Looks pretty bad to me:

• Inconsistent indentation.
• Excess vertical white space.
• Excessively long variable names.
• Repeated repetition again and again of y point lookup
• Needless manipulation of parallel arrays
• Too many items returned - huge possibility for mismatched lists
• Pointless copy of input arrays
• Silly loop variable assignment: my $x_point = $_;. Should use for my $x_point (... instead
• Dumb keys in stupidly named hashref

I'd rework it to look something like:

sub correlation {
    my ($x_ref, $y_ref) = @_;
    my $lfit = Statistics::LineFit->new ();

    $lfit->setData ($x_ref, $y_ref);

    my ($intercept, $slope) = $lfit->coefficients ();
    my $rSquared = $lfit->rSquared ();
    my %results =
        (intercept => $intercept, slope => $slope, rSquared => $rSquar
+ed);

    foreach my $index (0 .. $#$x_ref) {
        my ($xPoint, $yPoint) = ($x_ref->[$index], $y_ref->[$index]);
        if ($yPoint > $intercept + ($xPoint * $slope)) {
            push @{$results{above}}, [$xPoint, $yPoint];

        } elsif ($yPoint < $intercept + ($xPoint * $slope)) {
            push @{$results{below}}, [$xPoint, $yPoint];

        } else {
            push @{$results{on}}, [$xPoint, $yPoint];
        }
    }

    return \%results;
}
[download]