Correlation, Linear Regression, and Logistic Regression
| Home | | Advanced Mathematics |Chapter: Biostatistics for the Health Sciences: Correlation, Linear Regression, and Logistic Regression
The previous chapter presented various chi-square tests for determining whether or not two variables that represented categorical measurements were significantly associated.
Correlation, Linear Regression, and Logistic Regression
The previous chapter presented various chi-square
tests for determining whether or not two variables that represented categorical
measurements were significantly associated. The question arises about how to
determine associations between variables 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 measurement are Fahrenheit temperature and I.Q. scores; ratio
level measures include blood pressure, serum cholesterol, and many other
biomedical research variables that have a true zero point. In comparison to the
chi-square test, the correlation coefficient 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 regression equation.. In contrast to
correlation, linear regression is used for predicting status on a second
variable (e.g., a dependent variable) when the value of a predictor variable
(e.g., an independent variable) is known.
Another technique that provides information about
the strength of association between a predictor variable (e.g., a risk factor
variable) and an outcome variable (e.g., dead or alive) is logistic regression.
In the case of a logistic regression analysis, the outcome is a dichotomy; the
predictor can be selected from variables that represent several levels of
measurement (such as categorical or ordinal), as we will demonstrate in Section
12.9. For example, a physician may use a patient’s total serum cholesterol
value and race to predict high or low levels of coronary heart dis-ease risk.
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