Medical insurance cost prediction

1 · What the data says before any model

Each record is one primary beneficiary: age, sex, BMI, number of children covered, smoker status, US region and the annual charge. Charges run from $1,122 to $63,770, with a median of $9,382 and a mean of $13,270. A mean that far above the median means a long tail of very expensive policies.

Smokers average about 4× the cost of non-smokers, and their costs vary twice as much.

2 · Features that encode health risk

The scatter plots show the smoking effect gets much larger for people with obesity. A linear model can't see that on its own, so I gave it three explicit features:

# BMI of 30 or more is the clinical threshold for obesity
df['is_obese'] = (df['bmi'] >= 30).astype(int)

# the combination is far costlier than either trait alone
df['smoker_obese_interaction'] = ((df['smoker'] == 'yes') & (df['is_obese'] == 1)).astype(int)

# life stages rather than a straight line in age
df['age_group'] = pd.cut(df['age'], bins=[18, 30, 45, 65, 100],
                         labels=['Young_Adult', 'Middle_Adult', 'Senior_Adult', 'Elderly'], right=False)

3 · Four models, one held-out test set

I one-hot encoded the categories, held out 20% of policies for testing, and trained four regressors on log(charges). Lower error is better; R² is the share of variation the model explains.

Linear regression can't bend around the interactions. The tree ensembles can, and gradient boosting did best on every metric.

Tuning

A 5-fold grid search over 384 combinations of trees, learning rate, depth, split size and subsampling picked a slow, shallow model: 500 trees at a 0.01 learning rate, depth 3, with 80% subsampling. Shallow trees and subsampling keep it from memorising the training data. Train and test scores came out almost identical (R² 0.857 vs 0.866), so it generalises.

4 · What it means in dollars

Back in dollars, the typical prediction is within about $2,000 of the real charge. RMSE is higher because it weights the rare very expensive policies more heavily, and those are the hardest to predict. The most important features were smoking, age, number of children and BMI.