The DOI matches its Crossref record; 59 of the 59 references it cites were found in a registry or an index.
The Correlation Coefficient: An Overview
Abstract
Correlation and regression are different, but not mutually exclusive, techniques. Roughly, regression is used for prediction (which does not extrapolate beyond the data used in the analysis) whereas correlation is used to determine the degree of association. There situations in which the x variable is not fixed or readily chosen by the experimenter, but instead is a random covariate to the y variable. This paper shows the relationships between the coefficient of determination, the multiple correlation coefficient, the covariance, the correlation coefficient and the coefficient of alienation, for the case of two related variables x and y. It discusses the uses of the correlation coefficient r, either as a way to infer correlation, or to test linearity. A number of graphical examples are provided as well as examples of actual chemical applications. The paper recommends the use of z Fisher transformation instead of r values because r is not normally distributed but z is (at least in approximation). For either correlation or for regression models, the same expressions are valid, although they differ significantly in meaning.
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Cites
(2005) · Technometrics · doi:10.1198/tech.2005.s303 · Cited by 17,923
Applied Multivariate Statistical Analysis.
Johnson, A. R., & Wichern, D. W. (1988) · Biometrics · doi:10.2307/2531616 · Cited by 11,353
Robust Regression and Outlier Detection
Piepel, G. F. (1989) · Technometrics · doi:10.1080/00401706.1989.10488524 · Cited by 6,144
Robust Regression and Outlier Detection
Rousseeuw, P. J., & Leroy, A. M. (1987) · Wiley Series in Probability and Statistics · doi:10.1002/0471725382 · Cited by 5,609
Draper, N. R., & Smith, H. (1998) · Wiley Series in Probability and Statistics · doi:10.1002/9781118625590 · Cited by 5,024
Numerical Recipes in C: The Art of Scientific Computing.
Birchenhall, C., Press, W. H., Teukolsky, S. A., Vetterling, W. T., & Flannery, B. P. (1994) · The Economic Journal · doi:10.2307/2234664 · Cited by 4,355
Thirteen Ways to Look at the Correlation Coefficient
Lee Rodgers, J., & Nicewander, W. A. (1988) · The American Statistician · doi:10.1080/00031305.1988.10475524 · Cited by 4,052
Gunst, R. F. (1999) · Technometrics · doi:10.1080/00401706.1999.10485680 · Cited by 4,002
(1947) · The American Statistician · doi:10.1080/00031305.1947.10501534 · Cited by 3,660
An Introduction to Error Analysis
Taylor, J. R. (1982) · Medical Entomology and Zoology · Cited by 2,807
Cited by
Randhawa, G. S., Soltysiak, M. P. M., El Roz, H., de Souza, C. P. E., Hill, K. A., & Kari, L. (2020) · PLOS ONE · doi:10.1371/journal.pone.0232391 · Cited by 1,023
Ramos-Escudero, F., Muñoz, A. M., Alvarado-Ortíz, C., Alvarado, Á., & Yáñez, J. A. (2012) · Journal of Medicinal Food · doi:10.1089/jmf.2010.0342 · Cited by 204
Alexan, W., Alexan, N., & Gabr, M. (2023) · Fractal and Fractional · doi:10.3390/fractalfract7040287 · Cited by 144
Alexan, W., Elabyad, N., Khaled, M., Osama, R., El-Damak, D., Abd El Ghany, M. A., Korayem, Y., Mamdouh, E., & Gabr, M. (2024) · IEEE Access · doi:10.1109/access.2024.3446733 · Cited by 53
Makwakwa, T. A., Moema, D., Nyoni, H., & Msagati, T. A. M. (2023) · Talanta Open · doi:10.1016/j.talo.2023.100206 · Cited by 14
Metadata
- Authors
- Asuero, A. G., Sayago, A., & González, A. G.
- Venue
- Critical Reviews in Analytical Chemistry
- Publisher
- Informa UK Limited
- Published
- 2006-01
- Volume
- 36
- Issue
- 1
- Pages
- 41-59
- ISSN
- 1040-8347 (ISSN-L)
- 1547-6510
- OpenAlex
- W2027666102
- Cited by
- 1,510
- References
- 59
- FWCI
- 6.77
- Type
- journal article
- Language
- en
- Open access
- closed
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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