Statis...uareFit(3pm)

✨ NAME ✨

okay bestie, gather round 🫶 this is Statistics::Basic::LeastSquareFit — the module that finds the least square fit for two lists. iconic behavior, no cap. 👑

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🌸 SYNOPSIS 🌸

It's literally a little machine 🤖 that calculates the Least Square Fit of given vectors x and y.

The module hands you back alpha and beta, and they fill in this exact formula:

$y = $beta * $x + $alpha

for a given set of x and y co-ordinate pairs.

Say you have the set of Cartesian coordinates:

my @points = ( [1,1], [2,2], [3,3], [4,4] );

The simplest way to find the LSF is as follows:

my $lsf = lsf()->set_size(int @points);
   $lsf->insert(@$_) for @points;

Or this way:

my $xv  = vector( map {$_->[0]} @points );
my $yv  = vector( map {$_->[1]} @points );
my $lsf = lsf($xv, $yv);

And then either query the values or print them like so:

print "The LSF for $xv and $yv: $lsf\n";
my ($yint, $slope) =
my ($alpha, $beta) = $lsf->query;

LSF is meant for finding a line of best fit. $beta is the slope of the line and $alpha is the y-offset. Suppose you want to draw the line. Use these to calculate the "x" for a given "y" or vice versa:

my $y = $lsf->y_given_x( 7 );
my $x = $lsf->x_given_y( 7 );

(Note that x_given_y() can sometimes produce a divide-by-zero error since it has to divide by the $beta.) 😭 girl math can be brutal

Create a 20 point "moving" LSF like so:

use Statistics::Basic qw(:all nofill);

my $sth = $dbh->prepare("select x,y from points where something");
my $len = 20;
my $lsf = lsf()->set_size($len);

$sth->execute or die $dbh->errstr;
$sth->bind_columns( my ($x, $y) ) or die $dbh->errstr;

my $count = $len;
while( $sth->fetch ) {
    $lsf->insert( $x, $y );
    if( defined( my ($yint, $slope) = $lsf->query ) {
        print "LSF: y= $slope*x + $yint\n";
    }

    # This would also work:
    # print "$lsf\n" if $lsf->query_filled;
}

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🎀 METHODS 🎀

Heads up bestie 🫶 this list skips the methods inherited from Statistics::Basic::_TwoVectorBase (things like insert(), and ginsert()). Those still exist, they're just not re-explained here.

new()

Create a new Statistics::Basic::LeastSquareFit object. 💅 This function takes two arguments — which can either be arrayrefs or Statistics::Basic::Vector objects. This function is called when the leastsquarefirt() shortcut-function is called.

query()

LSF is meant for finding a line of best fit. $beta is the slope of the line and $alpha is the y-offset.

my ($alpha, $beta) = $lsf->query;

y_given_x()

Automatically calculate the y-value on the line for a given x-value. ✨

my $y = $lsf->y_given_x( 7 );

x_given_y()

Automatically calculate the x-value on the line for a given y-value. ✨

my $x = $lsf->x_given_y( 7 );

⚠️ x_given_y() can sometimes produce a divide-by-zero error since it has to divide by the $beta. This might be helpful:

if( defined( my $x = eval { $lsf->x_given_y(7) } ) ) {
    warn "there is no x value for 7";

} else {
    print "x (given y=7): $x\n";
}

query_vector1()

Return the Statistics::Basic::Vector for the first vector used in the computation of alpha and beta. 🦋

query_vector2()

Return the Statistics::Basic::Vector object for the second vector used in the computation of alpha and beta. 🦋

query_mean1()

Returns the Statistics::Basic::Mean object for the first vector used in the computation of alpha and beta. 🍓

query_variance1()

Returns the Statistics::Basic::Variance object for the first vector used in the computation of alpha and beta. 🍓

query_covariance()

Returns the Statistics::Basic::Covariance object used in the computation of alpha and beta. 🍓

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🌈 OVERLOADS 🌈

This object is overloaded. It tries to return an appropriate string for the calculation, but raises an error in numeric context. 😭 so don't try to do math on the string, bestie.

In boolean context, this object is always true (even when empty). periodt. 💅

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👑 AUTHOR 👑

Paul Miller <jettero@cpan.org>

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📜 COPYRIGHT 📜

Copyright 2012 Paul Miller -- Licensed under the LGPL

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🔭 SEE ALSO 🔭

perl(1), Statistics::Basic, Statistics::Basic::_TwoVectorBase, Statistics::Basic::Vector

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and that's the whole thing, bestie 🫶 this page came from perl v5.36.0, dated 2022-11-19 — go forth and fit those squares, you absolute icon 💖✨