Calculating Pearson correlation using Perl

My modification of code which is originally available here. Probably easier to understand the original code. I altered the code so that I could use an anonymous 2d array and with strictures, so that I could plug it into my own code.

Comments are included in the code below to assist use.

#!/usr/bin/perl

use strict;
use warnings;

#make up some matrix for demonstration purposes
my $x = [];
#generate 10 row
for (my $i=1;$i<11;++$i){
   #generate 2 columns, where column 1 = $i and column 2 = $i
   for (my $j=1;$j<3;++$j){
      $x->[$i][$j]= $i;
   }
}
#end matrix code

my $correlation = correlation($x);
#Since the values in the columns are identical in $x, the correlation will be 1
print "$correlation\n";

#to use this code, remove the matrix code above
#generate an anonymous 2D array where $x->[1] is the row
#$x->[1][1] is the value in row 1 column 1 and $x->[1][2] is the value of row 1 column 2
#once you build the entire array, pass it to the correlation subroutine as above
#my $corrleation = correlation($x)

#if you want to see what's inside $x use the code below
#for (my $i = 1; $i < scalar(@{$x}); ++$i){
#   my $line_to_print = '';
#   for (my $j = 1; $j < scalar(@{$x->[$i]}); ++$j){
#      $line_to_print .= "$x->[$i]->[$j]\t";
#   }
#   $line_to_print =~ s/\t$//;
#   print "$line_to_print\n";
#}

sub mean {
   my ($x)=@_;
   my $num = scalar(@{$x}) - 1;
   my $sum_x = '0';
   my $sum_y = '0';
   for (my $i = 1; $i < scalar(@{$x}); ++$i){
      $sum_x += $x->[$i][1];
      $sum_y += $x->[$i][2];
   }
   my $mu_x = $sum_x / $num;
   my $mu_y = $sum_y / $num;
   return($mu_x,$mu_y);
}

### ss = sum of squared deviations to the mean
sub ss {
   my ($x,$mean_x,$mean_y,$one,$two)=@_;
   my $sum = '0';
   for (my $i=1;$i<scalar(@{$x});++$i){
     $sum += ($x->[$i][$one]-$mean_x)*($x->[$i][$two]-$mean_y);
   }
   return $sum;
}

sub correlation {
   my ($x) = @_;
   my ($mean_x,$mean_y) = mean($x);
   my $ssxx=ss($x,$mean_x,$mean_y,1,1);
   my $ssyy=ss($x,$mean_x,$mean_y,2,2);
   my $ssxy=ss($x,$mean_x,$mean_y,1,2);
   my $correl=correl($ssxx,$ssyy,$ssxy);
   my $xcorrel=sprintf("%.4f",$correl);
   return($xcorrel);

}

sub correl {
   my($ssxx,$ssyy,$ssxy)=@_;
   my $sign=$ssxy/abs($ssxy);
   my $correl=$sign*sqrt($ssxy*$ssxy/($ssxx*$ssyy));
   return $correl;
}