Generalized Linear Regression (GLR) with Polynomial Order 2: Python Implementation

Here's how you can solve the Generalized Linear Regression (GLR) problem with a polynomial order of 2 and find the predicted value for x = [1, 1] using Python:

import numpy as np

# Training data
X = np.array([[1, 0], [2, 1], [3, 2], [2, 6]])
y = np.array([1, 0, 2, 1])

# Polynomial feature expansion
X_poly = np.column_stack((X, X[:, 0]**2, X[:, 0]*X[:, 1], X[:, 1]**2))

# Solve GLR using numpy's lstsq function
w, _, _, _ = np.linalg.lstsq(X_poly, y, rcond=None)

# Predict the value for x = [1, 1]
x_pred = np.array([1, 1])
x_pred_poly = np.concatenate((x_pred, [x_pred[0]**2, x_pred[0]*x_pred[1], x_pred[1]**2]))
y_pred = np.dot(w, x_pred_poly)

print('Predicted value for x = [1, 1]:', y_pred)

Running the above code will give you the predicted value for x = [1, 1] using GLR with a polynomial order of 2.