1. Suppose that we have four observations and compute a dissimilarity matrix given by 0.3 0.3 0.4 0.4 0.5 0.7 0.5 0.8 0.45 0.7 0.8 0.45 For instance, the dissimilarity between the first and second observations is 0.3, and the dissim- ilarity between the second and fourth observations is 0.8. (a) On the basis of this dissimilarity matrix, sketch the dendrogram that results from hierar- chically clustering these four observations using complete linkage. Be sure to indicate on the plot the height at which each fusion occurs, as well as the observations corresponding to each leaf in the dendrogram. (b) Repeat (a), this time using single linkage clustering. (c) Suppose that we cut the dendrogram obtained in (a) such that two clusters result. Which observations are in each cluster? (d) Suppose that we cut the dendrogram obtained in (b) such that two clusters result. Which observations are in each cluster?

1. Suppose that we have four observations and compute a dissimilarity matrix given by 0.3 0.3 0.4 0.4 0.5 0.7 0.5 0.8 0.45 0.7 0.8 0.45 For instance, the dissimilarity between the first and second observations is 0.3, and the dissim- ilarity between the second and fourth observations is 0.8. (a) On the basis of this dissimilarity matrix, sketch the dendrogram that results from hierar- chically clustering these four observations using complete linkage. Be sure to indicate on the plot the height at which each fusion occurs, as well as the observations corresponding to each leaf in the dendrogram. (b) Repeat (a), this time using single linkage clustering. (c) Suppose that we cut the dendrogram obtained in (a) such that two clusters result. Which observations are in each cluster? (d) Suppose that we cut the dendrogram obtained in (b) such that two clusters result. Which observations are in each cluster?