Topic$-$Data Mining Question $1$: For what type of data are the covariance and correlation matrices identical? In this case, what is $\backslash$Sigma $?$

Question $2$: What is special about the first principal component, in terms of variability?

Question $3$: Describe the four criteria for choosing how many components to extract. Explain the rationale for each.

Question $4$: Explain the concept of communality, so that someone new to the field could understand it$.$

Question $5$: Explain the difference between PCA and factor analysis. What is a drawback of factor analysis?

Question $6$: Describe two tests for determining whether there exists sufficient correlation within a data set for factor analysis to proceed. Which results from these tests would allow us to proceed?

Question $7$: Explain why we perform factor rotation. Describe three different methods for factor rotation.

Question $8$: What is a user$-$define composite, and what is the benefit of using it in place of individual variables?