$4.$ This problem will work with iris data $($available in base R$).$ Make sure to exclude the Species column before applying clustering algorithms.

$($a$)$ Apply K$-$Means clustering with K $=1,2,...,10$ via eclust$(),$ for nstarts $=50$ each. Provide the code and the plot of total within$-$cluster sum of squares $($WSS$)$ progression for the resulting clustering solutions.

$($b$)$ Run the gap statistic calculations for K $=1,...,10,$ with $50$ replicates each. Provide the gap statistic plot. Which K value appears to be optimal?

$($c$)$ Using external cluster validation, and comparing results of your clustering to the actual # of distinct iris species in the data $(3),$ is the answer in part $($b$)$ close to it$?$

$($d$)$ Proceed to scale iris data, and run the gap statistic calculations for K $=1,...,10,$ with $50$ replicates each. Which K value is optimal?

$($e$)$ Using external cluster validation, and comparing results of your clustering to the actual # of distinct iris species in the data $(3),$ is the answer in part $($d$)$ close to it$?$

$($f$)$ Apply K$-$means with optimal K selected in part $($d$).$ Compare the resulting cluster assignments to the actual species labels. Is there some correspondence?

E$.$g$.$ do any of your clusters contain only elements of a certain species? Or maybe a combination of two species?

give the answer to this question using r studio