🏥 Predictive Modeling: U.S. Health Insurance Cost Analysis

STAT 311 | Advanced Regression & Analytics | Fall 2025

📌 Executive Summary

Medical insurance charges in the U.S. are notoriously skewed and influenced by complex lifestyle interactions. This project bridges the gap between raw demographic data and accurate cost forecasting by developing a Log-Transformed Interaction Model. By stabilizing variance and addressing non-normality, I achieved a highly accurate predictive model with a CV of 4.77%.

🧠 The "Gap" Analysis: Why simple models failed

Standard linear models often fail on healthcare data because costs are not distributed normally. My analysis identified two critical "blind spots" in basic modeling:

1. The Variance Gap: Insurance charges are highly skewed; a Box-Cox transformation was required to normalize residuals.
2. The BMI-Smoker Interaction: I discovered that BMI does not affect everyone equally—it has a dramatically higher impact on costs for smokers than for non-smokers.

🛠️ Technical Methodology

I utilized JMP Statistical Software to build and validate three nested models:

• Model 1 (Baseline): Main effects only (Age, BMI, Smoking status).
• Model 2 (Interaction): Added $BMI \times Smoker$ interaction terms to capture non-linear cost spikes.
• Model 3 (Selected Final): Applied a Natural Log Transformation ($ln(charges)$) to address heteroscedasticity and stabilize variance.

Model Performance Metrics

Metric	Model 1	Model 3 (Final)
Model Type	Linear Main Effects	Log-Transformed Interaction
Predictive Accuracy	Baseline	CV = 4.77%
Variance Stability	Poor (Heteroscedastic)	Stable (Homoscedastic)
Key Insight	Smoking is a predictor	Smoking + BMI interaction drives 80%+ of cost

🗂️ Repository Structure

• STAT311_Final_Report.pdf: Comprehensive 20+ page analysis including variable screening (Stepwise), diagnostics, and influence/leverage plots.
• JMP_Files/: Complete reproducible environment including .jmpjournal files and model fit scripts.
• insurance.csv: Cleaned dataset (1,335 observations).

🚀 How to Reproduce

1. Open insurance.jmp in JMP.
2. Run the saved scripts for Model 3.
3. Model Specifications: $Y = ln(charges)$; $X = Age, BMI, Children, Smoker, (BMI \times Smoker)$.
4. Diagnostics used: VIF for multicollinearity, Box-Cox for transformation, and Cook's D for influence.

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Course: STAT 311 – Regression Analysis
Instructor: Dr. Iresha Premarathna
Author: Feifei Li (GPA: 3.9)