#robustness

Question 1: Single choice

mediumAI-checkedLinear Models & Regularization

You fit linear regression to data in which one label was mistyped as $y_5 = 10000$ . Compare the squared loss $\frac{1}{2}(\hat y - y)^2$ with the absolute loss $|\hat y - y|$ . Which statement is correct?

The outlier's squared-loss gradient grows with its residual and dominates; absolute loss caps it at 11
Both losses are affected equally, because the outlier's residual is exactly the same under both of them2
Absolute loss is affected more, because $|r|$ exceeds $\frac{1}{2}r^2$ for large residuals3
Squared loss ignores the outlier, because the gradient of the loss is zero at its minimum4

Timed test