Correlation and simple linear regression.

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 rho, 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.

[1]  P. E. Crewson,et al.  Hypothesis testing II: means. , 2003, Radiology.

[2]  Kimberly E Applegate,et al.  An introduction to biostatistics. , 2002, Radiology.

[3]  Kelly H. Zou,et al.  On estimating a transformation correlation coefficient , 2002 .

[4]  P F Judy,et al.  CT fluoroscopy-guided abdominal interventions: techniques, results, and radiation exposure. , 1999, Radiology.

[5]  Roger E. Kirk,et al.  Statistics: An Introduction , 1998 .

[6]  Joshua D. Angrist,et al.  Identification of Causal Effects Using Instrumental Variables , 1993 .

[7]  Deo Kumar Srivastava,et al.  A test of p-variate normality , 1992 .

[8]  M. Kendall,et al.  Rank Correlation Methods (5th ed.). , 1992 .

[9]  Douglas G. Altman,et al.  Practical statistics for medical research , 1990 .

[10]  Margaret G. Stineman,et al.  Designing Clinical Research: An Epidemiological Approach , 1990 .

[11]  D. Ruppert,et al.  Transformation and Weighting in Regression , 1988 .

[12]  Wojtek J. Krzanowski,et al.  Principles of multivariate analysis : a user's perspective. oxford , 1988 .

[13]  P. Holland.  Statistics and Causal Inference , 1985 .

[14]  G. Seber,et al.  Linear Regression Analysis , 1980 .

[15]  D. Rubin.  Estimating causal effects of treatments in randomized and nonrandomized studies. , 1974 .

[16]  Erwin Kreyszig,et al.  Introductory Mathematical Statistics. , 1970 .

[17]  O. D. Duncan.  Path Analysis: Sociological Examples , 1966, American Journal of Sociology.

[18]  D. Cox,et al.  An Analysis of Transformations , 1964 .

[19]  F. N. David,et al.  The variance of Spearman's rho in normal samples , 1961 .

[20]  E. S. Pearson,et al.  TESTS FOR RANK CORRELATION COEFFICIENTS. I , 1957 .

[21]  Maurice G. Kendall,et al.  Rank Correlation Methods , 1949 .

[22]  Thomas P. Hettmansperger,et al.  Statistical inference based on ranks , 1985 .

[23]  R. Fisher.  FREQUENCY DISTRIBUTION OF THE VALUES OF THE CORRELATION COEFFIENTS IN SAMPLES FROM AN INDEFINITELY LARGE POPU;ATION , 1915 .

[24]  K. Pearson.  Mathematical Contributions to the Theory of Evolution. III. Regression, Heredity, and Panmixia , 1896 .

[25]  F. Galton.  I. Co-relations and their measurement, chiefly from anthropometric data , 1889, Proceedings of the Royal Society of London.