Statistics::Basic::LeaUseruContributed PerStatistics::Basic::LeastSquareFit(3)NAMEStatistics::Basic::LeastSquareFit - find the least square fit for two
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SYNOPSIS
A machine to calculate the Least Square Fit of given vectors x and y.
The module returns the alpha and beta filling this 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.)
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;
}
METHODS
This list of methods skips the methods inherited from
Statistics::Basic::_TwoVectorBase (things like insert(), and
ginsert()).
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.
OVERLOADS
This object is overloaded. It tries to return an appropriate string
for the calculation, but raises an error in numeric context.
In boolean context, this object is always true (even when empty).
AUTHOR
Paul Miller "<jettero@cpan.org>"
COPYRIGHT
Copyright 2009 Paul Miller -- Licensed under the LGPL
SEE ALSOperl(1), Statistics::Basic, Statistics::Basic::_TwoVectorBase,
Statistics::Basic::Vector
perl v5.14.12009-06-Statistics::Basic::LeastSquareFit(3)
