Don't reinvent the wheel.  Use one of the existing libraries/packages for this.  For example Math::GSL, which is a binding to the GSL library.

The R-squared for a linear least squares fit of two vectors @$x, @$y (with x predicting y) can be computed as follows:

#!/usr/bin/perl -w
use strict;

use Math::GSL::Fit "gsl_fit_linear";
use Math::GSL::Statistics "gsl_stats_tss";

my $x = [1,2,3,4,5];
my $y = [5,7,8,12,13];
my $n = @$y;

my ($status, $c0, $c1, $cov00, $cov01, $cov11, $ss_resid)
    = gsl_fit_linear($x, 1, $y, 1, $n);

my $ss_total = gsl_stats_tss($y, 1, $n);

print "SS residual = $ss_resid\n";
print "SS total    = $ss_total\n";

my $R2 = 1 - $ss_resid / $ss_total;

print "R^2 = $R2\n";
[download]

SS residual = 1.9
SS total    = 46
R^2 = 0.958695652173913
[download]

If I'm understanding you correctly, you'd want to do this computation for every pair of lines.

(Note that for R^2 to be computable, there has to be some variance in the data to be predicted (as often with statistics).  In other words, $y = [2,2,2,2,2,2] wouldn't work, because here $ss_total would be 0, which would cause a division by zero error.)

Very nice code thank you so much Eliya!

A question in passing do you know why this online calculator http://ea
+sycalculation.com/statistics/r-squared.php can find r^2 (but not r) o
+n values:
"2,2,2,2"
"2,2,2,1"

Is that a bug on their software?

Thanks again for your help!
[download]

Strictly speaking, neither r nor R^2 can be computed with those vectors (so yes, you could consider it a bug).   This is because no line can be fitted with finite values for $c0 and $c1.  And when there's no line, there are no residuals, etc.

When you change the values slightly to

2,2,2,2.0001
2,2,2,1
[download]

a line can be fitted (so you also get correct values on that site), but the fitted line parameters are already rather large:

my $c0 = 20001.9999999578;    # as computed by gsl_fit_linear()
my $c1 = -9999.9999999789;
say $c0 + $c1 * $_ for 2, 2.0001;

__END__
2
1
[download]

The smaller you make the deviation from 2 for the last value of vector x, the larger the fitted parameters become, eventually approaching delicately balancing +/- "infinities".  And when all values are exactly 2, no fit can be computed any longer...   (try 2.0000001 and 2.00000001 on the linked site, and you'll already get nonsensical values (correct values should always be r = -1, r^2 = 1) — which means numerical precision is rather low).

I am kind of a math and science ignoramus, but I don't have any idea what "R-squared" is. Is it a math function? The square of some number you're reading? Or something else? What do you need your sub to return?

I think, immediately, you probably need to break the lines you read into fields. You seem to be passing whole lines of data to your sub, correct? Is that what you want to do? When the sub receives them, you probably need to have something like this:

my @dos = split(/\s*/, $dosage);     # Split $dosage into an array at 
+the spaces between the numbers
my @geno = split(/\s*/, $genotype);  # Do the same thing for $genotype
[download]

After that, I'm not sure what you want to do.

I am kind of a math and science ignoramus, but I don't have any idea what "R-squared" is.

That's why we have Google and Wikipedia. Really, if you don't know what it is, and are too lazy too look it up, you can also decide not to answer, and leave an answer for someone who knows what it is.

We don't want to spoon feed people who come here with questions, and expect people asking questions to do some research. But that works both way. "R-squared" is well known enough that it doesn't need explaining -- someone who can answer the question will know what it is; someone who doesn't know what it is, is likely not being able to answer the question.

Forgive me. I was under the mistaken impression that this forum was about Perl programming. Perl I know, and enjoy offering help regarding, and despite my other shortcomings, I hoped my comment might be helpful. I was also under the impression, perhaps mistakenly, that the person asking the question knew what the function was, and didn't need to be told this or how to work it mathematically.