Detecting Multicollinearity in OLS
You are examining an OLS regression with design matrix $X$. Four methods have been proposed to detect multicollinearity among the predictor variables:
1. Inspect the eigenvalues of $X^T X$ for near-zero values.
2. Compute the condition number of $X^T X$ (ratio of largest to smallest eigenvalue) and flag large values.
3. Inspect the correlation matrix of the rows of $X$.
4. Inspect the correlation matrix of the columns of $X$.
Which of these methods correctly detect multicollinearity? For each, explain why it works or why it fails.
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