sub correlation
{
  my( $x_ref, $y_ref ) = @_;

  my @x_values = @$x_ref;
  my @y_values = @$y_ref;

  my $output = "output_test.txt";

  open OUTPUT_TEST, ">$output" or die "can't write $output - $!";
  print OUTPUT_TEST Dumper ($x_ref, $y_ref);
  close OUTPUT_TEST;

  my $lfit = Statistics::LineFit->new();
  $lfit->setData( $x_ref, $y_ref );

  my( $intercept, $slope ) = $lfit->coefficients();
  my $rSquared = $lfit->rSquared();

  my $hashref = {
    a => $intercept,
    b => $slope,
    c => $rSquared
  };

  my(
    @x_values_for_points_above_the_trend_line,
    @y_values_for_points_above_the_trend_line,
    @distances_above_the_trend_line,
    @x_values_for_points_below_the_trend_line,
    @y_values_for_points_below_the_trend_line,
    @distances_below_the_trend_line,
    @x_values_for_points_on_the_trend_line,
    @y_values_for_points_on_the_trend_line,
  );

  for ( 0 .. $#x_values )
  {
    my( $x, $y ) = ( $x_values[$_], $y_values[$_] );
    my $fx = $intercept + ( $x * $slope );
    if ( $y > $fx )
    {
      push @x_values_for_points_above_the_trend_line, $x;
      push @y_values_for_points_above_the_trend_line, $y;
      push @distances_above_trend_line, $y - $fx;
    }
    elsif ( $y < $fx )
    {
      push @x_values_for_points_below_the_trend_line, $x;
      push @y_values_for_points_below_the_trend_line, $y;
      push @distances_below_trend_line, $fx - $y;
    }
    else
    {
      push @x_values_for_points_on_the_trend_line, $x;
      push @y_values_for_points_on_the_trend_line, $y;
    }
  }

  return(
    $hashref,
    \@x_values_for_points_above_the_trend_line,
    \@y_values_for_points_above_the_trend_line,
    \@distances_above_the_trend_line,
    \@x_values_for_points_below_the_trend_line,
    \@y_values_for_points_below_the_trend_line,
    \@distances_below_the_trend_line,
    \@x_values_for_points_on_the_trend_line,
    \@y_values_for_points_on_the_trend_line,
  );
}