Definition

Regression analysis

A family of models that predict an outcome from one or more predictors, quantifying each predictor’s contribution while holding the others constant.

Linear regression fits an equation (outcome = intercept + weights × predictors) whose coefficients state how the outcome shifts per unit of each predictor, all else equal. Logistic regression does the same for binary outcomes; the family extends to counts, survival times, and nested data (mixed models).

The "holding others constant" clause is regression’s power and its trap: it only adjusts for what you measured and modeled. Omitted confounders, overfitting with too many predictors per observation, and extrapolating beyond the data are the standard failure modes.