Weighted RMSE

Difficulty: Medium · Concept: Linear Regression — The Cost Function

A harder variant of Mean Squared Error From Scratch: real training data is often not equally trustworthy — some examples might be known to be noisier, less representative, or more expensive to get wrong, and a per-example weight lets the loss reflect that directly. This also switches from MSE to RMSE (take the square root at the end) — same information, but back in the original units of the target, which is what makes an error number actually interpretable ("off by 2 degrees," not "off by 4 degrees-squared").

$\text{weighted RMSE} = \sqrt{\frac{\sum_i w_i (\hat{y}^{(i)} - y^{(i)})^2}{\sum_i w_i}}$

The genuine edge case: if every weight is 0 (or the weights list is otherwise degenerate), the denominator is 0 and the result is undefined — a real implementation needs to raise, not silently produce a ZeroDivisionError or a nan.

Your task: implement weighted_rmse(y_true, y_pred, weights). Raise ValueError if the three lists aren't the same length, or if the weights sum to 0.

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