Multicollinearity arises when two predictors (X₁, X₂) are highly correlated. Geometrically, the data cloud collapses onto a line — the regression plane loses its support and can "wobble" wildly while still fitting Y well. This inflates standard errors and makes coefficients unreliable.

A concrete example: in personality psychology, the Dark Triad traits — Machiavellianism, narcissism, and psychopathy — are moderately to highly intercorrelated (typically r = 0.4–0.7). Suppose you regress workplace deviance on all three. Even if psychopathy is the strongest unique predictor, its confidence interval will be wide because the three predictors share so much variance. At r = 0.6, VIF ≈ 1.6 — tolerable. But with a short measure that conflates the traits (pushing r toward 0.85), VIF climbs to 3.6 and each SE is inflated by √3.6 ≈ 1.9×. The predictors individually "wash out" even though the model as a whole explains substantial variance. When researchers report that "none of the Dark Triad traits uniquely predicted the outcome" but the overall R² is large, multicollinearity is one common explanation — though short measures, conceptual overlap, and noisy outcomes can also play a role.

Common remedies: (1) Increase sample size — to achieve the same precision you would have with uncorrelated predictors, you need roughly VIF times as many observations (a useful heuristic, not a formal requirement). (2) Combine predictors — replacing near-identical measures with a composite eliminates the collinearity at the cost of granularity. (3) Ridge regression — a small penalty shrinks coefficients toward zero, dramatically reducing variance at the cost of slight bias. (4) Orthogonalize — residualizing one predictor on the other removes collinearity but changes what the coefficients mean, and if the residualized predictor retains little variance the estimates can become even more unstable (for a thorough treatment of why partialing is often a questionable practice, see Hoyle et al., 2023).