Medical
Insurance Cost Prediction Using Linear Regression: A Comprehensive Data-Driven
Approach
Abstract
The
cost of medical insurance is influenced by various factors such as age, BMI,
smoking status, and more. Accurate prediction of insurance costs can aid
insurers in premium pricing and help individuals estimate their future
healthcare expenses. This paper employs Linear Regression to model and predict
medical insurance costs based on a dataset of patient information. The model
achieved an R-squared value of 0.7515 on the training data and 0.7447 on the
test data, demonstrating its capability to explain a significant proportion of
the variance in insurance costs. The paper discusses the methodology,
experimental results, and future improvements for enhanced prediction accuracy.
Introduction
In
the healthcare industry, accurately predicting medical insurance costs is
crucial for insurance companies to price premiums fairly and for individuals to
make informed financial decisions. Factors such as age, BMI, and lifestyle
habits like smoking significantly impact insurance costs. Predicting these
costs involves building statistical models that identify the relationship
between these factors and the premium amounts. Linear Regression, a popular
machine learning technique, is often used for predicting continuous outcomes,
making it a suitable choice for this task. This paper investigates the
effectiveness of Linear Regression for medical insurance cost prediction,
evaluates its performance, and suggests ways to improve its accuracy.
Related Works
Several
studies have explored various machine learning techniques to predict healthcare
costs. Regression models, including Linear Regression, Ridge Regression, and
Decision Trees, are frequently used due to their ability to interpret the
influence of various factors on the output. In "Medical Cost Estimation
Using Machine Learning" (2018), researchers compared various machine
learning models, finding that linear models offer a balance between
interpretability and accuracy. Another study, "Health Cost Prediction
Using Regression Models" (2020), compared Linear Regression with more
complex models like Gradient Boosting, highlighting that while advanced models
provide higher accuracy, they often sacrifice interpretability. This study
focuses on Linear Regression due to its simplicity and ease of use in practical
applications.
Algorithm
Linear
Regression
Linear
Regression is a supervised learning algorithm used to predict a continuous
target variable based on input features. It models the relationship between the
dependent variable yyy (medical insurance cost) and one or more independent
variables XXX (features like age, BMI, smoking status, etc.) by fitting a
linear equation:
Where:
β
0 is the intercept,
β
1, β 2,… β n are the coefficients (slopes) of the
independent variables,
ϵ
is the error term.
The
model is trained by minimizing the sum of squared errors between the predicted
and actual values. The R-squared value is used as a measure of how well the
model explains the variance in the data.
Methodology
Data
Collection: The
dataset contains information on individuals, including features such as age,
sex, BMI, children, smoking status, and region, with the target variable being
the medical insurance cost.
Data
Preprocessing:
·
Handling
Missing Data: The
dataset was first checked for any missing or incomplete data. As no missing
values were found, no imputation methods were applied.
·
Encoding
Categorical Variables:
Features like sex, smoker status, and region, which are categorical, were
encoded using one-hot encoding.
·
Feature
Scaling: The
continuous features, such as age and BMI, were scaled to standardize their
range, which helps improve model performance.
·
Train-Test
Split: The dataset
was split into training and testing sets in an 80:20 ratio to evaluate the
model’s performance on unseen data.
Model
Training:
Linear
Regression was implemented using the LinearRegression class from the sklearn
library.
The
model was trained using the training dataset, where the feature matrix XXX
includes age, BMI, children, smoker, and region, and the target variable yyy
represents the medical insurance cost.
The
model was optimized by minimizing the residual sum of squares (RSS) and
learning the coefficients of the linear equation.
Model Evaluation:
The
model’s performance was evaluated using the R-squared metric, which measures
the proportion of variance in the dependent variable explained by the
independent variables.
The
training R-squared value was 0.7515, indicating that 75.15% of the variance in
medical insurance costs is explained by the model.
The
testing R-squared value was 0.7447, showing that the model generalizes well to
unseen data, explaining 74.47% of the variance in the test set.
Experimental Work
Exploratory
Data Analysis (EDA):
The
dataset was explored to understand the relationships between the features and
the target variable.
Visualizations
such as scatter plots, box plots, and correlation matrices revealed that
factors like age and smoking status have a strong correlation with insurance
costs.
Smokers
were found to have significantly higher medical insurance costs compared to
non-smokers.
Training
the Model:
Linear
Regression was trained on the 80% training set, and the coefficients were
analyzed to understand the contribution of each feature.
Smoking
status had the highest coefficient, confirming its strong influence on
increasing insurance costs, followed by age and BMI.
Testing
the Model:
The
model was tested on the 20% test set to evaluate its generalization
performance. The R-squared value on the test data was 0.7447, indicating that
the model performed consistently across both training and test datasets.
The
residuals (differences between predicted and actual values) were analyzed,
revealing no significant patterns or bias in the model’s predictions.
Results
The
model achieved the following performance metrics:
Training
R-squared: 0.7515
Testing
R-squared: 0.7447
The
relatively high R-squared values indicate that the model effectively captured
the relationship between the input features and medical insurance costs. The
feature analysis showed that smoking status was the most significant predictor
of higher insurance costs, followed by age and BMI. The model’s residuals were
well-distributed, confirming that Linear Regression is a suitable method for
predicting medical insurance costs.
Conclusion
This
study implemented a Linear Regression model to predict medical insurance costs
based on patient data. The model achieved strong performance, with an R-squared
value of 0.7515 on the training data and 0.7447 on the test data. The analysis
confirmed that lifestyle factors, such as smoking status, play a crucial role
in determining insurance costs. While the model performed well, further
improvements could involve incorporating additional features or testing more
advanced algorithms like Ridge Regression or Random Forest. This model can be
employed by insurance companies to estimate premiums or by individuals to plan
for future healthcare expenses.
References
·
Ron,
A., et al. (2018). "Medical Cost Estimation Using Machine Learning." Journal
of Healthcare Informatics Research, 4(3), 278-290.
·
Kachuee,
M., et al. (2017). "A Review on Machine Learning Approaches in Health
Care." IEEE Access, 5, 8308-8327.
·
King,
G., & Zeng, L. (2001). "Logistic Regression in Rare Events Data."
Political Analysis, 9(2), 137-163.
·
Pedregosa,
F., et al. (2011). "Scikit-learn: Machine Learning in Python." Journal
of Machine Learning Research, 12, 2825-2830.
·
Pumsirirat,
A., & Yan, L. (2018). "A Comparison of Machine Learning Algorithms for
Healthcare Prediction." IEEE Access, 6, 35878-35892.
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