From 80a712e8a86cdfdc8bfb8582bf2ef0d894b98b8e Mon Sep 17 00:00:00 2001
From: Arkadiusz Kondas <arkadiusz.kondas@gmail.com>
Date: Wed, 27 Apr 2016 23:51:14 +0200
Subject: [PATCH] implement Least Squares Regression

---
 src/Phpml/Math/Statistic/Mean.php           | 18 ++++++++++
 src/Phpml/Regression/LeastSquares.php       | 29 ++++++++++++++--
 src/Phpml/Regression/Regression.php         |  4 +--
 tests/Phpml/Regression/LeastSquaresTest.php | 37 +++++++++++++++++++++
 4 files changed, 84 insertions(+), 4 deletions(-)
 create mode 100644 src/Phpml/Math/Statistic/Mean.php
 create mode 100644 tests/Phpml/Regression/LeastSquaresTest.php

diff --git a/src/Phpml/Math/Statistic/Mean.php b/src/Phpml/Math/Statistic/Mean.php
new file mode 100644
index 0000000..2716b78
--- /dev/null
+++ b/src/Phpml/Math/Statistic/Mean.php
@@ -0,0 +1,18 @@
+<?php
+
+declare (strict_types = 1);
+
+namespace Phpml\Math\Statistic;
+
+class Mean
+{
+    /**
+     * @param array $a
+     *
+     * @return float
+     */
+    public static function arithmetic(array $a)
+    {
+        return array_sum($a) / count($a);
+    }
+}
diff --git a/src/Phpml/Regression/LeastSquares.php b/src/Phpml/Regression/LeastSquares.php
index b12966f..793ae95 100644
--- a/src/Phpml/Regression/LeastSquares.php
+++ b/src/Phpml/Regression/LeastSquares.php
@@ -4,6 +4,10 @@ declare (strict_types = 1);
 
 namespace Phpml\Regression;
 
+use Phpml\Math\Statistic\Correlation;
+use Phpml\Math\Statistic\StandardDeviation;
+use Phpml\Math\Statistic\Mean;
+
 class LeastSquares implements Regression
 {
     /**
@@ -34,14 +38,35 @@ class LeastSquares implements Regression
     {
         $this->features = $features;
         $this->targets = $targets;
+
+        $this->computeSlope();
+        $this->computeIntercept();
     }
 
     /**
-     * @param array $features
+     * @param float $feature
      *
      * @return mixed
      */
-    public function predict(array $features)
+    public function predict($feature)
     {
+        return $this->intercept + ($this->slope * $feature);
+    }
+
+    private function computeSlope()
+    {
+        $correlation = Correlation::pearson($this->features, $this->targets);
+        $sdX = StandardDeviation::population($this->features);
+        $sdY = StandardDeviation::population($this->targets);
+
+        $this->slope = $correlation * ($sdY / $sdX);
+    }
+
+    private function computeIntercept()
+    {
+        $meanY = Mean::arithmetic($this->targets);
+        $meanX = Mean::arithmetic($this->features);
+
+        $this->intercept = $meanY - ($this->slope * $meanX);
     }
 }
diff --git a/src/Phpml/Regression/Regression.php b/src/Phpml/Regression/Regression.php
index 34e0b6d..f1f5c8a 100644
--- a/src/Phpml/Regression/Regression.php
+++ b/src/Phpml/Regression/Regression.php
@@ -13,9 +13,9 @@ interface Regression
     public function train(array $features, array $targets);
 
     /**
-     * @param array $features
+     * @param float $feature
      *
      * @return mixed
      */
-    public function predict(array $features);
+    public function predict($feature);
 }
diff --git a/tests/Phpml/Regression/LeastSquaresTest.php b/tests/Phpml/Regression/LeastSquaresTest.php
new file mode 100644
index 0000000..eed7537
--- /dev/null
+++ b/tests/Phpml/Regression/LeastSquaresTest.php
@@ -0,0 +1,37 @@
+<?php
+
+declare (strict_types = 1);
+
+namespace tests\Regression;
+
+use Phpml\Regression\LeastSquares;
+
+class LeastSquaresTest extends \PHPUnit_Framework_TestCase
+{
+    public function testPredictSingleFeature()
+    {
+        $delta = 0.01;
+
+        //https://www.easycalculation.com/analytical/learn-least-square-regression.php
+        $features = [60, 61, 62, 63, 65];
+        $targets = [3.1, 3.6, 3.8, 4, 4.1];
+
+        $regression = new LeastSquares();
+        $regression->train($features, $targets);
+
+        $this->assertEquals(4.06, $regression->predict(64), '', $delta);
+
+        //http://www.stat.wmich.edu/s216/book/node127.html
+        $features = [9300,  10565,  15000,  15000,  17764,  57000,  65940,  73676,  77006,  93739, 146088, 153260];
+        $targets = [7100, 15500, 4400, 4400, 5900, 4600, 8800, 2000, 2750, 2550,  960, 1025];
+
+        $regression = new LeastSquares();
+        $regression->train($features, $targets);
+
+        $this->assertEquals(7659.35, $regression->predict(9300), '', $delta);
+        $this->assertEquals(5213.81, $regression->predict(57000), '', $delta);
+        $this->assertEquals(4188.13, $regression->predict(77006), '', $delta);
+        $this->assertEquals(7659.35, $regression->predict(9300), '', $delta);
+        $this->assertEquals(278.66, $regression->predict(153260), '', $delta);
+    }
+}