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 as the similarity measure and complete linkage as the clustering method.
a. Based on the following dendrogram, what is the most appropriate number of clusters to organize these utility companies?

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.

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6.5 6.0 5.5 5.0- 4.5 4.0F 4.5E Between-Cluster Distance 3.0- 2577 2.5 2.0 1.5 1.0- 0.5 1 18 14 19 6 3 9 10 13 4 20 2 21 5 7 12 15 17 8 16 11 Cluster Distance Observation 10 13 4 20 Income/Debt 0.032 0.195 -0.510 0.466 Return 0.741 0.875 0.207 0.474 Cost 0.700 0.748 -0.004 -0.490 Load Peak -0.892 -0.735 -0.219 0.655 -0.173 1.013 -0.943 0.083 Sales -0.693 -0.489 -0.702 -0.458 PercentNuclear 1.620 2.275 1.328 1.733 TotalFuelCosts -0.863 -1.035 -0.724 -0.721