$($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 $2\mathrm{.}577$ units as displayed in the dendrogram.

Observation

$\backslash$table$[[,10,13,4,20],[$Income$/$Debt$,0\mathrm{.}032,0\mathrm{.}195,-0\mathrm{.}510,0\mathrm{.}466],[$Return$,0\mathrm{.}741,0\mathrm{.}875,0\mathrm{.}207,0\mathrm{.}474],[$Cost$,0\mathrm{.}700,0\mathrm{.}748,-0\mathrm{.}004,-0\mathrm{.}490],[$Load$,-0\mathrm{.}892,-0\mathrm{.}735,-0\mathrm{.}219,0\mathrm{.}655],[$Peak$,-0\mathrm{.}173,1\mathrm{.}013,-0\mathrm{.}943,0\mathrm{.}083],[$Sales$,-0\mathrm{.}693,-0\mathrm{.}489,-0\mathrm{.}702,-0\mathrm{.}458],[$PercentNuclear$,1\mathrm{.}620,2\mathrm{.}275,1\mathrm{.}328,1\mathrm{.}733],[$TotalFuelCosts$,-0\mathrm{.}863,-1\mathrm{.}035,-0\mathrm{.}724,-0\mathrm{.}721]]$

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 of these four distances. Thus the increase in within$-$cluster dissimilarity of the new merged cluster $-$ Select your answer $-$ based on the distance between Observation $13$ and