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CHAPTER 12
Correlation, Linear Regression,
and Logistic Regression
Biological phenomena in their numerous phases, economic and
social, were seen to be only differentiated from the physical by
the intensity of their correlations. The idea Galton placed before
himself was to represent by a single quantity the degree of rela-
tionships, or of partial causality between the different variables
of our everchanging universe.
—Karl Pearson, The Life, Letters, and Labours of Francis Galton,
Volume IIIA, Chapter XIV, p. 2
The previous chapter presented various chi-square tests for determining whether or
not two variables that represented categorical measurements were significantly as-
sociated. The question arises about how to determine associations between vari-
ables that represent higher levels of measurement. This chapter will cover the Pear-
son product moment correlation coefficient (Pearson correlation coefficient or
Pearson correlation), which is a method for assessing the association between two
variables that represent either interval- or ratio-level measurement.
Remember from the previous chapter that examples of interval level measure-
ment are Fahrenheit temperature and . scores; ratio level measures include blood
pressure, serum cholesterol, and many other biomedical research variables that
have a true zero point. parison to the chi-square test, the correlation coeffi-
cient provides additional useful information—namely, the strength of association
between the two variables.
We will also see that linear regression and correlation are related because there
are formulas that relate the correlation coefficient to the slope parameter of the re-
gression equation.. In contrast to correlation, linear regression is used for predicting
status on a second variable (., a dependent variable) when the value of a predic-
tor variable (., an independent variable) is known