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DOI: 10.1148/radiol.2273011499
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Correlation and Simple Linear Regression1

Kelly H. Zou, PhD, Kemal Tuncali, MD and Stuart G. Silverman, MD

1 From the Department of Radiology, Brigham and Women’s Hospital (K.H.Z., K.T., S.G.S.) and Department of Health Care Policy (K.H.Z.), Harvard Medical School, 180 Longwood Ave, Boston, MA 02115. Received September 10, 2001; revision requested October 31; revision received December 26; accepted January 21, 2002. Address correspondence to K.H.Z. (e-mail: zou@bwh.harvard.edu).



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  		Figure 1. Scatterplots of four sets of data generated by means of the following Pearson correlation coefficients (from left to right): r = 0 (uncorrelated data), r = 0.8 (strongly positively correlated), r = 1.0 (perfectly positively correlated), and r = -1 (perfectly negatively correlated).

 


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  		Figure 2. Simple linear regression model shows that the expectation of the dependent variable Y is linear in the independent variable X, with an intercept a = 1.0 and a slope b = 2.0.

 


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  		Figure 3. Scatterplot of the log of dose (y axis) versus the log of total time (x axis). Each point in the scatterplot represents the values of two variables for a given observation.

 


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  		Figure 4. Scatterplot of the log of dose (y axis) versus the log of total time (x axis). The regression line has the intercept a = -9.28 and slope b = 2.83. We conclude that there is a possible association between the radiation dose and the total time of the procedure.

 




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