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What is VIF and when do you worry about multicollinearity?

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Answer

  • Variance Inflation Factor of feature xj  =  1  /  (1    Rj2)x_{j}\; = \;1\; / \;(1\; - \;R_{j}^{2}), where Rj2R_{j}^{2} is the R2R^{2} of regressing xjx_{j} on the other features.
  • VIF = 1 means no collinearity; VIF > 5 or 10 is a common warning threshold.
  • High VIF inflates coefficient standard errors, makes individual coefficients unstable and hard to interpret, but doesn't harm overall prediction.
  • Fixes: drop redundant features, combine them (PCA), or use ridge regression which is stable under collinearity.
Check yourself — multiple choice
  • Low VIF (<0.5) signals multicollinearity
  • High VIF (>5–10) signals multicollinearity and unstable coefficients
  • VIF measures overfitting
  • VIF is only used for classification

VIF > 5–10 flags multicollinearity — coefficients become unstable but predictions remain OK.

#linear-regression#assumptions#features

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