Project 10: Regression & Modeling Diagnostics Lab

Build a diagnostics-first modeling lab for linear/logistic regression and regularized alternatives.

Quick Reference

Attribute Value
Difficulty Level 3: Advanced
Time Estimate 2 weeks
Main Programming Language Python
Alternative Programming Languages R, Julia
Coolness Level Level 4: Hardcore Tech Flex
Business Potential 2. The “Micro-SaaS / Pro Tool”
Prerequisites Projects 6-9
Key Topics Linear and logistic regression, diagnostics, multicollinearity, Ridge/Lasso, AIC/BIC

1. Learning Objectives

  1. Build interpretable linear and logistic models.
  2. Diagnose assumption failures with residual and calibration checks.
  3. Identify and mitigate multicollinearity.
  4. Compare model choices with regularization and AIC/BIC.

2. All Theory Needed (Per-Concept Breakdown)

2.1 Regression Assumptions and Diagnostics

  • Fundamentals: Modeling without diagnostics is untrusted output.
  • Deep Dive into the concept: Residual structure, leverage, and heteroscedasticity affect confidence in coefficients and predictions.

2.2 Regularization and Model Selection

  • Fundamentals: Complexity control prevents overfitting.
  • Deep Dive into the concept: Ridge/Lasso trade coefficient stability vs sparsity; AIC/BIC balance fit and parsimony.

3. Project Specification

3.1 What You Will Build

A lab that trains baseline and regularized models, emits diagnostics, and recommends a deployment candidate.

3.2 Functional Requirements

  1. Train linear and logistic baseline models.
  2. Emit residual, influence, and calibration diagnostics.
  3. Compute multicollinearity signals and mitigation suggestions.
  4. Compare candidate models using AIC/BIC and validation metrics.

3.3 Non-Functional Requirements

  • Reproducible splits and model registry logs.
  • Human-readable model decision memo.

3.4 Example Usage / Output

$ python regression_diagnostics_lab.py --dataset data/churn.parquet
Best model: logistic_l2
AIC: 12431.8, BIC: 12607.4
Calibration slope: 0.96
VIF alerts: billing_cycle, annual_plan_flag
Saved diagnostics: outputs/regression_lab/

3.5 Real World Outcome

You deliver a model that is not only accurate but also diagnostically defensible for production decisions.

4. Solution Architecture

Data split -> feature prep -> model family runner -> diagnostics engine -> selection memo

5. Implementation Guide

5.1 Development Environment Setup

pip install numpy pandas scikit-learn statsmodels

5.2 Project Structure

P10/
  regression_diagnostics_lab.py
  configs/
  outputs/

5.3 The Core Question You Are Answering

“Which model remains reliable after assumption and stability checks?”

5.4 Concepts You Must Understand First

  1. Linear/logistic mechanics
  2. Residual diagnostics
  3. Multicollinearity
  4. Regularization paths

5.5 Questions to Guide Your Design

  1. Which diagnostics are release blockers?
  2. How will you compare calibration vs discrimination tradeoffs?
  3. How will you document interpretability limits?

5.6 Thinking Exercise

Choose between two models: one with better AUC, one with better calibration. Defend your deployment choice.

5.7 The Interview Questions They’ll Ask

  1. What does VIF signal?
  2. Why inspect residual plots with high R-squared?
  3. When would BIC disagree with AIC?
  4. Why can regularization improve test performance?
  5. How do you interpret logistic coefficients?

5.8 Hints in Layers

  • Hint 1: Baseline model first.
  • Hint 2: Add diagnostics bundle.
  • Hint 3: Add regularized variants.
  • Hint 4: Add model governance memo.

5.9 Books That Will Help

Topic Book Chapter
Regression fundamentals ISLR Ch. 3-4
Applied diagnostics regression references selected
Multilevel perspective Gelman & Hill early chapters

6. Testing Strategy

  • Synthetic truth-recovery tests.
  • Stability tests across seeds/splits.
  • Calibration and residual smoke tests.

7. Common Pitfalls & Debugging

Pitfall Symptom Solution
Leakage in features unrealistically high validation scores temporal feature audits
Ignoring collinearity unstable coefficients remove/combine correlated predictors
Metric-only selection fragile deployment behavior diagnostics+metric combined gate

8. Extensions & Challenges

  • Add interaction terms and nonlinear basis comparisons.
  • Add fairness/subgroup diagnostics.

9. Real-World Connections

  • Churn risk scoring.
  • Pricing/demand sensitivity modeling.

10. Resources

  • ISLR
  • Gelman & Hill

11. Self-Assessment Checklist

  • I can explain one failed assumption and mitigation.
  • I can justify model selection beyond a single metric.
  • I can communicate uncertainty and calibration clearly.

12. Submission / Completion Criteria

Minimum: baseline model + diagnostics + selection rationale.

Full: regularization and model-selection comparison with governance notes.