Linear regression

Linear regression models a response as a linear function of one or more predictors, estimating coefficients from observed data. It is used to describe relationships and predict responses.

Ordinary least squares: A method that estimates regression coefficients by minimizing the sum of squared residuals. It is the standard fitting rule for linear regression.
Statistical model: A mathematical description of how data are generated, including systematic structure and random variation. Linear regression is one specific way to represent a response-generating process.
Logistic regression: A regression model that predicts a categorical outcome through a link to its probabilities. It suits binary outcomes, unlike ordinary linear regression's unbounded predictions.
Trend estimation: The estimation of systematic change in a quantity over time or another ordered variable. A linear time predictor gives a compact estimate of a constant rate of change.
Residual: The difference between an observed response and its value predicted by a model. Residuals measure the errors that coefficient fitting tries to reduce.
Random variable: A quantity whose possible values are governed by a probability distribution. Regression treats responses and often errors as random quantities.
Polynomial regression: Regression using powers of predictors to represent curved relationships while remaining linear in coefficients. It adds curvature without changing the linear coefficient-fitting framework.
Econometrics: The use of statistical methods to analyze economic data and quantify economic relationships. Linear regression is a foundational tool for estimating empirical economic relationships.
Design matrix: A matrix whose rows encode observations and whose columns encode predictors and any intercept. It organizes predictors into the algebraic form used to fit a linear model.
Conditional expectation: The expected value of a random variable given information about other variables. The regression function often targets the response's conditional mean.

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