Final answer:
The criterion that should ONLY be used when the principal components are based on the correlation matrix is that they should represent 60% of the variability.
Step-by-step explanation:
The criterion that should ONLY be used when the principal components are based on the correlation matrix is that they should represent 60% of the variability.
To select the number of principal components, you can calculate the cumulative variance or eigenvalues. If the cumulative variance or eigenvalues reach 60%, you can stop and choose the corresponding number of principal components.
For example, if the first two principal components explain 40% and 20% of the variability respectively, you would select two principal components because they represent a total of 60% of the variability.