Sure, I can help you with that! Here's a simple implementation of linear regression for predicting house prices using Python and NumPy. I'll provide line-by-line explanations for each part of the code:
import numpy as np
# Generate some sample data for demonstration
# In a real-world scenario, you would load your dataset
# X represents the feature (e.g., house size)
# y represents the target variable (e.g., house price)
np.random.seed(42)
X = 2 * np.random.rand(100, 1)
y = 4 + 3 * X + np.random.randn(100, 1)
# Add a column of ones to the feature matrix X for the bias term
X_b = np.c_[np.ones((100, 1)), X]
# Initialize random values for the slope (theta1) and intercept (theta0)
theta = np.random.randn(2, 1)
# Set the learning rate and number of iterations
learning_rate = 0.1
num_iterations = 1000
# Perform gradient descent to update theta
for iteration in range(num_iterations):
# Calculate the predicted values (y_pred) using the current theta values
y_pred = X_b.dot(theta)
# Calculate the errors
errors = y_pred - y
# Calculate the gradients (partial derivatives) for theta0 and theta1
gradients = 2 / len(X) * X_b.T.dot(errors)
# Update theta using gradient descent
theta -= learning_rate * gradients
# Print the final theta values (intercept and slope)
print("Intercept:", theta[0][0])
print("Slope:", theta[1][0])
Explanation of the code:
1. Import the required NumPy library.
2. Generate sample data for demonstration purposes. Replace this with your actual dataset.
3. Add a column of ones to the feature matrix X to account for the bias term in the linear equation.
4. Initialize random values for the slope (theta1) and intercept (theta0).
5. Set the learning rate and the number of iterations for gradient descent.
6. Perform gradient descent for the specified number of iterations.
7. Calculate the predicted house prices (y_pred) using the current theta values and the feature matrix X_b.
8. Calculate the errors by subtracting the actual house prices (y) from the predicted prices (y_pred).
9. Calculate the gradients (partial derivatives) for both theta0 and theta1 using the feature matrix X_b and the errors.
10. Update the theta values using the gradient descent update rule.
11. Print the final values of theta0 and theta1, which represent the intercept and slope of the linear regression model.
Remember, this is a simplified example. In practice, you might need to add more features, preprocess the data, split it into training and testing sets, and implement techniques to prevent issues like overfitting.
