Linear Regression

Implement linear regression trained with gradient descent.

Functions to implement

1. predict(X, weights, bias)

Make predictions using linear model.

• Input: Features X (2D), weights (list), bias (float)
• Output: Predictions (list)

2. compute_loss(y_true, y_pred)

Compute mean squared error loss.

• Input: True values and predictions
• Output: MSE loss value

3. compute_gradients(X, y_true, y_pred)

Compute gradients of MSE with respect to weights and bias.

• Input: Features, true values, predictions
• Output: (weight_gradients, bias_gradient)

4. train(X, y, lr, n_epochs)

Train linear regression using gradient descent.

• Input: Features X, targets y, learning rate, number of epochs
• Output: (weights, bias, loss_history)

Examples

# Simple 1D regression: y = 2x + 1
X = [[1], [2], [3], [4]]
y = [3, 5, 7, 9]

weights, bias, losses = train(X, y, lr=0.1, n_epochs=100)
# weights ≈ [2.0], bias ≈ 1.0

predictions = predict(X, weights, bias)
# predictions ≈ [3, 5, 7, 9]

Notes

• Initialize weights to zeros
• X is (n_samples, n_features)
• Use batch gradient descent (all samples per update)