# Source: content/notes/ml/linear-models.md
# Independent CPU example; use the curriculum environment.
# See /notes/ml/#example-environment or /notes/deep-learning/#example-environment.

import numpy as np
from sklearn.linear_model import LinearRegression
from sklearn.metrics import mean_squared_error

X = np.array([0.0, 1.0, 2.0])[:, None]
y = np.array([1.0, 2.0, 2.0])
A = np.column_stack([np.ones(len(X)), X])
beta, _, rank, singular = np.linalg.lstsq(A, y, rcond=None)
model = LinearRegression().fit(X, y)
pred = model.predict(X)
assert rank == 2
assert np.allclose(beta, [7 / 6, 1 / 2])
assert np.allclose(A @ beta, pred)
assert np.allclose(A.T @ (y - pred), 0, atol=1e-12)
assert np.isclose(mean_squared_error(y, pred), 1 / 18)
print("Intercept and slope:", beta)
print("Residuals:", y - pred)
print("Singular values:", singular)