الانحدار الخطي واللوجستي

import numpy as np
from sklearn.datasets import make_regression

class="tok-comment"># ── Sample data ────────────────────────────────────────────────────────
X_raw, y = make_regression(n_samples=class="tok-num">200, n_features=class="tok-num">5, noise=class="tok-num">10, random_state=class="tok-num">42)
X = np.c_[np.ones(len(X_raw)), X_raw]   class="tok-comment"># prepend bias column
lam = class="tok-num">0.1                                 class="tok-comment"># Ridge regularisation strength

class LinearRegression:
    def __init__(self, lr=class="tok-num">0.01, n_iter=class="tok-num">1000):
        self.lr, self.n_iter = lr, n_iter

    def fit(self, X, y):
        n, p = X.shape
        self.beta = np.zeros(p)
        for _ in range(self.n_iter):
            y_hat = X @ self.beta
            residuals = y - y_hat
            grad = -(class="tok-num">2/n) * X.T @ residuals
            self.beta -= self.lr * grad
        return self

    def predict(self, X):
        return X @ self.beta

class="tok-comment"># Demo
model = LinearRegression(lr=class="tok-num">0.01, n_iter=class="tok-num">1000).fit(X, y)
print(class="tok-str">"GD beta:", model.beta[:class="tok-num">3].round(class="tok-num">2))

class="tok-comment"># Closed-form (Normal Equation):
beta_ols = np.linalg.solve(X.T @ X, X.T @ y)
class="tok-comment"># Ridge (L2 regularization):
p = X.shape[class="tok-num">1]
beta_ridge = np.linalg.solve(X.T @ X + lam * np.eye(p), X.T @ y)
print(class="tok-str">"OLS beta:  ", beta_ols[:class="tok-num">3].round(class="tok-num">2))
print(class="tok-str">"Ridge beta:", beta_ridge[:class="tok-num">3].round(class="tok-num">2))