Multiple Linear Regression in Actuarial Science and Risk Analysis Using SQL: A Step-by-Step Guide to Modeling Insurance Risk

This article demonstrates how multiple linear regression can be effectively applied using SQL to model insurance risks and support data-driven actuarial decision-making.

Article Outline:

1. Introduction Explain the importance of multiple linear regression in actuarial science and how it supports risk quantification, pricing, and forecasting. Describe its application in analyzing insurance claims, estimating reserves, and modeling loss severity and frequency.

2. Understanding Multiple Linear Regression in an Actuarial Context Define the multiple linear regression model and interpret its components: dependent variable, multiple predictors, coefficients, and residuals. Highlight actuarial use cases like claim cost modeling, lapse rate prediction, and underwriting risk assessment.

3. SQL for Data Analytics in Insurance and Risk Modeling Introduce how SQL is used to extract, transform, and analyze structured insurance data in relational databases. Discuss the growing use of SQL in actuarial data science pipelines and BI reporting tools.

4. Simulated Dataset: Insurance Claims and Risk Factors Describe the dataset structure: policyholder demographics, policy type, sum insured, tenure, past claims, and the response variable (e.g., annual claim amount). Explain why each variable is relevant for predicting claim outcomes.

5. Preprocessing and Feature Engineering with SQL Show how to clean and prepare data using SQL: handling NULLs, filtering records, encoding categorical variables (e.g., policy type), normalizing inputs, and creating interaction terms or derived fields (e.g., claim per sum insured).

6. Running Multiple Linear Regression Using SQL Extensions (e.g., BigQuery ML or PostgreSQL with PL/Python) Explain how SQL-based ML tools like BigQuery ML, SQL Server Machine Learning Services, or PostgreSQL with Python can run regression models. Provide syntax for creating a linear regression model within the SQL environment.

7. Interpreting Regression Output in a Risk Analysis Context Discuss how to interpret coefficients, R-squared, p-values, and confidence intervals. Link these outputs to actuarial insights—e.g., how age, policy type, and sum insured affect expected claim cost.

8. Validating and Evaluating Model Accuracy Demonstrate using SQL to compute prediction error metrics (e.g., MAE, RMSE) and compare actual vs. predicted claim costs to validate model robustness and actuarial relevance.

9. Practical Considerations in Actuarial Modeling with SQL Explore limitations and best practices: assumptions of linear regression, multicollinearity, outlier handling, and scalability for large insurance datasets. Recommend combining SQL with statistical tools like R or Python for deeper analysis.

10. Conclusion Summarize the power of integrating multiple linear regression with SQL for practical actuarial decision-making in pricing, reserving, and risk analytics.

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