a) Find Principal Components. Contruct a biplot of the universities in PC axes. Fromthis biplot, can you identify (by inspection) clusters of universities?
b) Calculate Euclidian distances between pairs of universities. Use them to clusterthe universities using complete and single linkage. For each type of linkage construct the dendrogram and cut it for K = 4 clusters.
c) Use K-means clustering to cluster the universities into K = 4 clusters. Use set.seed(2).
2. File brands.csv contains data on breakfast cereals produced by three different American manufacturers: General Mills (G), Kellogg (K), and Quaker (Q).
a) Find Principal Components and plot the cereals in PC axes, use different color fordifferent manufacturers. Does it appear as if some manufacturers are associated with more nutritional elements (high protein, low fat, high fiber, low sugar, etc.)?
b) Calculate Euclidian distances between pairs of cereal brands. Use them to cluster thecereals using complete and single linkage. For each type of linkage construct the dendrogram and cut it for four clusters. Construct a dataframe with the names of the breakfast cereals, and a column showing the assigned cluster to each row.
c) Use K-means clustering to cluster the cereals into K = 4 clusters. Add a column showing the assigned cluster to the dataframe created in part (b). How different are the clusters?
