Definition:Regression analysis
📉 Regression analysis is a statistical technique central to insurance actuarial work, underwriting, and risk management that quantifies the relationship between a dependent variable — such as claim frequency, loss severity, or lapse rate — and one or more independent predictor variables like policyholder age, vehicle type, geographic zone, or coverage limit. In insurance, the most widely used form is the generalized linear model (GLM), a flexible extension of ordinary least-squares regression that accommodates the non-normal error distributions typical of insurance data — Poisson for claim counts, gamma for claim amounts, and binomial for binary outcomes such as policy conversion.
⚙️ Actuaries and data scientists build regression models by fitting historical policy and claims data to estimate the marginal effect of each rating factor on the target variable. In motor insurance pricing, for example, a GLM might estimate how each year of driver age, each vehicle rating group, and each postal code independently influences expected claim cost, producing multiplicative or additive relativities that feed directly into the rating algorithm. Model selection involves testing variable significance, checking for multicollinearity, validating on holdout samples, and ensuring stability over time. Increasingly, insurers layer machine learning techniques — gradient-boosted trees, neural networks — on top of or alongside traditional regression to capture nonlinear interactions, though regulatory expectations for model transparency in many jurisdictions mean that interpretable regression models often remain the filed or approved basis for ratemaking.
🔬 Beyond pricing, regression analysis underpins reserving methodologies such as stochastic chain-ladder models, fraud detection scoring systems that flag anomalous claims patterns, catastrophe model calibration, and mortality and morbidity studies in life and health insurance. Under IFRS 17, the need to estimate future cash flows and discount rates with greater granularity has elevated the importance of regression-based projection models. In the insurtech space, startups building parametric products or usage-based insurance platforms rely heavily on regression frameworks to translate telematics and sensor data into actionable risk scores. For insurance professionals, a working fluency in regression analysis — understanding its assumptions, limitations, and outputs — is no longer confined to the actuarial department; it is becoming a baseline competency across strategy, product, and claims functions.
Related concepts: