1Statistics::Basic::LeasUtsSeqruaCroenFtirti(b3u)ted PerlStDaotciusmteinctsa:t:iBoansic::LeastSquareFit(3)
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6 Statistics::Basic::LeastSquareFit - find the least square fit for two
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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);
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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 + $yint\n";
65 }
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67 # This would also work:
68 # print "$lsf\n" if $lsf->query_filled;
69 }
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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.
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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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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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137 Paul Miller "<jettero@cpan.org>"
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140 Copyright 2012 Paul Miller -- Licensed under the LGPL
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143 perl(1), Statistics::Basic, Statistics::Basic::_TwoVectorBase,
144 Statistics::Basic::Vector
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148perl v5.30.1 2020-01-3S0tatistics::Basic::LeastSquareFit(3)