# Multivariate Statistical Methods | My Assignment Tutor

Source: Manly, Bryan F.J. Multivariate Statistical Methods: A Primer, Third Edition, CRC Press,07/2004.Page 1 of 1Tutorial – Week 5 (PCA)Question 1:a) Can the second PC explain more variation than the first PC when performing PCA on thecorrelation matrix?b) When could you use the covariance matrix rather than the correlation matrix?c) The sum of the eigenvalues should equal what?d) If PCA results based on the correlation matrix of 9 variables find that first 3 PC’s explain82%, 7% and 2.5% of the variance respectively; only the first PC has an eigenvalue>1;and the scree plot shows a distinct elbow at PC2 and another smaller elbow at PC3, howmany components would you choose?Question 2:Using the dataset ‘europeemploy.txt’ (from Manly Table 1.5) perform PCA on the correlationmatrix using the prcomp function. This process should include:a) Check the original correlation matrix to get an understanding of the data and the linearrelationships between variables.b) Produce the PCA output, calculate eigenvalues and % variance explained by each PC (allcalculations in R). Interpret.c) Construct a scree plot. Explain your choice of the number of relevant PCs.d) Construct the Z equation for PC3. Interpret.e) Produce a biplot of the first two PCs. Interpret. Explain any differences between yourordination plot and Manly Figure 6.2.f) Produce a biplot of the first and third PC. How does your R code need to change todisplay non-consecutive PCs?Question 3:Complete Exercise 2 at the end of Chapter 6 of Manly using the data file ‘protein.txt’. Thedata is the protein consumption (grams/person/day) from 9 different sources for 25European countries.a) Base your PCA on the correlation analysis using the prcomp function. You will first needto isolate the variables to be included in PCA.b) How many PCs should be considered based on the scree plot, eigenvalues and totalvariance methods?c) Explain the relationships between Albania and Ireland and between Portugal andBulgaria from the first 2 PCs. Try using biplots. What is a limitation inherent in yourinterpretation?

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