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Seemed like a warmup but they actually wanted precision.
Start with a clear, concise definition of regression as a supervised learning technique for predicting continuous outcomes. Then explain that linear regression specifically models the linear relationship between input features and a continuous target by fitting a line (or hyperplane) that minimizes the error between predictions and actual values. Use a simple example to illustrate, and connect it to how banks might use it for risk assessment or forecasting.
Pro tip: Emphasize that linear regression captures the conditional mean of the target given the features, and mention that it assumes a linear relationship, independence of errors, and homoscedasticity—showing you understand both its power and limitations. This demonstrates maturity and an ability to assess trade-offs, which is crucial in a banking context.
Explain that regression is a type of supervised learning used to predict a continuous output variable based on one or more input variables. It models the relationship between dependent and independent variables.
Describe linear regression as a specific regression model that assumes a linear relationship between the inputs and the output. It finds the best-fitting straight line (or hyperplane) by minimizing the sum of squared errors.
State that linear regression captures the conditional mean of the target variable given the features, i.e., the expected value of the output for given inputs. It quantifies the average change in the target associated with a one-unit change in a feature, assuming other features are held constant.
Mention key assumptions: linearity, independence of errors, homoscedasticity, and normality of errors. Note that violations can lead to biased or inefficient estimates, and that linear regression may not capture complex non-linear relationships.
Give a relevant example, such as predicting loan default probability based on income and credit score, or forecasting housing prices. This shows application in a banking context.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
I listed most of them but fumbled the exogeneity condition.
Start by defining OLS and its goal of minimizing squared residuals, then systematically list the classical assumptions (linearity, exogeneity, homoskedasticity, no autocorrelation, full rank, normality) and briefly explain each. Conclude by discussing the consequences when assumptions are violated and how they relate to real-world data modeling, especially in a financial context.
Pro tip: Emphasize that while normality is not required for unbiasedness or consistency, it is needed for exact inference in small samples; in large samples, asymptotic properties often suffice. This shows depth and practical awareness.
Briefly state that OLS estimates coefficients by minimizing the sum of squared residuals, providing the best linear unbiased estimator under certain conditions.
Enumerate the key assumptions: linearity in parameters, random sampling, no perfect multicollinearity, zero conditional mean (exogeneity), homoskedasticity, and no autocorrelation. Optionally include normality for inference.
For each assumption, give a one-sentence explanation of what it means and why it matters (e.g., exogeneity ensures unbiasedness, homoskedasticity ensures efficient standard errors).
Mention what happens if assumptions fail: omitted variable bias, inefficient estimates, invalid standard errors, etc., and briefly note potential remedies.
Connect the assumptions to real-world data challenges, such as heteroskedasticity in financial data, and how robust methods or alternative models can address them.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
This is the one I was most nervous about and it actually went fine.
Start by clearly stating the OLS objective: minimize the sum of squared residuals. Then derive the normal equations using matrix calculus, and solve for the coefficient vector to obtain the closed-form estimator. Emphasize the assumptions and conditions for the solution to exist.
Pro tip: Connect the derivation to practical implications, such as computational efficiency and numerical stability, and mention how this applies to large-scale data problems in banking.
State the linear regression model y = Xβ + ε and define the OLS objective as minimizing the residual sum of squares (RSS) = (y - Xβ)^T (y - Xβ).
Expand the RSS expression to y^T y - 2β^T X^T y + β^T X^T X β, which is a quadratic function in β.
Compute the gradient of RSS with respect to β: ∂RSS/∂β = -2X^T y + 2X^T X β, and set it to zero to obtain the normal equations.
Solve X^T X β = X^T y for β, yielding the closed-form estimator β_hat = (X^T X)^{-1} X^T y, assuming X^T X is invertible.
Mention the assumptions (e.g., full column rank of X) and practical considerations like using pseudo-inverse or regularization when X^T X is singular.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Talked about variance inflation and the instability of coefficient signs, which landed well.
Start by defining multicollinearity and explaining its impact on regression coefficients and model interpretability. Then discuss detection methods and a range of solutions, emphasizing trade-offs and practical considerations for a banking context.
Pro tip: In banking, multicollinearity often arises from correlated financial indicators; instead of automatically dropping variables, consider domain-driven feature engineering or regularization to retain predictive power while ensuring model stability and regulatory interpretability.
Explain that multicollinearity occurs when two or more predictor variables in a regression model are highly correlated, leading to unstable coefficient estimates.
Discuss how it inflates standard errors, makes coefficients sensitive to small changes in the model, and complicates interpretation of individual predictor effects.
Mention methods like correlation matrices, Variance Inflation Factor (VIF), and condition indices to identify problematic variables.
List options such as removing one of the correlated variables, combining them via PCA or factor analysis, using regularization (ridge, lasso), or collecting more data.
Emphasize that the best approach depends on the goal: prediction vs. inference, and in banking, consider regulatory requirements and interpretability.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by defining Lasso (L1) and Ridge (L2) regularization, then contrast their mathematical forms, geometric shapes, and probabilistic interpretations. Explain when to choose each based on feature sparsity, multicollinearity, and prediction goals, and tie it back to a practical example relevant to banking or software engineering.
Pro tip: Mention that in practice, Elastic Net often combines both, and that Lasso's sparsity can be a double-edged sword with correlated features—this shows you understand real-world trade-offs beyond textbook definitions.
Briefly state that Lasso adds an L1 penalty (sum of absolute weights) and Ridge adds an L2 penalty (sum of squared weights) to the loss function.
Describe how L1 constraint forms a diamond (or polytope) shape leading to sparse solutions at vertices, while L2 forms a circle/sphere resulting in small but non-zero coefficients.
Note that Lasso corresponds to a Laplace prior on coefficients, while Ridge corresponds to a Gaussian prior, linking to Bayesian interpretation.
Choose Lasso when you suspect many features are irrelevant and want feature selection; choose Ridge when features are correlated or you want to keep all features with shrinkage.
Relate to software engineering and banking: e.g., Lasso for high-dimensional sparse data like transaction features, Ridge for multicollinear financial indicators.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.