Factor analysis can be thought of as an extension to principal components. Here, we are interested in identifying the underlying factors that might explain a large number of variables. By finding the correlations between a group of variables, we look to find the underlying factors that describe them. The difference between the two techniques is that we are only interested in the correlations of the variables in PCA. Here, in factor analysis, we want to find the underlying factors that are not being described in the data currently. As such, rotations on the factors can be used to closely align the factors with structure in the variables.

The data has been collected from different automobile manufacturers. The variables look at weights of vehicles, fuel efficiency, engine power, capacity, and CO2 emissions.

We will use factor analysis to try and understand the underlying factors in the study. First, we try and identify the number of factors...