1Statistics::Basic::LeasUtsSeqruaCroenFtirti(b3u)ted PerlStDaotciusmteinctsa:t:iBoansic::LeastSquareFit(3)
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NAME

6       Statistics::Basic::LeastSquareFit - find the least square fit for two
7       lists
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SYNOPSIS

10       A machine to calculate the Least Square Fit of given vectors x and y.
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12       The module returns the alpha and beta filling this formula:
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14           $y = $beta * $x + $alpha
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16       for a given set of x and y co-ordinate pairs.
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18       Say you have the set of Cartesian coordinates:
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20           my @points = ( [1,1], [2,2], [3,3], [4,4] );
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22       The simplest way to find the LSF is as follows:
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24           my $lsf = lsf()->set_size(int @points);
25              $lsf->insert(@$_) for @points;
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27       Or this way:
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29           my $xv  = vector( map {$_->[0]} @points );
30           my $yv  = vector( map {$_->[1]} @points );
31           my $lsf = lsf($xv, $yv);
32
33       And then either query the values or print them like so:
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35           print "The LSF for $xv and $yv: $lsf\n";
36           my ($yint, $slope) =
37           my ($alpha, $beta) = $lsf->query;
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39       LSF is meant for finding a line of best fit.  $beta is the slope of the
40       line and $alpha is the y-offset.  Suppose you want to draw the line.
41       Use these to calculate the "x" for a given "y" or vice versa:
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43           my $y = $lsf->y_given_x( 7 );
44           my $x = $lsf->x_given_y( 7 );
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46       (Note that "x_given_y()" can sometimes produce a divide-by-zero error
47       since it has to divide by the $beta.)
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49       Create a 20 point "moving" LSF like so:
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51           use Statistics::Basic qw(:all nofill);
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53           my $sth = $dbh->prepare("select x,y from points where something");
54           my $len = 20;
55           my $lsf = lsf()->set_size($len);
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57           $sth->execute or die $dbh->errstr;
58           $sth->bind_columns( my ($x, $y) ) or die $dbh->errstr;
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60           my $count = $len;
61           while( $sth->fetch ) {
62               $lsf->insert( $x, $y );
63               if( defined( my ($yint, $slope) = $lsf->query ) {
64                   print "LSF: y= $slope*x + $yint\n";
65               }
66
67               # This would also work:
68               # print "$lsf\n" if $lsf->query_filled;
69           }
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METHODS

72       This list of methods skips the methods inherited from
73       Statistics::Basic::_TwoVectorBase (things like insert(), and
74       ginsert()).
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76       new()
77           Create a new Statistics::Basic::LeastSquareFit object.  This
78           function takes two arguments -- which can either be arrayrefs or
79           Statistics::Basic::Vector objects.  This function is called when
80           the leastsquarefirt() shortcut-function is called.
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82       query()
83           LSF is meant for finding a line of best fit.  $beta is the slope of
84           the line and $alpha is the y-offset.
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86               my ($alpha, $beta) = $lsf->query;
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88       y_given_x()
89           Automatically calculate the y-value on the line for a given
90           x-value.
91
92               my $y = $lsf->y_given_x( 7 );
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94       x_given_y()
95           Automatically calculate the x-value on the line for a given
96           y-value.
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98               my $x = $lsf->x_given_y( 7 );
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100           "x_given_y()" can sometimes produce a divide-by-zero error since it
101           has to divide by the $beta.  This might be helpful:
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103               if( defined( my $x = eval { $lsf->x_given_y(7) } ) ) {
104                   warn "there is no x value for 7";
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106               } else {
107                   print "x (given y=7): $x\n";
108               }
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110       query_vector1()
111           Return the Statistics::Basic::Vector for the first vector used in
112           the computation of alpha and beta.
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114       query_vector2()
115           Return the Statistics::Basic::Vector object for the second vector
116           used in the computation of alpha and beta.
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118       query_mean1()
119           Returns the Statistics::Basic::Mean object for the first vector
120           used in the computation of alpha and beta.
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122       query_variance1()
123           Returns the Statistics::Basic::Variance object for the first vector
124           used in the computation of alpha and beta.
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126       query_covariance()
127           Returns the Statistics::Basic::Covariance object used in the
128           computation of alpha and beta.
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OVERLOADS

131       This object is overloaded.  It tries to return an appropriate string
132       for the calculation, but raises an error in numeric context.
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134       In boolean context, this object is always true (even when empty).
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AUTHOR

137       Paul Miller "<jettero@cpan.org>"
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140       Copyright 2009 Paul Miller -- Licensed under the LGPL
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SEE ALSO

143       perl(1), Statistics::Basic, Statistics::Basic::_TwoVectorBase,
144       Statistics::Basic::Vector
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148perl v5.12.3                      2009-06-2S9tatistics::Basic::LeastSquareFit(3)
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