Sample Exam Questions for MB 813 Multivariate Statistics

1.   Define the following terms (formulas not necessary)

2. Compute (by hand) the product AB, where A and B are the matrices below. How would you interpret the result? What is the meaning of each column of AB?

<insert matrices> 

3. #9;Explain singular value decomposition (SVD). What is the objective? What are the inputs and outputs? What is the relationship between SVD and (a) principal components and (b) correspondence analysis? What do the scores mean? What are the singular values?

4. Explain multidimensional scaling (MDS).

5. Explain the difference between principal components and factor analysis.

6. The fundamental equation of factor analysis is R = FF’. What is the central idea that this equation expresses?

7.  Interpret the following MDS map.

<insert map>

8. Interpret the factor analysis output by annotating each section briefly, and then providing a summary of what the basic result was – the take-away story, what you learned from the analysis.

<insert output>

9. Explain Johnson's hierarchical clustering.

10. What are the differences between the various levels of measurement? How do they relate to measures of association and to different types of normalization?

11. Why do we standardize variables?

12. Explain what a QAP correlation is and why it works.

13. Suppose you run MDS on a proximity matrix and obtain a set of coordinates in 2-dimensional space. Now you compute Euclidean distances among the rows of the coordinate matrix, and submit the resulting distance matrix to MDS. How will the resulting map compare to the first map you obtained? Why? What will the stress be? Why?

14. Suppose you were going to compute Pearson correlations among the rows of a data matrix. Would it make sense to standardize the rows first? Under what circumstances would you standardize the columns before computing the correlations among the rows?

15. What is the form of the generic association measure of