9. Consider the USArrests data. We will now perform hierarchical clus- tering on the states. (a) Using hierarchical clustering with complete linkage and Euclidean distance, cluster the states. (b) Cut the dendrogram at a height that results in three distinct clusters. Which states belong to which clusters? (c) Hierarchically cluster the states using complete linkage and Eu- clidean distance, after scaling the variables to have standard de- viation one. (d) What effect does scaling the variables have on the hierarchical clustering obtained? In your opinion, should the variables be scaled before the inter-observation dissimilarities are computed? Provide a justification for your answer. [20 pts] Question three: Section 10.7 Questions 9. Also, do the following: e) Use the R codes for the Cluster Analysis chapter to obtain a possible optimal number of clusters for the hierarchical clustering. f) Use the R codes for the Cluster Analysis chapter to obtain a possible optimal number of clusters for the K-means clustering. g) Run both complete linkage hierarchical clustering and K-means clustering using the optimal number of clustering obtained in parts (f) and (g) h) Use the R codes for the Cluster Analysis chapter to plot the hierarchical clustering results in part (g) on the first two principal components axes. Comment on the quality of the hierarchical clustering results. i) Use the R codes for the Cluster Analysis chapter to plot the K-means clustering results in part (g) on the first two principal components axes. Comment on the quality of the K-means clustering results