How can I implement advanced linear regression using NumPy?

How can I implement advanced linear regression using NumPy?

You can implement advanced linear regression in NumPy by using matrix operations. Would you like a code example?

Yes, please provide a code example.

Here's a simple example:

import numpy as np

# Sample data
X = np.array([[1, 1], [1, 2], [2, 2], [2, 3]])
y = np.dot(X, np.array([1, 2])) + 3

# Adding a bias term
X_b = np.c_[np.ones((X.shape[0], 1)), X]  # add x0 = 1 to each instance

# Calculating theta using the Normal Equation
theta_best = np.linalg.inv(X_b.T.dot(X_b)).dot(X_b.T).dot(y)
print(theta_best)

What does the Normal Equation do in this context?

The Normal Equation provides a way to compute the optimal parameters (theta) for linear regression by minimizing the cost function.

Are there any limitations to using the Normal Equation?

Yes, the Normal Equation can be computationally expensive for large datasets and may not perform well if the feature matrix is not full rank.