Correlation and Regression

Definition & overview

• Two complementary techniques — Correlation and regression study the relationship (association) between two continuous quantitative variables measured on the same individuals — e.g. dose and response, age and creatinine clearance, height and anatomical dead space.
• Different questions — Correlation measures the degree of association — how closely two variables move together — and returns one dimensionless number, the coefficient r (symmetric: neither variable is privileged as cause).
• Regression — estimates the mathematical relationship — the equation of the line that best predicts the dependent / outcome variable y from the independent / predictor variable x; it is directional (regressing y on x ≠ x on y).
• Model dictated by outcome type — Within drug research these tools sit inside multivariable analysis, where the regression model is chosen by the type of outcome: continuous → linear; binary → logistic; rate → Poisson; time-to-event → Cox regression.