Multicollinearity & VIF: Why Correlated Predictors Break Regression

Regression textbooks warn that a Variance Inflation Factor above 10 signals trouble, but the number alone hides what's actually happening to the fit. This simulator draws two predictor variables with an adjustable correlation, fits a real ordinary-least-squares plane to a noisy response by solving the normal equations, and renders both the point cloud and the fitted plane in 3D so you can watch the plane's tilt become unstable as the predictors become collinear — exactly when VIF and the coefficient standard errors explode. A second plane fitted with Ridge regularization is drawn alongside it, showing the classic bias-variance trade the article describes: a small, deliberate bias in exchange for a fit that no longer swings wildly between samples.