Implement Gradient Descent for Linear Regression (MSE) and debug convergence

Implement linear regression trained by gradient descent. Given X of shape (n_samples, n_features) and y of shape (n_samples,), use the model: y_pred = X @ w + b. Use Mean Squared Error: MSE(w,b) = (1/n) * sum_i (y_i - (x_i^T w + b))^2. Requirements: Derive and implement gradients for w and b and update them with gradient descent. Inputs include learning rate lr and max_iter. Implement early stopping (e.g., stop if loss improvement < tol, optionally with patience). Be able to debug non-converging code (common issues: using SSE instead of MSE, missing the mean, missing factors like 2/n, not updating bias, wrong broadcasting/shapes, overly large learning rate). Constraints: n_samples up to 1e5, n_features up to 200. Example Input X=[[1],[2],[3]] y=[2,4,6] lr=0.1 max_iter=2000 tol=1e-12 patience=20 Output w≈[2.0], b≈0.0