comment  **********************************************************************

                              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:         February 4, 2002

           Language:     Algol-68

           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.

         *************************************************************  comment


co ----------------------------------------------------------------------------
      Variable declarations
   ------------------------------------------------------------------------- co

begin
   real b;                                  # y-intercept of best fit line    #
   real m;                                  # slope of best fit line          #
   real n := 0.0;                           # number of data points           #
   real r;                                  # correlation coefficient         #
   real sumx := 0.0;                        # sum of x                        #
   real sumx2 := 0.0;                       # sum of x ** 2                   #
   real sumxy := 0.0;                       # sum of x * y                    #
   real sumy := 0.0;                        # sum of y                        #
   real sumy2 := 0.0;                       # sum of y * y                    #
   real x;                                  # input x data                    #
   real y;                                  # input y data                    #


co ----------------------------------------------------------------------------
      Print introductory message
   ------------------------------------------------------------------------- co

   print (newline, "LINREG - Perform linear regression");
   print (newline);
   print (" (Enter X=-9999 to stop data entry and compute linear regression.");


co ----------------------------------------------------------------------------
      Input data and accumulate sums
   ------------------------------------------------------------------------- co

   do
      print (newline);                      # start new line                  #
      print ("Enter x: ")                   # prompt for x                    #
      read (x);                             # read in x                       #
      if x = -9999 then goto done fi        # if = -9999, then no more data   #
      print ("Enter y: ")                   # prompt for y                    #
      read (y);                             # read in y                       #

      n plusab 1;                           # increment number of data points #
      sumx plusab x;                        # sum of x                        #
      sumx2 plusab x * x;                   # sum of x ** 2                   #
      sumxy plusab x * y;                   # sum of x * y                    #
      sumy plusab y;                        # sum of y                        #
      sumy2 plusab y * y;                   # sum of y ** 2                   #
   od


co ----------------------------------------------------------------------------
      Compute results
   ------------------------------------------------------------------------- co

done:

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

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

   r := (sumxy - sumx * sumy / n) /         # compute correlation coefficient #
            sqrt((sumx2 - sumx*sumx/n) *
            (sumy2 - sumy*sumy/n));


co ----------------------------------------------------------------------------
      Print results
   ------------------------------------------------------------------------- co

   print ("Slope        m = ", m);
   print ("y-intercept  b = ", b);
   print ("Correlation  r = ", r)

end