I knew most of these but fumbled the normality one.
Structure your answer around the Gauss-Markov theorem, systematically walking through each OLS assumption with its property guarantee (unbiasedness, efficiency, consistency), a named diagnostic test, and a concrete remedy. This demonstrates both theoretical depth and practical modeling experience, which is critical for a quantitative role at a financial institution like Citibank.
Pro tip: Distinguish between assumptions needed for unbiasedness (linearity, exogeneity) versus efficiency (homoscedasticity, no autocorrelation) versus consistency — this precision signals graduate-level econometric fluency and sets you apart from candidates who just recite a memorized list.
Open by stating that OLS is BLUE (Best Linear Unbiased Estimator) under the Gauss-Markov assumptions, and briefly note that consistency requires additional conditions. This frames the entire answer and shows you understand the 'why' behind the assumptions.
Address linearity in parameters, random sampling, and strict exogeneity (E[ε|X]=0), explaining that violations — such as omitted variable bias or endogeneity — lead to biased and inconsistent estimates. Mention the Ramsey RESET test for misspecification and IV/2SLS as a remedy for endogeneity.
Discuss homoscedasticity and no autocorrelation, which are required for OLS to be efficient (minimum variance). Name the Breusch-Pagan or White test for heteroscedasticity and the Durbin-Watson or Breusch-Godfrey test for autocorrelation, with remedies of robust standard errors (HC/HAC) or GLS/WLS.
Explain that perfect multicollinearity makes OLS estimates indeterminate, while high multicollinearity inflates standard errors. Mention the Variance Inflation Factor (VIF) as the diagnostic and remedies such as ridge regression, dropping correlated predictors, or PCA.
Briefly tie the assumptions to practical consequences in a financial context — for example, autocorrelation is common in time-series credit or market data, making HAC standard errors or ARIMA-based residual modeling essential. This shows you can apply theory to Citibank's actual data environment.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Structure your answer around two distinct problems — heteroscedasticity (error variance proportional to x1²) and multicollinearity (x2/x3 correlation of 0.98) — and address each with diagnosis, remediation, and impact assessment. Walk through the diagnostic tests first, then the refitting strategy, and finally quantify the downstream effects on inference metrics like standard errors, CIs, and p-values. This demonstrates systematic thinking and deep statistical fluency, which Citibank's risk-sensitive environment demands.
Pro tip: Explicitly distinguish between how heteroscedasticity inflates/deflates standard errors asymmetrically across observations versus how multicollinearity inflates standard errors uniformly for the correlated predictors — interviewers at financial firms love when candidates show they understand these are orthogonal problems requiring separate fixes, not a single combined solution.
Run a Breusch-Pagan or White test for heteroscedasticity and plot residuals vs. x1² to confirm the variance structure. Compute the Variance Inflation Factor (VIF) for x2 and x3 — a correlation of 0.98 will yield VIFs well above 10, confirming severe multicollinearity.
Since the error variance is proportional to x1², use Weighted Least Squares with weights w_i = 1/x1_i² to stabilize variance across observations. Alternatively, apply a log or Box-Cox transformation on the response if theoretically justified, then verify residual homoscedasticity post-refit.
Evaluate whether x2 and x3 are theoretically redundant — if so, drop one based on domain knowledge or use Ridge Regression to shrink correlated coefficients. If both are theoretically necessary, consider creating a composite feature (e.g., PCA component) or applying regularization, and document the trade-off between interpretability and stability.
Refit using WLS (and Ridge if needed) and compare OLS vs. corrected model on: coefficient estimates, standard errors, 95% confidence intervals, and t-statistics/p-values. With n=10,000, expect OLS standard errors for x2 and x3 to be inflated by a factor of ~7x (≈1/√(1-0.98²)) due to multicollinearity, and heteroscedasticity-corrected SEs to shift asymmetrically based on x1 magnitude.
Use cross-validation (e.g., k-fold) to confirm predictive performance hasn't degraded, and run a likelihood ratio test or compare AIC/BIC between OLS and WLS. Clearly articulate that hypothesis tests in the original OLS model were unreliable — some significant predictors may become insignificant and vice versa — which is critical in a financial modeling context where regulatory interpretability matters.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Structure your answer by first establishing OLS as the baseline and its core assumptions, then systematically walk through the specific data conditions or modeling goals that motivate each alternative method. Ground your reasoning in both statistical theory and practical business consequences, which is especially relevant in a financial context like Citibank where model interpretability and regulatory compliance matter.
Pro tip: Mention that in a banking/finance context, LASSO's automatic feature selection is valuable for regulatory model documentation and explainability, while ridge is preferred when you need to retain all predictors but control multicollinearity — this shows you understand real-world constraints beyond just model accuracy.
Briefly state when OLS is ideal — low-dimensional data, no severe multicollinearity, normally distributed errors, and homoscedasticity. This sets the baseline and shows you understand why you'd ever deviate from it.
Explain that ridge is appropriate when multicollinearity is present or when p is large relative to n, as the L2 penalty shrinks correlated coefficients together without zeroing them out, reducing variance at the cost of a small bias. Emphasize it retains all predictors, which is useful when all features are theoretically meaningful.
Describe LASSO as the go-to when you suspect only a sparse subset of features are truly predictive, since the L1 penalty drives irrelevant coefficients exactly to zero, performing automatic feature selection. This is particularly valuable in high-dimensional settings like credit risk modeling with hundreds of potential predictors.
Explain that GLMs are necessary when the response variable violates OLS's normality and constant-variance assumptions — for example, using logistic regression for binary default outcomes, Poisson regression for count data like transaction frequencies, or Gamma regression for skewed positive continuous outcomes like loan amounts.
Close by noting that the choice also depends on non-statistical factors such as interpretability requirements, regulatory scrutiny (SR 11-7 model risk guidelines at banks), computational constraints, and whether prediction accuracy or inference is the primary goal.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.