Jolicoeur and Mosimann measured the length, width, and height of 48 painted turtle shells and con-ducted PCA on the data. Their work has been influential in the field of allometry, the study of the relative growth of a part of an organism in relation to an entire organism.9
a. Conduct principal component analysis on the entire data set (ignore gender). Can a majority of the variability in the data be explained with just one or two principal components?
b. Calculate and interpret the principal component loadings.
c. Create a scatterplot of PC1 versus PC2 where each point is grouped by gender. Was PCA useful in differentiating the genders? Other multivariate techniques are designed to classify or cluster data into clear groups.
d. Conduct principal component analysis on all three variables using only the male data. Repeat the process using only the female data. Compare the loadings for the two analyses. Would you expect the results to be similar? Why or why not?