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(Circulation. 2006;114:2083-2088.)
© 2006 American Heart Association, Inc.

Statistical Primer for Cardiovascular Research

Correlation and Regression

Sybil L. Crawford, PhD

From the University of Massaschusetts Medical School, Worcester, Mass.

Correspondence to Sybil L. Crawford, PhD, Preventive and Behavioral Medicine, University of Massachusetts Medical School, 55 Lake Ave N, Shaw Bldg, Room 228, Worcester, MA 01655. E-mail Sybil.Crawford@umassmed.edu

Key Words: statistics • epidemiology • computers

An extract of the first 250 words of the full text is provided, because this article has no abstract.

	Introduction

 
In many health-related studies, investigators wish to assess the strength of an association between 2 measured (continuous) variables. For example, the relation between high-sensitivity C-reactive protein (hs-CRP) and body mass index (BMI) may be of interest. Although BMI is often treated as a categorical variable, eg, underweight, normal, overweight, and obese, a noncategorized version is more detailed and thus may be more informative in terms of detecting associations. Correlation and regression are 2 relevant (and related) widely used approaches for determining the strength of an association between 2 variables. Correlation provides a unitless measure of association (usually linear), whereas regression provides a means of predicting one variable (dependent variable) from the other (predictor variable). This report summarizes correlation coefficients and least-squares regression, including intercept and slope coefficients.

	Correlation

 
Correlation provides a "unitless" measure of association between 2 variables, ranging from –1 (indicating perfect negative association) to 0 (no association) to +1 (perfect positive association). Both variables are treated equally in that neither is considered to be a predictor or an outcome.

	Pearson Product-Moment Coefficient of Correlation

 
The most commonly used version is the Pearson product-moment coefficient of correlation, r. Suppose one wants to estimate the correlation between X=BMI, denoted for the i^th subject as X_i, and Y=hs-CRP, denoted for the i^th subject as Y_i. This is estimated for a sample of size n (i=1,..., n) using the following formula¹: equation

where equation

and equation

Here, indicates the sample mean of X (=BMI), and the sample mean of Y (=hs-CRP). The numerator of . . . [Full Text of this Article]

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