sub correlation {

  my ($x_ref, $y_ref) = @_;


  
  my @array_of_x_values = @$x_ref;
  my @array_of_y_values = @$y_ref;



  my $output = "output_test.txt";

  open (OUTPUT_TEST, ">$output");

  print OUTPUT_TEST Dumper ($x_ref, $y_ref);

  #print Dumper length($x_ref);
  #print Dumper length($y_ref);

  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 $number_of_elements_in_array = -1;


  my @x_values_for_points_above_the_trend_line;
  my @y_values_for_points_above_the_trend_line;

  my @x_values_for_points_below_the_trend_line;
  my @y_values_for_points_below_the_trend_line;

  my @x_values_for_points_on_the_trend_line;
  my @y_values_for_points_on_the_trend_line;
  


  foreach (@array_of_x_values){
    #chomp;
    $number_of_elements_in_array++;
    
    my $x_point = $_;
    

    
   # print "\n$array_of_y_values[$number_of_elements_in_array] > $intercept + ($x_point * $slope)\n\n";

    if (defined($x_point)){
      
      if ($array_of_y_values[$number_of_elements_in_array] > $intercept + ($x_point * $slope)){
	
	#points are above the trend line
	

####	my  $Distance_above_trend_line = 


	push (@x_values_for_points_above_the_trend_line, $x_point);
	push (@y_values_for_points_above_the_trend_line, $array_of_y_values[$number_of_elements_in_array]);
	
	
      }
      elsif ($array_of_y_values[$number_of_elements_in_array] < $intercept + ($x_point * $slope)){
	
	#points are below the trend line
	
	#  $y_values_for_points_below_the_trend_line = 
	
	push (@x_values_for_points_below_the_trend_line, $x_point);
	push (@y_values_for_points_below_the_trend_line, $array_of_y_values[$number_of_elements_in_array]);
	
      }
      else {
	
	push (@x_values_for_points_on_the_trend_line, $x_point);
	push (@y_values_for_points_on_the_trend_line, $array_of_y_values[$number_of_elements_in_array]);
	
      }
    }
  }

  return $hashref, \@x_values_for_points_above_the_trend_line, \@y_values_for_points_above_the_trend_line, \@x_values_for_points_below_the_trend_line, \@y_values_for_points_below_the_trend_line, \@x_values_for_points_on_the_trend_line, \@y_values_for_points_on_the_trend_line;



}