Linear Regression Interview Study Roadmap (Practical Timeline)

🤖 Core ML Fundamentals

1.1: Master the Core Theory and Assumptions

• Understand the mathematical formulation: $y = X\beta + \epsilon$.
• Be able to explain the role of each component:
  • $X$: features matrix
  • $\beta$: coefficients
  • $\epsilon$: irreducible error
• Grasp the OLS (Ordinary Least Squares) objective: minimizing $|y - X\beta|^2$.
• Internalize the assumptions: Linearity, Independence, Homoscedasticity, Normality of errors.

Deeper Insight: Interviewers probe whether you understand what happens when assumptions break. For instance: heteroscedasticity → unreliable variance estimates, multicollinearity → unstable coefficients. Be able to discuss detection (residual plots, VIF) and mitigation (transformations, regularization).

1.2: Cost Function and Optimization

• Define Mean Squared Error (MSE): $\text{MSE} = \frac{1}{n}\sum (y_i - \hat{y}_i)^2$.
• Compare MSE vs MAE: sensitivity to outliers, optimization behavior.
• Walk through Gradient Descent: initialization, iterative coefficient updates, convergence criteria.
• Explain learning rate trade-offs.

Probing Question: “What happens if your learning rate is too high or too low?” Be ready to discuss divergence, slow convergence, and practical tuning methods like learning rate schedules or adaptive optimizers.

1.3: Scratch Implementation in Python

• Implement fit and predict methods using NumPy.
• Explicitly map code lines to math formulas (gradient calculation and weight update).
• Practice debugging your gradient descent by printing loss every iteration.

Probing Question: Expect questions like “How would you speed up a naive Python loop?” Answer with vectorization, batching strategies, and when to use stochastic vs. batch gradient descent.

📊 Statistical Intuition

2.1: R-squared and Adjusted R-squared

• Understand R-squared as “proportion of variance explained.”
• Know why Adjusted R-squared penalizes unnecessary features.

Probing Question: “Can R-squared decrease when adding more features?” (No, but Adjusted R-squared can). Interviewers use this to test whether you understand overfitting risks.

2.2: p-values and Confidence Intervals

• Learn how hypothesis testing applies to coefficients.
• Be ready to explain what a p-value tells you in regression.

Deeper Insight: At scale, strict significance testing often matters less. What matters is stability of coefficients and predictive performance.

⚡ Practical Trade-offs

3.1: Regularization (Ridge, Lasso, ElasticNet)

• Understand L2 (Ridge) vs L1 (Lasso) penalties.
• Explain why Lasso leads to feature selection (sparsity).
• Be able to write the modified cost functions.

Probing Question: “If you have thousands of sparse features, which penalty would you prefer and why?” (Hint: L1 encourages sparsity, making it a better fit).

3.2: Feature Scaling

• Know why scaling matters for gradient descent convergence and regularization penalties.
• Be ready to show how to standardize features.

Deeper Insight: Scaling doesn’t matter for OLS closed-form solutions, but it’s critical in iterative optimization and when penalties are applied.

3.3: Outliers and Robust Regression

• Be able to explain how outliers distort OLS estimates.
• Discuss robust alternatives (Huber loss, RANSAC).

Probing Question: “If your regression is heavily skewed by a single point, how would you detect and address it?” Expect to talk about residual analysis and robust fitting.

🛠️ MLOps & Engineering Perspective

4.1: Feature Pipelines

• Learn to build reproducible feature pipelines.
• Stress test your regression with missing values, categorical encoding, and data drift.

Probing Question: “What happens if your training pipeline normalizes features differently from your serving pipeline?” (Silent prediction errors—a high-signal question).

4.2: Monitoring and Drift Detection

• Define what metrics to track post-deployment (prediction distributions, residuals, input drift).
• Be able to describe retraining triggers.

Deeper Insight: Regression may degrade silently. Drift monitoring and alerts are often more valuable than one-time accuracy scores.

4.3: Scaling Solutions

• Explain why $O(n^3)$ closed-form inversion doesn’t scale.
• Show understanding of approximate solvers (SGD, mini-batch GD) for massive data.

Probing Question: “If you have 100M rows, would you compute the closed-form OLS solution?” (Expected: No. Use iterative methods).

🧠 Advanced Extensions

5.1: Generalized Linear Models (GLMs)

• Know how regression extends beyond Gaussian errors (e.g., Logistic Regression).
• Be prepared to describe link functions.

5.2: Polynomial and Interaction Terms

• Be able to explain feature engineering for non-linearity.
• Discuss risks of overfitting and multicollinearity.

Deeper Insight: A strong candidate recognizes that while polynomial terms increase flexibility, they also demand stronger regularization and validation.