Linear Regression in Actuarial Science and Risk Analysis Using SQL: Practical Methods for Modeling Insurance Claims Data

This article demonstrates how SQL-based linear regression enables actuaries and risk professionals to model claims, quantify insurance risk, and support robust, data-driven pricing, reserving, and portfolio management.

Article Outline:

1. Introduction

   • The pivotal role of statistical modeling in actuarial science and risk management

   • Why linear regression remains a foundational tool for actuaries analyzing insurance claims

   • The increasing importance of SQL for scalable, transparent data analytics in the actuarial profession

2. Linear Regression in Actuarial Risk Analysis

   • The linear regression model: interpreting coefficients, intercept, and residuals

   • Key actuarial applications:

     • Quantifying the impact of policyholder and policy features on claim amounts

     • Supporting rating and pricing strategies

     • Loss reserving, experience studies, and risk monitoring

   • Comparing linear regression with other actuarial models (GLMs, credibility, reserving methods)

3. Structuring Actuarial Data in SQL

   • Designing a SQL table for policy and claims data

   • Data preparation: handling missing values, encoding categorical variables, transforming skewed data

   • Exploratory analysis: descriptive statistics and initial insights using SQL queries

4. Implementing Linear Regression with SQL Queries

   • Calculating means, variances, and covariances for regression analysis

   • Computing regression coefficients (intercept, slopes) for one or more predictors

   • Generating fitted values, residuals, and calculating R-squared

   • Outputting results for further actuarial analysis

5. Interpreting Results for Actuarial Decision-Making

   • Translating regression coefficients into rating factors and risk indicators

   • Using fitted values for risk segmentation and portfolio assessment

   • Residual analysis to identify model limitations or unusual risks

6. Forecasting and Scenario Analysis with SQL

   • Applying regression models to predict claim amounts for new or hypothetical policy profiles

   • Scenario tables for stress testing, pricing, and capital modeling

   • Integrating regression output into actuarial dashboards and risk management workflows

7. Best Practices, Limitations, and Extensions

   • Ensuring valid model assumptions: linearity, homoscedasticity, independence

   • Recognizing limitations of linear regression with insurance claims data (skewness, heterogeneity, zero-inflation)

   • Extending SQL analytics to multi-factor models, GLMs, and integration with actuarial platforms

8. Conclusion

   • The enduring value of linear regression for transparent, data-driven actuarial modeling

   • The strengths of SQL for repeatable, large-scale analysis in insurance and risk management

   • Next steps: from linear regression to advanced analytics for better pricing, reserving, and capital adequacy

Subscribe to get the full article …

---