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 Journal of Statistics and Management Systems cover
Hybrid ·Peer-reviewed·ISSN (Online): 2169-0014·ISSN (Print): 0972-0510

Monthly Journal: Publishes peer-reviewed aticles on theoretical and applied statistics and management systems, expoloring industrial statistics, actuarial and decision sciences.

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Open Access Research Article

Visualizing and removing the bias in R-squared

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pp. 267–275Vol. 28Issue 2March 2025DOI: 10.47974/JSMS-1016XML
Received:
05 Jul 2022
Published Online:
01 Mar 2025
Article type:
Research Article
Language:
EN
Article no.:
JSMS-1016
Pages:
267–275

Abstract

The R-squared for multiple regression is positively biased. Bootstrap can be utilized to simulate the empirical distribution of the R2 and remove its estimation bias. The bootstrapping method does not require strong distributional assumptions. An example of multiple regression is included to visualize the estimation bias in the R2. Compared to the bias estimate from the adjusted R-squared, the bias estimate based on bootstrap is smaller. So, the bootstrap bias corrected R2 is rightfully between the regular R2 and the adjusted R-squared.

Keywords

Subject Classifications

62J0562J20

References

[1] I. Olkin and J. W. Pratt, “Unbiased estimation of certain correlation coefficients,” The Annals of Mathematical Statistics, pp. 201-211 (1958).
[2] B. Efron and R. J. Tibshirani, An Introduction to the Bootstrap, Boca Raton, FL: CRC Press LLC (1998).
[3] B. Efron, The Jackknife, the Bootstrap and Other Resampling Plans, Philadelphia, PA: Society for Industrial and Applied Mathematics (1982).
[4] B. Efron, “More efficient bootstrap computations,” J. Amer. Stat. Assoc., vol. 85, pp. 79-89 (1990).
[5] C. Samprit, S. H. Ali, and P. Bertram, Regression Analysis by Example, New York: John Wiley & Sons (2006).
[6] A. Canty and B. D. Ripley, “boot: Bootstrap R (S-Plus) Functions,” R package version 1. 3-28 (2021).

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