Why Your Betas Explode: The Hidden Geometry of Multicollinearity
A deep dive into multicollinearity in linear regression, explaining why OLS coefficients become unstable when features are highly correlated. Using Linear TV vs. Digital TV as a running example, the piece traces the problem from the OLS closed-form solution through linear algebra (Gram matrix, determinant, matrix inverse) to a geometric interpretation: correlated feature vectors collapse the volume of the feature space, causing the inverse of the Gram matrix to blow up and standard errors to explode. The same phenomenon is then translated into VIF and condition number diagnostics. A Python code demo with statsmodels shows how standard errors inflate as correlation rises from 0.3 to 0.99, while an independent channel (OOH) remains unaffected.