I listed the usual suspects: linearity, independence, homoscedasticity, normality of errors, no perfect multicollinearity.
Start by distinguishing between assumptions needed for unbiasedness (linearity, exogeneity, no perfect collinearity) and those needed for valid inference (homoskedasticity, normality of errors, independence). Then explain each assumption's role and consequences if violated, and briefly mention diagnostics and remedies.
Pro tip: Emphasize that while normality is often cited, it's only required for small-sample inference; with large samples, the CLT makes OLS inference robust to non-normality. This shows you understand the practical nuances beyond textbook lists.
Explain that OLS assumptions serve two purposes: ensuring unbiased coefficient estimates (model validity) and ensuring valid standard errors, confidence intervals, and hypothesis tests (inference validity).
Cover linearity in parameters, exogeneity (zero conditional mean of errors), no perfect multicollinearity, and correct specification. Mention that these are the Gauss-Markov assumptions for unbiasedness (except normality).
Discuss homoskedasticity (constant error variance), independence of errors (no autocorrelation), and normality of errors (for exact t- and F-tests in small samples). Note that the Gauss-Markov theorem requires homoskedasticity and independence for BLUE.
For each assumption, briefly state what happens if violated: e.g., omitted variable bias, inefficient estimates, biased standard errors, invalid test statistics.
Highlight common checks (residual plots, Breusch-Pagan, Durbin-Watson, VIF) and possible fixes (robust standard errors, transformations, instrumental variables).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Talked through residual plots, Q-Q plots for normality, VIF for multicollinearity, Durbin-Watson for autocorrelation.
Start by outlining the four key OLS assumptions (linearity, independence, homoscedasticity, normality of residuals) and then explain how you would check each one using both graphical and statistical methods. Emphasize a systematic diagnostic process, from exploratory plots to formal tests, and discuss potential remedies if violations are found.
Pro tip: Focus on the practical implications of violations rather than just listing tests—explain how each violation affects coefficient estimates, standard errors, and predictions, and when it's acceptable to proceed despite minor issues.
Plot residuals vs. fitted values or each predictor to detect non-linear patterns. Consider adding polynomial terms or transformations if curvature is evident.
Use residual plots against time or order of data collection, or run Durbin-Watson test for autocorrelation. For clustered data, consider mixed-effects models.
Inspect residual plots for funnel shapes and apply Breusch-Pagan or White tests. If violated, use robust standard errors or weighted least squares.
Create Q-Q plots and run Shapiro-Wilk or Kolmogorov-Smirnov tests. For large samples, normality is less critical due to CLT, but outliers may still be problematic.
If violations are found, discuss transformations, robust methods, or alternative models. Always assess the impact on your specific analysis goals.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Said things like robust standard errors for heteroscedasticity, transformations for non-linearity, GLS for autocorrelation, ridge or dropping correlated features for multicollinearity.
Start by briefly listing the key OLS assumptions (linearity, independence, homoscedasticity, normality, no multicollinearity) and then systematically discuss remedies for each violation. Emphasize that the choice of remedy depends on the goal (inference vs. prediction) and the nature of the violation, and mention that sometimes the best approach is to use a different model.
Pro tip: Always connect the remedy to the business context and the model's purpose—interviewers at BNP care about practical impact, so explain how the fix improves interpretability or predictive performance. Also, mention that you would validate the remedy using diagnostic plots and metrics.
Diagnose which assumption is violated using residual plots, statistical tests (e.g., Breusch-Pagan, Durbin-Watson, VIF), and domain knowledge. Clearly state the violation before jumping to solutions.
Explain how the violation affects the model: e.g., heteroscedasticity biases standard errors, affecting inference but not predictions. This determines whether a remedy is necessary and which one to choose.
For each violation, list common fixes: transformations (log, Box-Cox) for non-linearity/heteroscedasticity, robust standard errors for heteroscedasticity, weighted least squares, adding polynomial terms, removing or combining correlated features, using regularized regression (Ridge/Lasso) for multicollinearity, and generalized least squares for autocorrelation.
If assumptions are severely violated, suggest switching to models that don't require them, such as tree-based models, GLMs, or non-parametric methods. Highlight trade-offs in interpretability and complexity.
After applying a remedy, re-check diagnostics and compare model performance (e.g., AIC, cross-validation). Emphasize that addressing violations is an iterative process.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.