Regression analysis

Regression analysis is a set of statistical methods for modeling how an outcome varies with explanatory variables. It estimates relationships and can predict outcomes from those variables.

Least squares: An estimation principle that chooses parameters by minimizing the sum of squared residuals. Ordinary least squares fits coefficients by minimizing squared prediction errors.
Random variable: A variable whose value is determined by a random process and described by a probability distribution. Regression treats outcomes and often errors as random quantities.
Logistic regression: A regression model for binary outcomes that represents their probability through a link function. It models event probabilities when the outcome has two categories.
Analysis of variance: A method for comparing group means by partitioning observed variation into components. ANOVA emphasizes group comparisons, though it can be represented within the linear-model framework.
Omitted-variable bias: Bias in an estimated relationship caused by excluding a relevant variable associated with both a predictor and outcome. Leaving out confounders can distort regression coefficients.
Residual: The difference between an observed value and the value predicted by a model. Residuals reveal the errors left after a regression model is fitted.
Explanatory variable: A variable used to account for or predict variation in another variable. Regression relates explanatory variables to a modeled outcome.
Poisson regression: A generalized linear model commonly used for counts, with a logarithmic link and Poisson response distribution. It models counts such as events occurring over time or space.
Classification: A predictive task that assigns observations to discrete categories. Classification predicts labels, whereas regression usually models numerical outcomes.
Multicollinearity: A condition in which predictors in a regression model are strongly linearly related. Redundant predictors can make individual coefficient estimates unstable.

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