/*****************************************************************************/
/*                                                                           */
/*                            L I N R E G                                    */
/*                                                                           */
/*  Program:      LINREG                                                     */
/*                                                                           */
/*  Programmer:   Dr. David G. Simpson                                       */
/*                Department of Physical Science                             */
/*                Prince George's Community College                          */
/*                Largo, Maryland  20774                                     */
/*                                                                           */
/*  Date:         January 21, 2002                                           */
/*                                                                           */
/*  Language:     C                                                          */
/*                                                                           */
/*  Description:  This program performs a linear regression analysis for a   */
/*                set of data given as (x,y) pairs.  The output from the     */
/*                program is the slope and y-intercept of the least-squares  */
/*                best fit straight line through the data points.            */
/*                                                                           */
/*****************************************************************************/


/*****************************************************************************/
/*  #includes                                                                */
/*****************************************************************************/

#include <stdio.h>                          /* standard i/o                  */
#include <string.h>                         /* string functions              */
#include <math.h>                           /* math functions                */



/*****************************************************************************/
/*  function prototypes                                                      */
/*****************************************************************************/

void   chop (char *str);                    /* remove \n from end of string  */
double sqr (double x);                      /* compute the square of a number*/



/*****************************************************************************/
/*  global variables                                                         */
/*****************************************************************************/

double   b;                                 /* y-intercept of best fit line  */
double   m;                                 /* slope of best fit line        */
double   n = 0.0;                           /* number of data points         */
double   r;                                 /* correlation coefficient       */
char     str[81];                           /* input string                  */
double   sumx = 0.0;                        /* sum of x                      */
double   sumx2 = 0.0;                       /* sum of x**2                   */
double   sumxy = 0.0;                       /* sum of x * y                  */
double   sumy = 0.0;                        /* sum of y                      */
double   sumy2 = 0.0;                       /* sum of y**2                   */
double   x;                                 /* input x data                  */
double   y;                                 /* input y data                  */





/*****************************************************************************/
/*  main()                                                                   */
/*****************************************************************************/

int main (void)
{

/*---------------------------------------------------------------------------*/
/*  Print introductory message.                                              */
/*---------------------------------------------------------------------------*/

   printf("LINREG - Perform linear regression\n");
   printf("  (Enter END to stop data entry and "
          "compute linear regression.)\n\n");

/*---------------------------------------------------------------------------*/
/*  Enter data and accumulate sums.                                          */
/*---------------------------------------------------------------------------*/

   for (;;)                                 /* loop for all data points      */
      {
      printf ("Enter x y:  ");              /* prompt for x and y            */
      fgets (str, 80, stdin);               /* read x and y into string str  */
      chop (str);                           /* remove trailing \n            */
      if (!strcmp(str,"end") ||             /* if no more data..             */
          !strcmp(str,"END"))
         break;                             /* ..then go compute least sqrs  */
      sscanf (str, "%lf %lf", &x, &y);      /* else read data from string    */

      n += 1.0;                             /* increment num of data points  */
      sumx  += x;                           /* compute sum of x              */
      sumx2 += x * x;                       /* compute sum of x**2           */
      sumxy += x * y;                       /* compute sum of x * y          */
      sumy  += y;                           /* compute sum of y              */
      sumy2 += y * y;                       /* compute sum of y**2           */
      }                                     /* loop again for more data      */

/*---------------------------------------------------------------------------*/
/*  Compute least-squares best fit straight line.                            */
/*---------------------------------------------------------------------------*/

   m = (n * sumxy  -  sumx * sumy) /        /* compute slope                 */
       (n * sumx2 - sqr(sumx));

   b = (sumy * sumx2  -  sumx * sumxy) /    /* compute y-intercept           */
       (n * sumx2  -  sqr(sumx));

   r = (sumxy - sumx * sumy / n) /          /* compute correlation coeff     */
            sqrt((sumx2 - sqr(sumx)/n) *
            (sumy2 - sqr(sumy)/n));

/*---------------------------------------------------------------------------*/
/*  Print results and return to operating system.                            */
/*---------------------------------------------------------------------------*/

   printf("\nSlope        m = %15.6e\n",m);
   printf("y-intercept  b = %15.6e\n",b);
   printf("Correlation  r = %15.6e\n",r);

   return 0;                                /* return to operating system    */

}




/*****************************************************************************/
/*  chop()                                                                   */
/*                                                                           */
/*  Remove final \n from end of string.                                      */
/*****************************************************************************/

void chop (char *str)
{
   int  len;                                /* length of str (incl \n)       */

   len = strlen (str);                      /* get length of str incl \n     */
   if (str[len-1] == '\n')                  /* if final char is \n ..        */
      str[len-1] = '\0';                    /* ..then remove it              */
}





/*****************************************************************************/
/*  sqr()                                                                    */
/*                                                                           */
/*  Returns the square of a number.                                          */
/*****************************************************************************/

double sqr (double x)
{
   return x * x;                            /* compute square of argument    */
}