STAT 403 Final Project — Bootstrapping Regression & Jackknife+ Conformal Prediction

This repository contains my final project for STAT/QSci 403: Introduction to Statistical Methods for Data Science at the University of Washington (Spring 2025).
The project focuses on regression modeling, uncertainty quantification, and distribution-free prediction using modern resampling methods.

---

📌 Project Overview

The goal of the analysis is to model log10-transformed house prices in King County (Seattle area) using features such as:

• square footage (sqft_living)
• number of bathrooms and bedrooms
• house grade
• log-transformed predictors to improve linearity and reduce heteroscedasticity

The project includes:

1. Linear regression modeling
2. Gaussian confidence intervals
3. Bootstrap confidence intervals
4. Jackknife+ conformal prediction intervals
5. Uncertainty quantification and empirical coverage assessment

All results are implemented in R, and code is available in the project files.

---

📈 Regression Modeling

I fit the model:

log10(price) = β₀

• β₁ * log10(sqft_living)
• β₂ * bedrooms
• β₃ * bathrooms
• β₄ * grade
• ε

Key findings:

• log_sqft and grade are highly significant predictors
• Bedrooms and bathrooms show weak marginal effects once other variables are controlled
• Adjusted R² ≈ 0.556, indicating moderate explanatory power

(Visuals available in the PDF report.)

---

🔁 Bootstrap Confidence Intervals

I computed 95% bootstrap CIs for all coefficients using 1,000 bootstrap resamples.

Example (log_sqft):

• Gaussian CI: (0.23, 0.54)
• Bootstrap CI: (0.23, 0.55)
• Both methods confirm the robustness of this predictor.

Histograms of bootstrap estimates for each coefficient are shown in the report (see page 5).

---

🔮 Jackknife+ Conformal Prediction

To produce distribution-free prediction intervals, I implemented Jackknife+:

• 500 leave-one-out models
• 200 test-set predictions per model
• Constructed (Li, Ui) bounds from residuals
• Exponentiated back to the price scale

Empirical coverage:

• 196 out of 200 test cases (98%)
• Exceeds the target 95% coverage

Interval widths:

• Median width: $840,652
• Range: $286k – $3.39M

(First 20 prediction intervals plotted in the report, page 6.)

---

📁 File Structure

• 403_final_report.pdf # Full project write-up
• Project_template.Rmd/ # R scripts for regression, bootstrap, Jackknife+
• data/ # Training and test datasets
• CI.dat # Jackknife+ interval outputs
• guess.dat # Test-set MSE and coverage summary
• README.md # This file

---

🧠 Methods Used

• Linear regression
• Gaussian confidence intervals
• Bootstrap resampling (percentile & BCa)
• Jackknife+ conformal prediction
• Diagnostic plots & residual analysis

---

✨ Highlights

• Demonstrates statistical rigor beyond simple modeling
• Shows understanding of model assumptions and violations
• Uses modern distribution-free prediction methods
• Connects theory with applied predictive modeling

This project represents my interest in statistical learning, uncertainty quantification, and methods that remain reliable in noisy real-world settings—topics I hope to further explore in the ETH Zürich MSc in Data Science program.

---