I'm trying to write a quick script fragment to find the Least Squares Regression line of some data points. To find the line of best fit y = ax + b (through the above mentioned method) with given a set of data {(x1,y1),(x2,y2),...,(xn,yn)}, the following system is solved for:

(The math is hard to write, and therefore to read, but not fundamental to reading the rest of this)

EQ1: nb + SUM(xi,i=1 TO n)a = SUM(yi,i=1 TO n)
EQ2: SUM(xi,i=1 TO n)b + SUM(xi^2,i=1 TO n)a = SUM(xi*yi, i=1 TO n)

The (x,y) points I need (quite a few of them!) are read in line by line, so the problem comes up with storage; it requires far too much space to store these, so I decided to make a closure (with the hope of) summing as we go along, and then (when passed the right argument) calculating the data (actually, I was rather happy with the code I wrote to solve the sytem of equations; when I looked at it I didn't know what to do, and thought that it was the type of thing complex C code has been written for. . . but where there's perl there's a way, and eval popped in my head, but I'd be interested to hear other ideas).

I'm not familiar with closures (I haven't used them often), so I looked through this site and at perldoc's closure information (including perlref). Well, even after all that I'm still getting some problems. Now, I imagine its a simple (as in basic/fundamental) closure issue which I'm missing, but when I call the closure (&$closure($args)) and through a debugging statement print the arguments, I get . . . NOTHING.

If closures aren't the way to go, fine (but I'd be interested in knowing what to do). The code is below (just the closure; I just made up some simple data through a 1..10 and 20..30 statement for x y coordinates and tested it with that; the call mimicks what I have above).

I wrote this just now quickly in an attempt to see what I'll need to do with the final thing, so any suggestions are more than welcome. 

# bf stands for best fit; eventually I'll need several that
# will mimick this format closely.

my $bf_1 = sub {
              # Arguments are: Add|Equate; [x value; y value].
              my $sum_x;
              my $sum_y;
              my $sum_x2;
              my $sum_xy;
              my $n;

              $sum_x  = 0 unless $sum_x;
              $sum_y  = 0 unless $sum_y;
              $sum_x2 = 0 unless $sum_x2;
              $sum_xy = 0 unless $sum_xy;
              $n      = 0 unless $n;

              if($ARGV[0] eq 'Add') {
                my @args = @_;
                $sum_x  += $args[1];
                $sum_y  += $args[2];
                $sum_x2 += $args[1]*$args[2];
                $sum_xy += $args[1] ** 2;
                $n++;
              } elsif ($ARGV[0] eq 'Equate') {
                my $a;
                my $b;
                $a = "(($sum_y - $n*$b)/$sum_x)";
                $b = "($sum_xy-$sum_x2*$a)/$sum_x";
                eval $b;
                eval $a;
                ($a,$b);
              } else { print "Called with unkown argument\n" }
};

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In reply to Closures and Statistics by dimmesdale

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