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

This article explains how to apply multiple linear regression using R for insurance risk modeling and provides actionable insights for actuaries involved in pricing, reserving, and risk assessment.

Article Outline:

1. Introduction Introduce the role of multiple linear regression in actuarial science and its value in predicting outcomes such as claim frequency, severity, and policyholder behavior. Explain why R is a preferred language among actuaries for statistical modeling.

2. Conceptual Foundation of Multiple Linear Regression in Risk Analysis Define multiple linear regression and explain how it models the relationship between a continuous dependent variable and several independent variables. Relate its use to core actuarial activities such as reserving, pricing, and lapse modeling.

3. Key Actuarial Applications of Multiple Regression Models Describe real-world scenarios where actuaries apply multiple regression: modeling claim costs, assessing underwriting risk, forecasting reserves, and estimating lapse probabilities.

4. Preparing an Actuarial Dataset in R Discuss the structure of a typical insurance dataset, including variables like age, gender, sum insured, tenure, and previous claims. Explain how to structure and prepare such a dataset using R.

5. Data Cleaning and Feature Engineering in R Demonstrate steps in R to clean, transform, and encode data: handling missing values, converting factors, creating new features (e.g., claim ratios), and scaling.

6. Fitting a Multiple Linear Regression Model in R Show how to build a linear regression model using lm() in R. Include model specification, fitting, and summary interpretation.

7. Model Diagnostics and Assumptions Checking Explain how to assess linearity, homoscedasticity, multicollinearity, normality of residuals, and influential points using R diagnostic plots and statistical tests.

8. Evaluating Model Performance and Predictive Accuracy Discuss how to evaluate the model using R metrics such as RMSE, MAE, and adjusted R-squared. Include splitting data into training and test sets.

9. Interpreting the Model for Risk Analysis Translate model coefficients into actuarial insights: the effect of age, policy type, or claim history on expected claim costs.

10. Conclusion and Best Practices Summarize the strengths and limitations of using multiple regression in R for actuarial modeling. Offer tips for improving model robustness and integrating with other actuarial methods like GLMs or credibility theory.

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