Prepare the dataset for input for a PCA via SAS. – Perform a principal component analysis using…

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i. Prepare the dataset for input for a PCA via SAS. (2 marks)

ii. Perform a principal component analysis using SAS on the correlation matrix for the p=9

variables. Show your full SAS code and output. Perform a PCA on the whole data set of

molecules using SAS. (6 marks)

iii. Also perform the procedures to obtain the following 5 plots related to PROC PCA.

Refer to Irene’s SAS notes for Assignment 2 & Lab for PCA Week 8-9.pdf (sent in Week 8)

• Scree plot

• Profile plot

• Component Pattern plots

• Score plots

• Loading Plots

Using the plots and SAS notes and your SAS outputs report and answer the following (justify your

answers).

a) Report the eigenvalues and the eigenvectors. (2 marks)

b) What percentage of the total sample variation is accounted for by each of the first PC, 2nd PC to

the ninth PC? (5 marks)

c) What percentage of the total sample variation is accounted for by the first PC to the ninth PC? (1

mark)

d) Write out the formulation for the PCs. (5 marks)

e) Interpret the PCs via eigen values. (5 marks)

f) Interpret the PCs using your component pattern profiles from SAS. (4 marks)

g) Can the data be effectively summarised in fewer than 9 dimensions? Justify your answer using

BOTH relevant plots and eigenvalues. (5 marks)

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