To understand the theory and details behind the factor analysis read the Introduction to Factor Analysis.
In this post, an example for factor analysis is given.
Example
Suppose a customer survey was conducted while purchasing car. In the questionnaire, 9 different variables were included, and 75 customers were participated for the study. The survey questions were framed using 5-point likert scale with 1 being very low and 5 being very high.
Factor analysis is used to describe the covariance relationships among many variables in terms of a few underlying, but unobservable random quantities called factors. If variables can be grouped (not the observations) by their correlations, then all variables within a particular group are highly correlated among themselves. This means, each group of variables represents a single underlying hidden factor that is responsible for the observed correlations.
For example, correlations from a group of test scores in Mathematics, Statistics, Chemistry and Physics might correspond to a factor named “intelligence”.