Regression analysis

Regression analysis estimates how an outcome variable changes as one or more predictor variables change, producing a coefficient for each predictor that summarizes the strength and direction of its association with the outcome. The simplest form, linear regression, fits a straight-line relationship; logistic regression, polynomial terms, and other variants extend the approach to different types of outcomes and relationships.

Fitting a regression model involves choosing predictors, checking whether the data meets the method's assumptions (such as a roughly linear relationship and independent errors), and evaluating each coefficient's statistical significance and confidence interval to judge how reliable the estimate is. Model fit statistics indicate how well the predictors explain variation in the outcome, but a good fit alone does not establish that a predictor causes the outcome.

Regression is one of the most widely used tools in analytics: it underlies much of predictive analytics, feeds into simpler machine learning pipelines, and is a common tool in diagnostic analytics for isolating which factors are associated with a change. Its most common misuse is causal overreach—reading a significant coefficient as proof that the predictor causes the outcome, when regression on observational data only establishes association unless it is paired with a genuine causal inference design.