Univariate Linear Regression using the solution of the Normal Equations for the Least Square problem.

main.py

import numpy as np

x = np.array([-0.5, -0.43, -0.23, 0.12, 0.40, 0.71, 1]).reshape(-1, 1)
y = np.array([-2, -0.2, 0.1, 0.83, 1.4, 0.98, 2.2]).reshape(-1, 1)

# Add a column of ones to the input data for the intercept term
X = np.concatenate((np.ones_like(x), x), axis=1)

xxT = X.T.dot(X)
inv = np.linalg.inv(xxT)
xTy = X.T.dot(y)

w = inv @ xTy

y_pred = X @ w
mse_train = np.mean((y - y_pred) ** 2)

print("Mean Squared Error (MSE) on train:", mse_train)

x_test = np.array([-1.02, 0.56, 1.2]).reshape(-1, 1)
# Add a column of ones to the input data for the intercept term
X = np.concatenate((np.ones_like(x), x), axis=1)

xxT = X.T.dot(X)
inv = np.linalg.inv(xxT)
xTy = X.T.dot(y)

w = inv @ xTy

y_pred = X @ w

print("Predictions of y in test: ", y_pred[:, 0])