Instrumental Variables: 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, renders it as a live 3D point cloud (X, Y, and the normally-invisible U as depth), 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. Sliders let you dial the true causal effect, the confounding strength, the instrument's strength, and the noise level, 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.