How do you detect multicollinearity?

• Correlation Matrix — Check for high correlation (e.g., |r| > 0.8 or 0.9) between independent variables.
• Variance Inflation Factor (VIF) — VIF > 5 (or >10) indicates significant multicollinearity.
• Tolerance — Tolerance < 0.2 (or <0.1) suggests multicollinearity.
• Condition Number (Condition Index) — Values > 30 indicate severe multicollinearity.
• **Eigenvalues Analysis** — Very small eigenvalues suggest dependency among predictors.
• Regression Coefficient Instability — Large changes in coefficients when variables are added/removed.
• High Standard Errors — Inflated standard errors of regression coefficients.
• Unexpected Coefficient Signs — Coefficients may have incorrect signs or insignificant p-values despite strong model fit.
• Pairwise Scatter Plots — Visualize linear relationships among predictor variables.
• Determinant of Correlation Matrix — A value close to zero indicates multicollinearity.