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📉 '''Regression analysis''' is a statistical technique central to insurance [[Definition:Actuarial analysis | actuarial work]], [[Definition:Underwriting | underwriting]], and [[Definition:Risk management | risk management]] that quantifies the relationship between a dependent variable — such as [[Definition:Claims | claim]] frequency, [[Definition:Loss severity | loss severity]], or [[Definition:Lapse rate | 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 [[Definition:Generalized linear model (GLM) | 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.

⚙️ [[Definition:Actuary | Actuaries]] and [[Definition:Data scientist | data scientists]] build regression models by fitting historical policy and claims data to estimate the marginal effect of each [[Definition:Rating factor | rating factor]] on the target variable. In [[Definition:Motor insurance | motor insurance]] pricing, for example, a GLM might estimate how each year of driver age, each vehicle [[Definition:Insurance rating group | rating group]], and each postal code independently influences expected claim cost, producing multiplicative or additive [[Definition:Relativity | relativities]] that feed directly into the [[Definition:Rating algorithm | rating algorithm]]. Model selection involves testing variable significance, checking for [[Definition:Multicollinearity | multicollinearity]], validating on holdout samples, and ensuring stability over time. Increasingly, insurers layer [[Definition:Machine learning | machine learning]] techniques — gradient-boosted trees, neural networks — on top of or alongside traditional regression to capture nonlinear interactions, though regulatory expectations for [[Definition:Explainability | model transparency]] in many jurisdictions mean that interpretable regression models often remain the filed or approved basis for [[Definition:Rate filing | ratemaking]].

🔬 Beyond pricing, regression analysis underpins [[Definition:Reserving | reserving]] methodologies such as stochastic [[Definition:Chain-ladder method | chain-ladder]] models, [[Definition:Fraud detection | fraud detection]] scoring systems that flag anomalous claims patterns, [[Definition:Catastrophe model | catastrophe model]] calibration, and [[Definition:Mortality table | mortality]] and [[Definition:Morbidity risk | morbidity]] studies in [[Definition:Life insurance | life]] and [[Definition:Health insurance | health insurance]]. Under [[Definition:IFRS 17 | 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 [[Definition:Insurtech | insurtech]] space, startups building parametric products or [[Definition:Usage-based insurance (UBI) | usage-based insurance]] platforms rely heavily on regression frameworks to translate [[Definition:Telematics | 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 [[Definition:Claims management | claims]] functions.

'''Related concepts:'''
{{Div col|colwidth=20em}}
* [[Definition:Generalized linear model (GLM)]]
* [[Definition:Actuarial analysis]]
* [[Definition:Rating factor]]
* [[Definition:Machine learning]]
* [[Definition:Predictive modeling]]
* [[Definition:Loss development]]
{{Div col end}}

Definition:Regression analysis - Revision history

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