Linear Regression for Actuarial Science and Risk Analysis Using Python: A Complete Guide to Modeling Insurance Claims

This article explains how actuaries and risk professionals can use Python-based linear regression to model insurance claims, develop rating structures, and support transparent, data-driven decisions for pricing, reserving, and portfolio management.

Article Outline:

1. Introduction

   • The role of predictive analytics in actuarial science and risk management

   • Why linear regression is essential for quantifying insurance risk and modeling claims

   • The value of Python for building robust, transparent actuarial models

2. Linear Regression in Actuarial Science

   • The linear regression model: structure, assumptions, and interpretation

   • Common actuarial applications:

     • Modeling claim severity and loss costs

     • Developing and validating rating factors

     • Portfolio risk segmentation and monitoring

   • Linear regression vs. GLMs and other statistical tools

3. Preparing Insurance Claims Data in Python

   • Structuring policy and claims data for regression

   • Cleaning, transforming, and encoding variables (handling missing values, categorical data, and skewed outcomes)

   • Exploratory data analysis for understanding patterns and distributions

4. Building and Fitting a Linear Regression Model in Python

   • Selecting predictors and the response variable

   • Fitting the model using statsmodels and interpreting key outputs

   • Checking regression diagnostics: residuals, normality, multicollinearity

5. Interpreting Model Results for Risk Analysis

   • Translating coefficients into actuarial insights and rating adjustments

   • Using fitted values for pricing, risk segmentation, and decision support

   • Residual analysis to uncover data issues or model limitations

6. Scenario Analysis and Forecasting with Python

   • Applying the regression model to new business or policy scenarios

   • Forecasting claim amounts and stress-testing the portfolio

   • Integrating regression results with capital management and reporting

7. Visualizing Regression Results for Communication

   • Creating diagnostic plots (residuals, actual vs. predicted, coefficient plots)

   • Presenting model insights to business and regulatory stakeholders

8. Best Practices, Limitations, and Next Steps

   • Ensuring valid assumptions and data integrity

   • Recognizing limitations of linear regression for actuarial data

   • Extending to GLMs, machine learning, and advanced analytics in Python

9. Conclusion

   • The importance of linear regression for actuarial decision-making

   • How Python empowers actuaries to deliver transparent, reproducible risk analytics

   • Future directions for actuarial modeling and automation

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