Regression Diagnostics¶
Belsley, D. A., Kuh, E., & Welsch, R. E. (1980). Regression Diagnostics: Identifying Influential Data and Sources of Collinearity. John Wiley & Sons.
Cited by¶
7 citations across 7 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Linear Independence
- In statistics and regression it is the diagnosis of multicollinearity — collinear predictors make coefficients unstable and uninterpretable — measured by the variance inflation factor, with principal components constructed precisely to be uncorrelated.
This sourceDiagnoses multicollinearity via the variance inflation factor and condition number, with near-singular X'X destabilizing coefficients.
- In statistics and regression it is the diagnosis of multicollinearity — collinear predictors make coefficients unstable and uninterpretable — measured by the variance inflation factor, with principal components constructed precisely to be uncorrelated.
- Outlier Leverage
- Consider ordinary least squares fit to a scatter of \(n = 500\) points whose bulk lies in a tight cloud near the origin, plus a single point placed far out along the \(x\)-axis at \((x_0, y_0)\) with large \(x_0\).
This sourceHat-value (leverage) diagnostics; a single point far in x-space attains a hat value approaching 1.
- Consider ordinary least squares fit to a scatter of \(n = 500\) points whose bulk lies in a tight cloud near the origin, plus a single point placed far out along the \(x\)-axis at \((x_0, y_0)\) with large \(x_0\).
Domain-specific¶
Mechanisms¶
- Correlation or Covariance Audit
- The guarding discipline is to estimate correlations conditional on the stressed regime, not just the placid average, an application of the multicollinearity concept from regression, where redundant inputs inflate variance and carry less joint information than their count implies.
This sourceTreats multicollinearity as redundant relations among regression inputs that inflate the variance and impair the reliability of coefficient estimates.
- The guarding discipline is to estimate correlations conditional on the stressed regime, not just the placid average, an application of the multicollinearity concept from regression, where redundant inputs inflate variance and carry less joint information than their count implies.
- Experimental Design-Matrix Rank Check
- A barely-full-rank design — columns independent but nearly collinear — is estimable yet yields enormous variances; that is a conditioning problem, not a rank problem, and this check will pass it.
This sourceDistinguishes full-rank but ill-conditioned regression designs from exact rank deficiency and shows that near dependencies can leave coefficients estimable while greatly inflating their variances.
- A barely-full-rank design — columns independent but nearly collinear — is estimable yet yields enormous variances; that is a conditioning problem, not a rank problem, and this check will pass it.
- Feature Collinearity Heatmap
- It is systematically blind to multi-way dependence — a set can be pairwise-clean yet jointly rank-deficient
This sourceExplains why pairwise correlations can miss multivariate collinearity and rank deficiency.
- It is systematically blind to multi-way dependence — a set can be pairwise-clean yet jointly rank-deficient
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