arXiv 15 May 2025 · Statistics — Methodology · publishedQeios (2025) · 1 citations (OpenAlex)
arXiv:2505.10738 · PDF · DOI · OpenAlex · Extracted main text
In this paper, we investigate the impact of outliers on the statistical significance of coefficients in linear regression. We demonstrate, through numerical simulation using R, that a single outlier can cause an otherwise insignificant coefficient to appear statistically significant. We compare this with robust Huber regression, which reduces the effects of outliers. Afterwards, we approximate the influence of a single outlier on estimated regression coefficients and discuss common diagnostic statistics to detect influential observations in regression (e.g., studentized residuals). Furthermore, we relate this issue to the optional normality assumption in simple linear regression [14], required for exact finite-sample inference but asymptotically justified for large n by the Central Limit Theorem (CLT). We also address the general dangers of relying solely on p-values without performing adequate regression diagnostics. Finally, we provide a brief overview of regression methods and discuss how they relate to the assumptions of the Gauss-Markov theorem.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Jeffrey M. Wooldridge (2019) Introductory Econometrics: A Modern Approach | 0.874 | 7 | 2 | 100% |
| 2 | Peter J. Huber (1964) Robust estimation of a location parameter | 0.843 | 3 | 3 | 100% |
| 3 | David A. Belsley, Edwin Kuh, and Roy E. Welsch (1980) Regression Diagnostics: Identifying Influential Data and Sources of Collinearity | 0.737 | 3 | 2 | 100% |
| 4 | Tobias E. Ugah, Emmanuel I. Mba, Micheal C. Eze, Kingsley C. Arum, I… (2021) On the upper bounds of test statistics for a single outlier test in linear regression models | 0.644 | 2 | 2 | 100% |
| 5 | R. Dennis Cook (1977) Detection of influential observations in linear regression | 0.644 | 2 | 2 | 100% |
| 6 | Amand F. Schmidt and Chris Finan (2018) Linear regression and the normality assumption | 0.405 | 1 | 1 | 100% |
| 7 | Vic Barnett and Toby Lewis (1978) Outliers in Statistical Data | 0.405 | 1 | 1 | 100% |
| 8 | William S. Cleveland (1979) Robust locally weighted regression and smoothing scatterplots | 0.405 | 1 | 1 | 100% |
| 9 | P. J. Cornbleet and N. Gochman (1989) Incorrect least-squares regression coefficients in method-comparison analysis | 0.405 | 1 | 1 | 100% |
| 10 | Carl de Boor (1978) A Practical Guide to Splines | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 20 scored citations.