Final answer:
No, it is not necessary to remove correlated variables before running PCA, as PCA is designed to handle multicollinearity and transform the dataset into uncorrelated principal components.
Step-by-step explanation:
When you are asked to run PCA (Principal Component Analysis) on a dataset with highly correlated variables, it is generally not necessary to remove these correlated variables beforehand. PCA is a technique specifically designed to handle multicollinearity by transforming the data into a set of orthogonal components. These components represent the directions of maximal variance and are uncorrelated with each other. Thus, PCA can be particularly useful when you have variables with high correlation.
The purpose of PCA is to reduce the dimensionality of data while retaining as much variability as possible. By doing so, PCA combines the correlated variables in a way that retains the essential information. Removing correlated variables prior to PCA might discard valuable information and is not typically done because PCA accounts for correlation in its methodology.
Thus, it is not only acceptable to include highly correlated variables when running PCA; in many cases, it is precisely these relationships that PCA seeks to understand and quantify.