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The Essentials of Biostatistics for Physicians, Nurses, and Clinicians,
First Edition. Michael R. Chernick.
© 2011 John Wiley & Sons, Inc. Published 2011 by John Wiley & Sons, Inc.

CHAPTER 7

Correlation, Regression,

and Logistic Regression

In this chapter, we will cover correlation, discussing the Pearson

product moment correlation coeffi cient. The Pearson correlation coef-

fi cient (due to Karl Pearson) is a common measure of association that

is interrelated with simple linear regression and goes back to the begin-

ning of the twentieth century. It is a natural parameter of the bivariate

normal distribution. So its properties and interpretation apply to two

variables whose joint distribution is at least, approximately, a bivariate

normal distribution. An example of a nonparametric measure of asso-

ciation will be discussed in Chapter 9.

Specifi cally, there is a mathematical relationship between the slope

of the regression line in simple linear regression (only one independent

variable) and the correlation coeffi cient. This will be shown when we

cover simple linear regression. Multiple regression is an extension of

linear regression to two or more independent variables, and the multiple

correlation coeffi cient is an extension of the square of the Pearson cor-

relation coeffi cient.

Logistic regression is similar to multiple regression, but whereas

in multiple regression the dependent variable is a continuous numerical

variable, in logistic regression, the dependent variable is binary (it

can be an outcome like success or failure). The expected value of the