# Explain the least squares method Explain the **least squares** method: - What optimization problem does ordinary least squares (OLS) solve? - Derive the closed-form solution for linear regression in matrix form. - What assumptions are typically made (noise model, full rank, independence)? - How do numerical stability and regularization (e.g., ridge regression) change the solution/implementation? ### Constraints & Assumptions - Preserve the scope, facts, inputs, and requested outputs from the prompt above. - If the prompt leaves a detail unspecified, state a reasonable assumption before relying on it. - Keep the answer interview-ready: concise enough to present, but concrete enough to implement or evaluate. ### Clarifying Questions to Ask - Clarify the task, data shape, labels, constraints, and evaluation metric. - State assumptions behind the math or modeling technique you choose. - Connect theory to practical training, debugging, and deployment implications. ### What a Strong Answer Covers - Correct definitions and formulas where the prompt requires them. - A practical explanation of how the method behaves on real data. - Trade-offs, failure modes, diagnostics, and mitigation strategies. - Evaluation choices that match the product or modeling objective. ### Follow-up Questions - How would noisy labels, class imbalance, or distribution shift affect the answer? - What would you monitor after deployment? - Which baseline would you compare against first?