Correlation gates pass a singular design matrix, and widen the dependency to quieten them further

The reason the heatmap goes quiet is arithmetic you can do without a laptop. If k parts are independent and equally scaled and you also carry their sum, each part correlates with that sum at 1/sqrt(k) ^[1]. Two parts gives 0.707, which is the roughly 0.7 the dev.to example reports ^[3]. Five channel spends adding to a budget line gives 0.447 ^[2]. The dependency is exact in both cases and the matrix is equally rank deficient ^[4], but the loudest cell on the heatmap has gone from 0.71 to 0.45 ^[2].

That number is worth sitting next to the author's own marketing mix experience. He reports his controls sitting at 0.8 and above and the media variables he needed to report on sitting between 0.4 and 0.6 ^[13]. A five-way budget identity scores 0.447 ^[2], which lands inside that media band ^[3]. On correlation alone, a set of columns that sum exactly to another column is indistinguishable from a driver you actually want a coefficient for.

The post carries two failures under one heading, and they need different fixes. The first is rank deficiency in the design matrix: x3 regressed on x1 and x2 returns R squared of 1, so VIF is infinite ^[7]. The second is screening on correlation with the target, which fit beautifully and pushed every media driver out of the model ^[12], because distribution, seasonality and holiday flags were more tightly coupled to the December peak that media spend was also competing to explain ^[14]. VIF does not diagnose the second at all; it never looks at the target. The response described is to start dropping variables for being too correlated with sales ^[15], which is a judgement about what you want the coefficients to mean rather than a collinearity test.

The variance inflation name is literal, and that is the part worth keeping. A VIF of 10 means the coefficient's variance is ten times its orthogonal value and the standard error is about 3.2 times larger, so the estimate is not biased, just unstable enough to swing across zero on a resample ^[8]. Note what infinity does to that reading: an exact dependency gives you no severity to rank, only a column to delete. The ranking use the author recommends over pass/fail gates ^[9] works on near-dependence and degenerates on the exact kind.

Correlation answers a two-variable question and multicollinearity is a property of the whole matrix ^[5], so the cheapest available check is not a diagnostic at all. Most of these dependencies are ones the feature engineering created: a total column, a ratio, a set of spends that add to a budget, a one-hot encoding with every level retained ^[6]. Those can be found by reading your own transformation code, before any threshold gets a chance to pass them.