Linear Regression in Actuarial Science and Risk Analysis Using R: A Comprehensive Guide to Modeling and Quantifying Insurance Risk

This article demonstrates how to apply linear regression in R for actuarial science and risk analysis, empowering actuaries to model claim costs, quantify insurance risk, and support robust, data-driven decisions for pricing, reserving, and risk management.

Article Outline:

1. Introduction

   • The expanding role of statistical modeling in actuarial science and risk analysis

   • Why linear regression is a cornerstone for analyzing insurance data and quantifying risk

   • The benefits of using R for actuarial modeling and reproducible analytics

2. Understanding Linear Regression in the Actuarial Context

   • The linear regression model and its components: intercept, coefficients, residuals

   • Actuarial applications:

     • Modeling claim costs as a function of policyholder characteristics

     • Pricing risk and developing rating factors

     • Loss reserving and experience analysis

   • Comparing linear regression to other actuarial models (GLMs, credibility, time series)

3. Preparing Actuarial Data in R

   • Loading and structuring policy and claims data for regression

   • Data cleaning: dealing with missing values, outliers, and categorical variables

   • Exploratory data analysis: descriptive statistics and visualizations

4. Building a Linear Regression Model in R for Risk Analysis

   • Specifying the regression formula (e.g., claim amount ~ age + sum insured + region)

   • Fitting the model and extracting coefficients, confidence intervals, and diagnostics

   • Understanding and testing model assumptions in the actuarial context

5. Interpreting Regression Output for Actuarial Decision-Making

   • Interpreting regression coefficients as rating factors

   • Using the model for premium calculation and risk segmentation

   • Residual analysis: detecting unusual risks and assessing model fit

6. Forecasting and Scenario Analysis in Risk Management

   • Using the regression model for claim cost forecasting and what-if scenarios

   • Stress-testing portfolios and quantifying uncertainty

   • Incorporating regression results into capital modeling and solvency analysis

7. Visualizing Results for Stakeholders

   • Policyholder segmentation plots and risk maps

   • Residual and leverage plots for actuarial diagnostics

   • Communicating risk insights with reproducible R graphics

8. Best Practices, Limitations, and Extensions

   • Ensuring valid model assumptions and dealing with non-linearity

   • Limitations of linear regression in actuarial work (heteroscedasticity, non-normality, claim frequency/severity)

   • Extending to generalized linear models (GLMs), machine learning, and actuarial reserving models

9. Conclusion

   • The foundational value of linear regression in actuarial science and risk analysis

   • How R enhances transparency, flexibility, and reproducibility in actuarial analytics

   • Next steps: advanced regression, predictive analytics, and integration with actuarial software

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