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📈 '''Linear regression''' is one of the most widely used statistical techniques in insurance, providing a method for modeling the relationship between a dependent variable — such as [[Definition:Loss cost | loss cost]], [[Definition:Claims frequency | claim frequency]], or [[Definition:Loss severity | severity]] — and one or more explanatory variables such as policyholder age, property value, or coverage limit. At its core, the technique fits a straight-line (or hyperplane, in the multivariate case) equation to observed [[Definition:Data | data]], estimating coefficients that quantify how each predictor influences the outcome while minimizing the sum of squared errors. In [[Definition:Actuarial science | actuarial]] work, linear regression laid much of the groundwork for modern [[Definition:Rating | rating]] plan construction and remains a benchmark against which more complex [[Definition:Machine learning | machine learning]] models are compared.

🛠️ Insurance practitioners deploy linear regression across a remarkably broad set of tasks. In [[Definition:Pricing | pricing]], ordinary least squares regression and its generalized variants — particularly [[Definition:Generalized linear model (GLM) | generalized linear models (GLMs)]], which extend the linear regression framework to non-normal distributions like Poisson and gamma — are the workhorses for constructing [[Definition:Rating factor | rating factors]] in [[Definition:Property and casualty insurance | property and casualty]] lines worldwide. [[Definition:Loss reserving | Reserving]] actuaries use regression-based approaches to project ultimate losses from development triangles, and [[Definition:Reinsurance | reinsurance]] analysts apply regression to model the relationship between industry loss indices and a portfolio's actual experience. The simplicity and transparency of linear regression make it especially attractive in regulated environments: supervisory authorities in jurisdictions from the United States to Europe and Asia generally expect insurers to demonstrate a clear, interpretable link between [[Definition:Rating factor | rating variables]] and predicted outcomes, a standard that linear models satisfy almost by definition. Even in organizations that have adopted [[Definition:Artificial intelligence | AI]]-driven pricing, a linear regression benchmark often serves as a governance check and an anchor for [[Definition:Model explainability | explainability]] requirements.

💡 Despite its elegance, linear regression carries assumptions — linearity, independence of errors, homoscedasticity, and absence of multicollinearity — that real-world insurance data frequently violates. Heavy-tailed [[Definition:Loss distribution | loss distributions]], non-linear exposure relationships, and interaction effects among variables can all degrade the performance of a naïve linear model. This is precisely why [[Definition:Generalized linear model (GLM) | GLMs]], [[Definition:Generalized additive model (GAM) | generalized additive models]], and ensemble techniques emerged as natural extensions within the insurance analytics toolkit. Nonetheless, understanding linear regression remains indispensable: it provides the conceptual vocabulary — coefficients, residuals, confidence intervals, goodness-of-fit — that underpins virtually all quantitative insurance work. For anyone entering [[Definition:Underwriting | underwriting]], [[Definition:Actuarial science | actuarial practice]], or [[Definition:Insurtech | insurtech]] product development, fluency in linear regression is the starting point from which more sophisticated methods build.

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

Definition:Linear regression - Revision history

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