Use the principal components defined in Exercise 14.2 to construct Gabriel’s biplot. Use enough dimensions to account for 75% of the dispersion in Z-space. Interpret the biplots with respect to the...

Use the principal components defined in Exercise 14.2 to construct Gabriel’s biplot. Use enough dimensions to account for 75% of the dispersion in Z-space. Interpret the biplots with respect to the correlation structure of the variables, the similarity of the sampling sites, and the major differences in the sampling sites.

Exercise 14.2

Extract from the 9×15 matrix of centered and standardized variables the 14 independent variables to obtain Z. Do the principal component analysis on this matrix. Explain why only eight eigenvalues are nonzero. Describe the composition (in terms of the original variables) of the three principal components that account for the most dispersion. What proportion of the dispersion do they account for? Compare these principal components to those given for the case study using all observations.