Performing Linear Regression in Perl

Linear regression is a very commonly used data analysis technique that can easily be performed in Perl using the module Statistics::Regression. This module is capable of performing multivariate linear regressions, but this code snippet will demonstrate a simple regression to the basic equation of a line y=mx +b, using the following data set:

X	Y
1	1.3
2	2.9
3	4.2
4	5.4

#!usr/bin/perl

use Statistics::Regression;
use strict;
use warnings;

my $reg=Statistics::Regression->new(
   "Title", ["Intercept", "Slope"]
   );
 
#the use of 1.0 in the includes allows
#for the computation of a y intercept     
$reg->include(1.3, [1.0, 1.0]);
$reg->include(2.9, [1.0, 2.0]);
$reg->include(4.2, [1.0, 3.0]);
$reg->include(5.4, [1.0, 4.0]);

$reg->print;

To understand how the module works, let’s consider the equation in a more multivariate form by rewriting it as y=bx₁ + mx₂.  Considering the equation in this form, will make the “include” statements that provide the data points to the module much easier to understand.  The include statements could be considered as using the following data entry format:

$reg->include(y, [x₁, x₂]);

Thus by always putting 1.0 in the x₁ position it allows for the computation of a Y-intercept since it is telling the regression module that the x₁ variable does not influence the outcome of bx₁, whereas the x₂ values correspond to the X values, since we want mx₂ to change with a change in X.

A look at the output generated by the Perl module demonstrates the following results:

****************************************************************

Regression 'Title'

****************************************************************

Name                   Theta          StdErr     T-stat

[0='Intercept']       0.0500          0.1775       0.28

[1='Slope']           1.3600          0.0648      20.99

R^2= 0.995, N= 4, K= 2

****************************************************************

The plot of the line that would result from the regression is as follows: