To identify the key determinants of health insurance charges in the US
Evaluate predictive models to determine health insurance charges.
Observations: 1,338 individuals
Target variable: Insurance charges (USD)
Predictors: age, BMI, number of children, sex, smoking status, and region (one-hot encoded).
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Exploratory Analysis: Charges exhibited strong right skew and extreme outliers.
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Statistical Models:
- Ordinary Least Squares (OLS) on raw and log-transformed charges
- Robust Linear Model (Huber loss)
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Predictive Models:
- Baseline Linear Regression
- Ridge and Lasso regression
- Random Forest Regressor
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Evaluation:
- Train–test split (80/20)
- Metrics: R² and RMSE
- 5-fold cross-validation for Random Forest
Test Set Performance:
- Linear Regression: R² = 0.784, RMSE = 5,796
- Ridge Regression: R² = 0.783, RMSE = 5,796
- Lasso Regression: R² = 0.783, RMSE = 5,796
- Random Forest: R² = 0.864, RMSE = 4,587
Cross-Validation (Random Forest):
- Mean R² = 0.837 (SD = 0.032)
- Mean RMSE = 4,853 (SD = 338)
- Smoking status (≈61%)
- BMI (≈21%)
- Age (≈13%) Remaining variables each contributed <2%.
Residual–prediction plots showed reduced heteroskedasticity relative to linear models, with mild remaining error spread at high charge levels.
Smoking status dominates insurance cost prediction, followed by BMI and age. This reflects actuarial risk pricing but raises fairness concerns, particularly for behavioral and health-related variables.
- Random Forest lacks interpretability compared to linear models.
- Regional effects may be underestimated due to coarse geographic encoding.
- External validity is limited to populations similar to the dataset.
The Random Forest model provides the best predictive performance and robustness to outliers. For inference and policy discussion, robust and log-linear regressions remain essential complements.