In an effort to inform political leaders and economists discussing the deregulation of electric and gas utilities, data on eight numerical variables from utility companies have been grouped using hierarchical clustering based on Euclidean distance to measure dissimilarity between observations and complete linkage as the agglomeration method.

(a)

Based on the following dendrogram, what is the most appropriate number of clusters to organize these utility companies?

clusters are appropriate based on complete linkage.

(b)

Using the following data on the Observations 10, 13, 4, and 20, confirm that the complete linkage distance between the cluster containing {10, 13} and the cluster containing {4, 20} is 2.577 units as displayed in the dendrogram.

If required, round your answers to three decimal places. Do not round intermediate calculations.

Distance from Observation 10 and Observation 4:
Distance from Observation 10 and Observation 20:
Distance from Observation 13 and Observation 4:
Distance from Observation 13 and Observation 20:

Based on complete linkage, the merger of cluster {10, 13} and cluster {4, 20} is - Select your answer -the lowestthe largestbetween the lowest and the largestItem 6 of these four distances. Thus, the increase in within-cluster dissimilarity of the new merged cluster - Select your answer -isis notItem 7 based on the distance between Observation 13 and Observation 4.