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線形回帰の単回帰をPHPで実装

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線形回帰の単回帰をPHPで実装してみた。

例のxとyの間に、y=a+bx+eというモデルで示せる関係を持てば、ある程度のxとyのペアの配列から、最小二乗分析によって最小二乗モデルを計算することができる。つまり、条件付き期待値をy=A+Bxとして表示できる。

コードは下の通りである。

/**
* Copyright 2015 Sinri Edogawa.
*/
class LinearRegression
{
	private $xs;
	private $ys;
	private $element_count;

	private $a;
	private $b;
	
	function __construct()
	{
		$this->xs=array();
		$this->ys=array();
		$this->element_count=0;
	}

	public function addElement($x,$y){
		$this->xs[]=$x;
		$this->ys[]=$y;
		$this->element_count+=1;
	}

	//y=a+bx
	public function getConstBase(){
		return $this->a;
	}
	public function getParamFactor(){
		return $this->b;
	}

	public function computeLR(){
		if($this->element_count<=0)return false;
		if($this->element_count!=count($this->xs) || $this->element_count!=count($this->ys))return false;
		$x_sum=0;
		$y_sum=0;
		for ($i=0; $i < $this->element_count; $i++) { 
			$x_sum+=$this->xs[$i];
			$y_sum+=$this->ys[$i];
		}
		$x_ave=1.0*$x_sum/$this->element_count;
		$y_ave=1.0*$y_sum/$this->element_count;

		$up=0;
		$down=0;

		for ($i=0; $i < $this->element_count; $i++) { 
			$up+=($this->xs[$i]-$x_ave)*($this->ys[$i]-$y_ave);
			$down+=($this->xs[$i]-$x_ave)*($this->xs[$i]-$x_ave);
		}	
		if($down==0)return false;
		$this->b=$up/$down;
		$this->a=$y_ave-$x_ave*$this->b;
		return true;
	}
}

以下は使用例である。

$LR=new LinearRegression();

//xとyのペアを繰り返して記録する
$LR->addElement($x,$y);

$lr_done=$LR->computeLR();
if($lr_done){
	echo "y=".$LR->getConstBase()."+".$LR->getParamFactor()."x";
}else{
	echo "FAILED";
}
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