//*******************************************************************************************************************************
//
//                                                          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-intercpt of least-squares best fit line
double   m;                                                                         // slope of least-squares best fit line
double   n = 0.0;                                                                   // number of data points
double   r;                                                                         // squared 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)
{

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

   for (;;)                                                                         // loop for all data points
      {
      printf ("Enter x y:  ");
      fgets (str, 80, stdin);
      chop (str);
      if (!strcmp(str,"end") || !strcmp(str,"END"))
         break;
      sscanf (str, "%lf %lf", &x, &y);

      n += 1.0;                                                                     // increment number of data points by 1
      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
      }

   m = (n * sumxy  -  sumx * sumy) / (n * sumx2 - sqr(sumx));                       // compute slope
   b = (sumy * sumx2  -  sumx * sumxy) / (n * sumx2  -  sqr(sumx));                 // compute y-intercept
   r = (sumxy - sumx * sumy / n) /                                                  // compute correlation coefficient
            sqrt((sumx2 - sqr(sumx)/n) * (sumy2 - sqr(sumy)/n));

   printf ("\nSlope        m = %15.6e\n", m);                                       // print results
   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;

   len = strlen (str);
   if (str[len-1] == '\n')
      str[len-1] = '\0';
}





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

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