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Multicollinearity

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Detection

VIF (Variance Inflation Factor):

VIF_j = \frac{1}{1 - R_j^2}

where

R_j^2

is from regressing

x_j

on all other predictors.

VIF $> 5$ : Moderate multicollinearity
VIF $> 10$ : Severe multicollinearity (needs attention) Condition number: $\kappa = \sqrt{\lambda_{\max}/\lambda_{\min}}$ . $\kappa > 30$ indicates serious multicollinearity.

Method	Description
Remove variables	Drop one of the correlated predictors
PCA	Replace correlated predictors with principal components
Ridge regression	Add $\lambda\sum\beta_j^2$ penalty
Partial least squares	Find latent components that predict both X and y