Full Linear Regression Training Loop

Implement:

def train_linear_regression(
    input: np.ndarray,
    target: np.ndarray,
    lr: float,
    epochs: int,
) -> tuple[np.ndarray, np.ndarray]:
    """
    input:  shape (batch_size, in_features)
    target: shape (batch_size,), one target value per sample
    lr: learning rate
    epochs: number of full-batch gradient-descent steps

    Returns:
        weight: shape (1, in_features)
        bias: shape (1,)
    """

Your function should:

1. Initialize weight to zeros, shape (1, in_features), and bias to zeros, shape (1,). One output feature, matching target.
2. Reshape target once, up front, to (batch_size, 1), the shape 01-hypothesis-function's linear actually produces, never leave it (batch_size,) and let it silently broadcast against a prediction later.
3. Repeat, epochs times: compute gradients with 03-mse-gradient's mse_gradient, then apply one step with 04-gd-step's gd_step.
4. Return the final weight, bias.

Use the functions you already implemented in the earlier questions rather than reimplementing their logic inside the training loop.