# want $constant, $slope, and $error coefficients for regression equation fitting this data, where the distribution line is approximated by
# Y = $constant + $slope * x + $error
# Y = Dependent Variable (eg, widgets purchased at point in time)
# $constant = Y-axis Intercept
# $slope = Slope of the regression line
# x is Independent Variable(eg, time)
# $error = error factor, should be large for random distributions, small for 
# strongly correlated distrubions
# See http://www.tufts.edu/~gdallal/slr.htm
#dummy for now -- what's the best way to do this?

##</code><code>##

$ perl trend.t
slow_increase distribution, constant 0, slope 0, error 0
random distribution, constant 0, slope 0, error 0
fast_increase distribution, constant 0, slope 0, error 0
not ok 1 - $slow_increase_error < $random_error
#   Failed test '$slow_increase_error < $random_error'
#   in trend.t at line 96.
not ok 2 - $fast_increase_error < $random_error
#   Failed test '$fast_increase_error < $random_error'
#   in trend.t at line 97.
not ok 3 - $slow_increase_slope < $fast_increase_slope
#   Failed test '$slow_increase_slope < $fast_increase_slope'
#   in trend.t at line 102.
1..3
# Looks like you failed 3 tests of 3.
$

##</code><code>##

#!/usr/bin/perl
use strict;
use warnings;
use Test::More qw(no_plan);

my $distributions = { random =>
		      { distribution => {
					 1 => 3,
					 2 => 5,
					 3 => 2,
					 4 => 7,
					 5 => 1,
					 6 => 3,
					 7 => 2,
					 8 => 6,
					 9 => 1,
					 10 => 1,
					 11 => 3,
					 12 => 5,
					 13 => 6,
					 14 => 2,
					 15 => 8,
					 16 => 9,
					 17 => 1,
					 18 => 4,
					 19 => 5,
					 20 => 6
					}
		      },
		      slow_increase =>
		      { distribution => {
					 1 => 1,
					 2 => 1,
					 3 => 3,
					 4 => 2,
					 5 => 3,
					 6 => 2,
					 7 => 3,
					 8 => 4,
					 9 => 3,
					 10 => 2,
					 11 => 5,
					 12 => 4,
					 13 => 6,
					 14 => 5,
					 15 => 7,
					 16 => 4,
					 17 => 8,
					 18 => 6,
					 19 => 9,
					 20 => 8
					}
		      },
		      fast_increase =>
		      { distribution => {
					 1 => 2,
					 2 => 2,
					 3 => 6,
					 4 => 4,
					 5 => 6,
					 6 => 4,
					 7 => 6,
					 8 => 8,
					 9 => 6,
					 10 => 4,
					 11 => 10,
					 12 => 8,
					 13 => 12,
					 14 => 10,
					 15 => 14,
					 16 => 8,
					 17 => 16,
					 18 => 12,
					 19 => 18,
					 20 => 16
					} }
		    };

for  my $distribution_name ( keys %$distributions ) {
  my $distribution = $distributions->{$distribution_name};

  my $regression_coefficients =  calculate_regression_coefficients($distribution);
  my ($constant, $slope, $error) = map { $regression_coefficients->{$_} } qw(constant slope error);

  print "$distribution_name distribution, constant $constant, slope $slope, error $error\n";

  $distributions->{$distribution_name}->{constant}=$constant;
  $distributions->{$distribution_name}->{slope}   =$slope;
  $distributions->{$distribution_name}->{error}   =$error;
}

# error of random distribution should be greater than either of the other two distributions
my $random_error = $distributions->{random}->{error};
my $slow_increase_error = $distributions->{slow_increase}->{error};
my $fast_increase_error = $distributions->{fast_increase}->{error};
ok( $slow_increase_error < $random_error  , '$slow_increase_error < $random_error');
ok( $fast_increase_error < $random_error  , '$fast_increase_error < $random_error');

#fast increase slope should be greater than slow increase slope
my $slow_increase_slope = $distributions->{slow_increase}->{slope};
my $fast_increase_slope = $distributions->{fast_increase}->{slope};
ok( $slow_increase_slope < $fast_increase_slope, '$slow_increase_slope < $fast_increase_slope' );

# want $constant, $slope, and $error coefficients for regression equation fitting this data, where the distribution line is approximated by
# Y = $constant + $slope * x + $error
# Y = Dependent Variable (eg, widgets purchased at point in time)
# $constant = Y-axis Intercept
# $slope = Slope of the regression line
# x is Independent Variable(eg, time)
# $error = error factor, should be large for random distributions, small for 
# strongly correlated distrubions
# See http://www.tufts.edu/~gdallal/slr.htm
#dummy for now -- what's the best way to do this?
sub calculate_regression_coefficients {
  my $distribution = shift or die "no distribution";
  {constant => 0, slope => 0, error => 0}
}