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Machine Learning · Hard

Deriving OLS

Original interpretation · Match confidence: medium

Citadel · Topic guidance
About this question’s source match

The title with subcategory Linear Models specifies the method assessed. This is an original worked scenario using the standard method documented in the public reference. The inaccessible Trading Interview statement has not been verified; numerical data, conventions and framing are newly authored rather than claimed source reproductions.

Derive ordinary least squares for y=X beta+epsilon by minimizing ||y-X beta||². State the full-column-rank condition. For observations (x,y)=(0,1),(1,2),(2,2), with an intercept, compute the fitted intercept, slope, residuals and residual sum of squares.

Assumptions and constraints

  • All data and timing conventions are those explicitly stated in the prompt.
  • Show intermediate calculations; use the specified normalization and boundary conventions.

Examples

x=[0,1,2], y=[1,2,2]
→ beta=[7/6,1/2]

Orthogonal residuals verify the normal equations.

Company preparation relevance

These links connect this exercise to companies’ public examples or stated interview topics. They do not establish that a company asked this exact Learnr question.

  • Citadel

    Official topic guidance

    Topic overlap: least-squares modeling “Deriving OLS”, Gaussian parameter estimation “Maximum Likelihood Estimation for a Gaussian” and dependence/variance “Variance of Two Variables” practice the mathematical/statistical intuition and data-modeling skills named in the FAQ.

    Candidate FAQs: Quantitative Research ↗
    Evidence scope and uncertainty

    Research skill preparation. The FAQ describes candidate strengths and work rather than publishing these particular interview exercises.

    These are Learnr-authored exercises selected for topic overlap. The company does not name these catalogue titles or verify that these exact questions were asked.

References

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Catalogue metadata captured 2026-10-12. Metadata source.