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    Statistical Concepts Series

    Correlation and Simple Linear Regression

    Published Online:Jun 1 2003https://doi.org/10.1148/radiol.2273011499

    Abstract

    In this tutorial article, the concepts of correlation and regression are reviewed and demonstrated. The authors review and compare two correlation coefficients, the Pearson correlation coefficient and the Spearman ρ, for measuring linear and nonlinear relationships between two continuous variables. In the case of measuring the linear relationship between a predictor and an outcome variable, simple linear regression analysis is conducted. These statistical concepts are illustrated by using a data set from published literature to assess a computed tomography–guided interventional technique. These statistical methods are important for exploring the relationships between variables and can be applied to many radiologic studies.

    © RSNA, 2003

    References

    • 1 Krzanowsk WJ. Principles of multivariate analysis: a user’s perspective Oxford, England: Clarendon, 1988; 405-432. Google Scholar
    • 2 Rodriguez RN. Correlation. In: Kotz S, Johnson NL, eds. Encyclopedia of statistical sciences. New York, NY: Wiley, 1982; 193-204. Google Scholar
    • 3 Applegate KE, Crewson PE. An introduction to biostatistics. Radiology 2002; 225:318-322. Link, Google Scholar
    • 4 Goldman RN, Weinberg JS. Statistics: an introduction Upper Saddle River, NJ: Prentice Hall, 1985; 72-98. Google Scholar
    • 5 Freund JE. Mathematical statistics 5th ed. Upper Saddle River, NJ: Prentice Hall, 1992; 494-546. Google Scholar
    • 6 Spearman C. The proof and measurement of association between two things. Am J Psychol 1904; 15:72-101. Crossref, Google Scholar
    • 7 Fieller EC, Hartley HO, Pearson ES. Tests for rank correlation coefficient. I. Biometrika 1957; 44:470-481. Crossref, Google Scholar
    • 8 Fieller EC, Pearson ES. Tests for rank correlation coefficients. II. Biometrika 1961; 48:29-40. Google Scholar
    • 9 Kruskal WH. Ordinal measurement of association. J Am Stat Assoc 1958; 53:814-861. Crossref, Google Scholar
    • 10 David FN, Mallows CL. The variance of Spearman’s rho in normal samples. Biometrika 1961; 48:19-28. Crossref, Google Scholar
    • 11 Silverman SG, Tuncali K, Adams DF, Nawfel RD, Zou KH, Judy PF. CT fluoroscopy-guided abdominal interventions: techniques, results, and radiation exposure. Radiology 1999; 212:673-681. Link, Google Scholar
    • 12 Daniel WW. Biostatistics: a foundation for analysis in the health sciences 7th ed. New York, NY: Wiley, 1999. Google Scholar
    • 13 Altman DG. Practical statistics for medical research Boca Raton, Fla: CRC, 1990. Google Scholar
    • 14 Neter J, Wasserman W, Kutner MH. Applied linear models: regression, analysis of variance, and experimental designs 3rd ed. Homewood, Ill: Irwin, 1990; 38-44, 62–104. Google Scholar
    • 15 Galton F. Typical laws of heredity. Proc R Inst Great Britain 1877; 8:282-301. Google Scholar
    • 16 Galton F. Correlations and their measurements, chiefly from anthropometric data. Proc R Soc London 1888; 45:219-247. Google Scholar
    • 17 Pearson K. Mathematical contributions to the theory of evolution. III. Regression, heredity and panmixia. Phil Trans R Soc Lond Series A 1896; 187:253-318. Crossref, Google Scholar
    • 18 Hulley SB, Cummings SR. Designing clinical research: an epidemiological approach Baltimore, Md: Williams & Wilkins, 1988. appendix 13.C. Google Scholar
    • 19 Hettmansperger TP. Statistical inference based on ranks Malabar, Fla: Krieger, 1991; 200-205. Google Scholar
    • 20 Kendall M, Gibbons JD. Rank correlation methods 5th ed. New York, NY: Oxford University Press, 1990; 8-10. Google Scholar
    • 21 Zou KH, Hall WJ. On estimating a transformation correlation coefficient. J Appl Stat 2002; 29:745-760. Crossref, Google Scholar
    • 22 Fisher RA. Frequency distributions of the values of the correlation coefficient in samples from an indefinitely large population. Biometrika 1915; 10:507-521. Google Scholar
    • 23 Duncan OD. Path analysis: sociological examples. In: Blalock HM, Jr, eds. Causal models in the social sciences. Chicago, Ill: Alpine-Atherton, 1971; 115-138. Google Scholar
    • 24 Rubin DB. Estimating casual effects of treatments in randomized and nonrandomized studies. J Ed Psych 1974; 66:688-701. Crossref, Google Scholar
    • 25 Holland P. Statistics and causal inference. J Am Stat Assoc 1986; 81:945-970. Crossref, Google Scholar
    • 26 Angrist JD, Imbens GW, Rubin DB. Identification of causal effects using instrumental variables. J Am Stat Assoc 1996; 91:444-455. Crossref, Google Scholar
    • 27 Seber GAF. Linear regression analysis New York, NY: Wiley, 1997; 48-51. Google Scholar
    • 28 Carroll RJ, Ruppert D. Transformation and weighting in regression New York, NY: Chapman & Hall, 1988; 2-61. Google Scholar
    • 29 Box GEP, Cox DR. An analysis of transformation. J R Stat Soc Series B 1964; 42:71-78. Google Scholar
    • 30 Tello R, Crewson PE. Hypothesis testing II: means. Radiology 2003; 227:1-4. Link, Google Scholar
    • 31 Mudholkar GS, McDermott M, Scrivastava DK. A test of p-variate normality. Biometrika 1992; 79:850-854. Crossref, Google Scholar

    Article History

    Published in print: June 2003