Multicollinearity
Multicollinearity arises in multiple regression when two or more explanatory variables are highly correlated, making their individual effects impossible to separate cleanly.
Also known ascollinearity
FrameworkOrdinary least squares (OLS)
See it move
The infographic is a Venn diagram with two overlapping circles labelled Regressor X₁ and Regressor X₂. Each circle contains a region of unique variation, but the overlapping area — labelled "Shared variation: effect can't be separated" — represents the portion of each variable's movement that cannot be attributed to one regressor alone. A note below the diagram explains that a large shared region inflates standard errors and widens confidence intervals, while the point estimates of the coefficients remain unbiased.
The formula
Variables
- Variance inflation factor for regressor Xⱼ
- R-squared from regressing Xⱼ on all other regressors in the model
A VIF above 10 (some thresholds use 5) flags damaging multicollinearity. A VIF of 1 means no correlation with the other regressors.