Full Linear Regression Training Loop

The problem, from first principles

01-hypothesis-function, 02-mse-loss, 03-mse-gradient, and 04-gd-step each solve one part of fitting a line. A model becomes useful only when those parts run repeatedly: make predictions, measure their error, find which direction reduces it, and move the parameters. This question wires that full-batch loop together without losing the single-output shapes established earlier.

From theory to code

Implement train_linear_regression. Initialize the parameters once, turn the one-dimensional targets into the one-column form expected by the earlier helpers, then use their gradient and update operations for each epoch.

Constraints

• input has shape (batch_size, in_features) and target has shape (batch_size,).
• Return weight with shape (1, in_features) and bias with shape (1,).
• Start both returned parameters at zero before any updates.
• Reshape target once to (batch_size, 1) before computing gradients.
• Run exactly epochs full-batch gradient-descent steps; epochs=0 returns the zero initialization.
• Reuse mse_gradient and gd_step; do not reimplement either calculation.

Hints

Open one at a time. Each gives away a little more than the last.