What is the purpose of robust or outlier-tolerant least squares?

• A. To reduce the influence of anomalous observations on the final solution.
• B. To maximize the influence of anomalous observations on the final solution.
• C. To simplify computation by discarding most data.
• D. To enforce exact equality constraints on all observations.

Answer: (A)

The main idea is to limit how much a few aberrant observations can pull the fitted model away from the overall pattern in the data. In ordinary least squares, residuals are squared, so a single large outlier can dominate the objective and skew the solution. Robust methods change the loss they optimize or apply weights so that large residuals contribute less, effectively downweighting outliers. This keeps the estimate anchored to the bulk of the data and makes it more resistant to anomalies. So the purpose is to reduce the influence of anomalous observations on the final solution. The other options don’t fit: robust methods don’t maximize outlier influence, they don’t discard most data, and they don’t enforce exact equality for every observation.