Citadel·Data Scientist·Technical Phone Screen·Senior

SeniorPrefer not to say

Jun 2026

Summary

Citadel data scientist interview with a deep dive into OLS diagnostics. One question but it had a lot of moving parts and I definitely didn't nail all of them.

Questions Asked (1)

In OLS regression, how do you define outliers, high-leverage points, and influential observations? Walk through how Cook's distance is derived, how it connects to leverage and studentized residuals, how you'd build a diagnostic workflow to detect each type, what happens to your conclusions if you drop the most influential point, what robust alternatives exist, and how you'd justify any decisions about these points in a model review.

Technical Trade-offsData ModelingRoot Cause Analysis

Author's notes

This question is basically three questions stapled together and I treated it that way, which was probably a mistake.

Create a free account to read the full note

AI HintsAI Generated

Suggested Approach

Start by clearly defining outliers, high-leverage points, and influential observations, emphasizing their distinct roles in regression diagnostics. Then walk through Cook's distance derivation, linking it to leverage and studentized residuals, and outline a diagnostic workflow. Finally, discuss the impact of dropping influential points, robust alternatives, and how to justify decisions in a model review.

Pro tip: Emphasize that influential points are not necessarily outliers or high-leverage points alone, but a combination of both; always assess influence using multiple diagnostics and consider the context of the data before making decisions.

1. Define the concepts

Clearly distinguish outliers (unusual Y values), high-leverage points (unusual X values), and influential observations (disproportionately affect model coefficients).

2. Derive Cook's distance

Explain Cook's distance as a measure of influence, derived from the change in predicted values when removing an observation, and show its formula involving leverage and studentized residuals.

3. Build a diagnostic workflow

Outline a step-by-step process: compute leverage (hat values), studentized residuals, and Cook's distance; use thresholds and plots to flag potential issues.

4. Assess impact and alternatives

Discuss how dropping the most influential point can change conclusions, and present robust alternatives like robust regression, trimming, or Winsorizing.

5. Justify decisions in model review

Explain how to document and justify any removal or retention of points, considering domain knowledge, sensitivity analysis, and reproducibility.

Key Points to Mention

Cook's distance formula: D_i = (e_i^2 / (p * MSE)) * (h_ii / (1 - h_ii)^2), where e_i is residual, h_ii is leverage, p is number of predictors.
Leverage (hat values) measures how far an observation's predictor values are from the mean; high leverage points have h_ii > 2p/n or 3p/n.
Studentized residuals are residuals divided by their estimated standard deviation, useful for detecting outliers.
Influential points often have high leverage and large residuals; Cook's distance combines both.
Dropping an influential point can drastically change coefficients, standard errors, and significance, so sensitivity analysis is crucial.
Robust alternatives: robust regression (e.g., Huber, Tukey), quantile regression, or using weighted least squares.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.