How do you detect and handle multicollinearity?

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Answer

$Symptoms: unstable β̂ across subsets, huge SEs, opposite-sign coefficients from univariate expectation, high pairwise correlation.$
$\mathrm{VIF}\; = \;1\; / \;(1\; - \;R_{j}^{2})$
$Condition number of X'X (>30 problematic).$
$Fixes: drop redundant features, PCA / partial-least-squares, ridge regression (shrinks coefficients), domain-based feature engineering.$
$Doesn't hurt PREDICTION accuracy on new data much — mainly wrecks coefficient interpretability and inference.$

Check yourself — multiple choice

Not detectable
Diagnose with VIF > 5-10 or cond(X'X) > 30; fix with dropping features, PCA, ridge; hurts inference, not always prediction
Same as heteroscedasticity
No fix

Multicollinearity: VIF > 5-10 or cond > 30; fix drop/PCA/ridge; hurts inference not prediction.

#regression#assumptions

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