#!perl
# *********************************************************************************************************************************
#
#                                                          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 16, 2002
#
#  Language:     Perl
#
#  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.
#
# *********************************************************************************************************************************


# ---------------------------------------------------------------------------------------------------------------------------------
#   sqr()  -  Return the square of a number.
# ---------------------------------------------------------------------------------------------------------------------------------

sub sqr {
$_[0] * $_[0];
}



# ---------------------------------------------------------------------------------------------------------------------------------
#   Main program
# ---------------------------------------------------------------------------------------------------------------------------------

print "LINREG - Perform linear regression\n";                                       # print introductory message
print "  (Enter 'end' to stop data entry and compute linear regression.)\n";

# ---------------------------------------------------------------------------------------------------------------------------------
#   Read in x and y data and accumulate sums.
# ---------------------------------------------------------------------------------------------------------------------------------

while (1) {                                                                         # loop for all data points
   print "\nEnter x:  ";                                                            # prompt for x
   chomp($line = <STDIN>);                                                          # read in line
   if ($line eq 'end') {                                                            # check for 'end'
      last;                                                                         # if so, break out of loop
   }
   $x = $line;                                                                      # else assign input to x
   print "Enter y:  ";                                                              # prompt for y
   chomp($line = <STDIN>);                                                          # read in line
   $y = $line;                                                                      # assign input to line

   $n++;                                                                            # 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
}


# ---------------------------------------------------------------------------------------------------------------------------------
#   Compute and print results.
# ---------------------------------------------------------------------------------------------------------------------------------

$m = ($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;