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] > $inte
+rcept + ($x_point * $slope)\n\n";

    if (defined($x_point)){
      
      if ($array_of_y_values[$number_of_elements_in_array] > $intercep
+t + ($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, $array_of_y_value
+s[$number_of_elements_in_array]);
    
    
      }
      elsif ($array_of_y_values[$number_of_elements_in_array] < $inter
+cept + ($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, $array_of_y_value
+s[$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_val
+ues_for_points_above_the_trend_line, \@x_values_for_points_below_the_
+trend_line, \@y_values_for_points_below_the_trend_line, \@x_values_fo
+r_points_on_the_trend_line, \@y_values_for_points_on_the_trend_line;



}
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