Instrumental Variables (2D): Untangling a Confounded Cause

Correlation between a treatment X and an outcome Y is not proof that X causes Y — a hidden confounder U can drive both and bias any naive regression. This simulator generates a synthetic cohort where that is exactly what happens, plots it as a draggable 2D scatter that tilts to reveal U as it fans the points apart, and fits two regression lines side by side: the biased naive OLS line, and a two-stage-least-squares line built from a valid instrument Z that moves the treatment without ever touching the outcome directly. A second panel diagnoses the instrument itself (how strongly Z moves X), and a third sweeps confounding strength across its full range to chart how naive bias grows while the IV estimate stays anchored to the truth. Sliders let you dial the true causal effect, the confounding strength, the instrument's strength, the noise level and the cohort size, while live readouts track the true β against both estimates and the instrument's relevance — the same diagnostic economists and epidemiologists run before trusting an IV study.