Regression Diagnostics¶
Belsley, D. A., Kuh, E., & Welsch, R. E. (1980). Regression Diagnostics: Identifying Influential Data and Sources of Collinearity. Wiley.
Cited by¶
4 citations across 4 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 $x_0$.
Mechanisms¶
- 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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