Introduction
Regression analysis is a group of statistical methods that model how one variable, the outcome, depends on one or more other variables, the predictors. In medicine it is used to quantify associations, adjust for confounding, and predict outcomes. This note covers the basic idea, the main types of regression models and when each is used, and the assumptions and pitfalls an examiner may ask about. Simple linear regression and the least squares method are covered in the next topic.
Basic idea and key terms
Regression estimates a mathematical relationship between a dependent (response) variable and one or more independent (explanatory) variables. The model produces regression coefficients that show the size and direction of each predictor's effect, and it estimates the effect of one predictor while the others are held constant.
- Dependent variable: the outcome being explained, for example systolic blood pressure or time to death.
- Independent variables: predictors such as age, drug dose, smoking status or treatment group.
- Regression coefficient: the change in the outcome (or in its transformed value) for a one-unit change in the predictor, adjusted for the other predictors in the model.
- Intercept: the predicted outcome when all predictors equal zero; it is often not meaningful on its own.
- Difference from correlation: correlation measures the strength of a symmetric association (see the previous topic), whereas regression assumes a direction, predicts the outcome from the predictors and expresses the effect per unit of the predictor.