NAME

SYNOPSIS

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

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

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

AUTHOR

COPYRIGHT

SEE ALSO