
/* Usage: cc -o covariance covariance.c               */
/*        ./covariance < datafile                     */

#include <stdio.h>
#include <stdlib.h>

int main()
  {
    float xval, yval;
    float sumx, sumy, sumxy;
    float meanx, meany, meanxy;
    int i, n;

    /* Read in data values and sum them up */
    sumx = 0;
    sumy = 0;
    sumxy = 0;
    n = 0;
    while( scanf("%f %f\n", &xval, &yval) == 2 )
      {
	sumx += xval;
	sumy += yval;
	sumxy += xval*yval;
	n++;
      }

    /* Compute the means of each */
    meanx = sumx/n;
    meany = sumy/n;
    meanxy = sumxy/n;

    /* Report the results */
    printf("Number of values: %d\n", n);
    printf("E[X] = %8.6f, E[Y] = %8.6f, E[XY] = %8.6f\n",
	   meanx, meany, meanxy);
    printf("Cov[XY] = E[XY] - E[X]E[Y] = %8.6f\n",
	   meanxy - meanx * meany);
  }