Predicting Insurance Costs with Multiple Regression: Age and BMI Analysis

Welcome to the first lesson of PredictHealth's Multi-Factor Cost Models course. In this lesson, you will learn how to analyze and predict insurance costs using combined factor analysis. Combined factor analysis means looking at more than one variable at a time to understand how they work together to affect insurance costs. This approach is at the heart of PredictHealth's cost modeling, where we use real-world data to make better predictions and decisions.

By the end of this lesson, you will know how to build a simple multiple regression model using two important factors — age and BMI — to predict insurance charges. You will also learn how to interpret the results, evaluate the model's performance, and visualize the predictions. This lesson will give you a strong foundation for more advanced cost modeling techniques later in the course.

Let's start by understanding the insurance dataset we will use. The insurance dataset contains information about individuals, including their age, sex, BMI (Body Mass Index), number of children, smoking status, region, and the insurance charges they paid. Here is a quick look at what the data might look like:

In this lesson, we will focus on two numerical features: age and bmi. These are important because age often affects health risks, and BMI is a common measure of body fat, which can also impact health and insurance costs. While there are other features in the dataset, starting with these two helps us build a clear and simple model.

Before we can build a model, we need to prepare the data. First, let's import all the necessary libraries:

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from sklearn.model_selection import train_test_split
from sklearn.linear_model import LinearRegression
from sklearn.metrics import mean_squared_error, r2_score

Next, we need to separate the features (the variables we use to predict) from the target (the value we want to predict, which is charges). We also need to split the data into a training set and a testing set. The training set is used to build the model, and the testing set is used to see how well the model works on new data.

Here is how you can do this in Python:

# Separating features and target
X = insurance_data.drop('charges', axis=1)
y = insurance_data['charges']

# First, let's build a model with just age and BMI
X_simple = insurance_data[['age', 'bmi']]
X_train, X_test, y_train, y_test = train_test_split(X_simple, y, test_size=0.2, random_state=42)

While age (typically 18-65 years) and BMI (typically 15-50) are on similar scales in our dataset, it's important to know when standardization is needed. Standardization (scaling variables to have mean 0 and standard deviation 1) is recommended when features have very different scales (e.g., age vs. income in dollars), when using regularized models (Ridge, Lasso), when using distance-based algorithms, or when coefficients need to be directly compared for importance. In our case, since both features are on comparable scales, standardization is optional, but it's good practice to consider it for more robust modeling.