What is a model in the mathematical sense

Function as the basis of the model

Let's say we want to predict the price of an apartment based on its square footage. In the simplest case, we can use a linear model: $ŷ = w x + b$

This is a fully-fledged model. It says, "Price ($ŷ$) is approximately equal to area ($x$) multiplied by some coefficient ($w$), plus some shift ($b$)."

If you rewrite this in PHP, you get almost trivial code:

Example of use:


<?php

// Simple linear model: ŷ = w * x + b
class LinearModel {
    // Slope (weight) of the linear function
    public float $w;

    // Intercept (bias) of the linear function
    public float $b;

    // Initialize model parameters w and b
    public function __construct(float $w, float $b) {
        $this->w = $w;
        $this->b = $b;
    }

    // Make a prediction for a single input value x
    public function predict(float $x): float {
        return $this->w * $x + $this->b;
    }
}