Calculate quadratic polynomial regression

quadratic_polynom.php

<?php
function quadraticRegression($dataPoints) {
    $sumX = 0;
    $sumX2 = 0;
    $sumX3 = 0;
    $sumX4 = 0;
    $sumY = 0;
    $sumXY = 0;
    $sumX2Y = 0;
    
    $n = count($dataPoints);
    
    foreach ($dataPoints as $dataPoint) {
        $x = $dataPoint[0];
        $y = $dataPoint[1];
        
        $sumX += $x;
        $sumX2 += pow($x, 2);
        $sumX3 += pow($x, 3);
        $sumX4 += pow($x, 4);
        $sumY += $y;
        $sumXY += $x * $y;
        $sumX2Y += pow($x, 2) * $y;
    }
    
    $matrix = [
        [$sumX4, $sumX3, $sumX2],
        [$sumX3, $sumX2, $sumX],
        [$sumX2, $sumX, $n]
    ];
    
    $vector = [
        $sumX2Y,
        $sumXY,
        $sumY
    ];
    
    $coefficients = solveLinearSystem($matrix, $vector);
    
    return $coefficients;
}

function solveLinearSystem($matrix, $vector) {
    $n = count($matrix);
    for ($i = 0; $i < $n; $i++) {
        $pivot = $matrix[$i][$i];
        
        for ($j = $i; $j < $n; $j++) {
            $matrix[$i][$j] /= $pivot;
        }
        $vector[$i] /= $pivot;
        
        for ($k = 0; $k < $n; $k++) {
            if ($k != $i) {
                $factor = $matrix[$k][$i];
                
                for ($j = $i; $j < $n; $j++) {
                    $matrix[$k][$j] -= $factor * $matrix[$i][$j];
                }
                $vector[$k] -= $factor * $vector[$i];
            }
        }
    }
    
    return array_slice($vector, 0, $n);
}

$dataPoints = [
    [1, 3],
    [2, 8],
    [3, 12],
    [4, 20],
    [5, 30]
];

$coefficients = quadraticRegression($dataPoints);

$a = $coefficients[0];
$b = $coefficients[1];
$c = $coefficients[2];

echo "The quadratic polynomial is: y = $a * x^2 + $b * x + $c";