Describe a method to detect and handle multicollinearity in a dataset.
Instruction: Explain how you would identify multicollinearity in your variables and the steps you would take to address it.
Updated
Official answer
First inspect the design matrix for duplicated columns, redundant category indicators and predictors derived exactly from others. Pairwise correlations alone can miss a dependence involving several columns.
For an ordinary linear model with an intercept, regress predictor j on the other predictors and calculate VIF_j = 1/(1 - R_j²). If that auxiliary R² is 0.8, the VIF is 5. Under the usual variance comparison, that multiplies coefficient variance by 5 and standard error by sqrt(5), not by 5. Perfect linear dependence makes the denominator zero.
Treat cutoffs as prompts to investigate. Remove a redundant measurement when it adds no information, combine variables only when their meaning supports it, or consider ridge regularization for a prediction task. Tune preprocessing and penalties inside training folds. PCA changes the feature interpretation; it is not a free interpretability improvement.
For causal analysis, preserve required adjustment variables and assess identification. A smaller VIF does not justify omitting a confounder. Document how the chosen remedy affects uncertainty, predictions and the question the model answers.