$2.$ Along with this homework assignment you are given the file Q$2.$csv$.$ The file is a comma$-$separated listing of $14,760$ instances. Each point has $6$ real$-$valued features $\backslash (\backslash$left$($X$\_\{1\}\backslash$ldots X$\_\{6\}\backslash$right$)\backslash ).$ The data is synthetic and naturally clustered. There are no missing values.

Estimate the number of clusters in the data. To do this you may utilize any way you like, given that at the end you can objectively and clearly justify your result. Ultimately, your score will depend on how close your answer is to the true answer. Accuracy is the most important factor but precision will also earn you points. So$,$ be precise if you can $($i$.$e$.$ give an exact number$).$ If you cannot be certain, give an accurate interval that is as precise as possible. Q$2$

$\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|$c$|$c$|$c$|\}$

$\backslash$hline $-1\mathrm{.}6571$ & $2\mathrm{.}1805$ & $2\mathrm{.}7777$ & $-5\mathrm{.}3499$ & $-0\mathrm{.}67157$ & $-2\mathrm{.}0437\backslash \backslash$

$\backslash$hline $-0\mathrm{.}10734$ & $-2\mathrm{.}2044$ & $-6\mathrm{.}4758$ & $2\mathrm{.}6445$ & $5\mathrm{.}224$ & $-0\mathrm{.}20602\backslash \backslash$

$\backslash$hline $3\mathrm{.}3367$ & $-3\mathrm{.}6666$ & $0\mathrm{.}14219$ & $-0\mathrm{.}064717$ & $5\mathrm{.}2609$ & $1\mathrm{.}4644\backslash \backslash$

$\backslash$hline $-2\mathrm{.}3691$ & $0\mathrm{.}82265$ & $6\mathrm{.}4417$ & $-0\mathrm{.}29984$ & $-4\mathrm{.}5482$ & $0\mathrm{.}61803\backslash \backslash$

$\backslash$hline $0\mathrm{.}58848$ & $3\mathrm{.}9537$ & $3\mathrm{.}0093$ & $1\mathrm{.}7207$ & $4\mathrm{.}5287$ & $-2\mathrm{.}1186\backslash \backslash$

$\backslash$hline $2\mathrm{.}5329$ & $1\mathrm{.}9177$ & $-0\mathrm{.}76072$ & $1\mathrm{.}1809$ & $1\mathrm{.}5268$ & $0\mathrm{.}3838\backslash \backslash$

$\backslash$hline $-0\mathrm{.}1101$ & $-0\mathrm{.}28177$ & $-4\mathrm{.}1806$ & $2\mathrm{.}4519$ & $0\mathrm{.}64435$ & $2\mathrm{.}5827\backslash \backslash$

$\backslash$hline $-2\mathrm{.}2158$ & $-1\mathrm{.}2754$ & $-5\mathrm{.}5441$ & $2\mathrm{.}2467$ & $6\mathrm{.}47$ & $3\mathrm{.}0464\backslash \backslash$

$\backslash$hline $-3\mathrm{.}5077$ & $1\mathrm{.}0429$ & $2\mathrm{.}108$ & $-1\mathrm{.}3582$ & $-4\mathrm{.}4929$ & $-2\mathrm{.}0032\backslash \backslash$

$\backslash$hline $2\mathrm{.}4878$ & $0\mathrm{.}08078$ & $-2\mathrm{.}9752$ & $-4\mathrm{.}8839$ & $-5\mathrm{.}0536$ & $-0\mathrm{.}80169\backslash \backslash$

$\backslash$hline $-3\mathrm{.}8163$ & $0\mathrm{.}7338$ & $3\mathrm{.}2195$ & $1\mathrm{.}2471$ & $-3\mathrm{.}7984$ & $2\mathrm{.}376\backslash \backslash$

$\backslash$hline $2\mathrm{.}0468$ & $0\mathrm{.}65864$ & $-3\mathrm{.}0993$ & $-3\mathrm{.}2217$ & $5\mathrm{.}4056$ & $0\mathrm{.}31886\backslash \backslash$

$\backslash$hline $0\mathrm{.}41175$ & $-2\mathrm{.}0246$ & $-0\mathrm{.}53639$ & $-3\mathrm{.}6579$ & $-2\mathrm{.}6172$ & $2\mathrm{.}5575\backslash \backslash$

$\backslash$hline $1\mathrm{.}0163$ & $0\mathrm{.}80906$ & $6\mathrm{.}9398$ & $1\mathrm{.}6154$ & $-2\mathrm{.}7408$ & $-0\mathrm{.}045187\backslash \backslash$

$\backslash$hline $0\mathrm{.}97748$ & $0\mathrm{.}74871$ & $-1\mathrm{.}9401$ & $0\mathrm{.}46447$ & $-0\mathrm{.}41323$ & $1\mathrm{.}1177\backslash \backslash$

$\backslash$hline $1\mathrm{.}9572$ & $-4\mathrm{.}5986$ & $-0\mathrm{.}21388$ & $3\mathrm{.}9825$ & $-1\mathrm{.}419$ & $2\mathrm{.}2952\backslash \backslash$

$\backslash$hline $1\mathrm{.}0678$ & $-0\mathrm{.}16688$ & $5\mathrm{.}6812$ & $1\mathrm{.}3594$ & $-1\mathrm{.}2763$ & $-0\mathrm{.}90521\backslash \backslash$

$\backslash$hline $5\mathrm{.}2351$ & $3\mathrm{.}848$ & $3\mathrm{.}9839$ & $3\mathrm{.}3721$ & $-0\mathrm{.}39785$ & $-1\mathrm{.}2874\backslash \backslash$

$\backslash$hline $-7\mathrm{.}8419$ & $1\mathrm{.}6827$ & $4\mathrm{.}6165$ & $1\mathrm{.}8433$ & $\backslash (-0\mathrm{.}83323\backslash )$ & $-2\mathrm{.}5916\backslash \backslash$

$\backslash$hline $0\mathrm{.}85009$ & $1\mathrm{.}1213$ & $-0\mathrm{.}023259$ & $-3\mathrm{.}8408$ & $-3\mathrm{.}6457$ & $0\mathrm{.}058208\backslash \backslash$

$\backslash$hline $-0\mathrm{.}26924$ & $1\mathrm{.}2441$ & $1\mathrm{.}1401$ & $2\mathrm{.}3782$ & $3\mathrm{.}7643$ & $-2\mathrm{.}2278\backslash \backslash$

$\backslash$hline $0\mathrm{.}58897$ & $-3\mathrm{.}37$ & $0\mathrm{.}69876$ & $-2\mathrm{.}4936$ & $0\mathrm{.}8162$ & $7\mathrm{.}0742\backslash \backslash$

$\backslash$hline $-3\mathrm{.}4669$ & $-2\mathrm{.}903$ & $5\mathrm{.}3985$ & $-2\mathrm{.}1806$ & $-3\mathrm{.}1052$ & $5\mathrm{.}7766\backslash \backslash$

$\backslash$hline $5\mathrm{.}7621$ & $-5\mathrm{.}8832$ & $-0\mathrm{.}13337$ & $-1\mathrm{.}6303$ & $-0\mathrm{.}8268$ & $3\mathrm{.}273\backslash \backslash$

$\backslash$hline $1\mathrm{.}5744$ & $-1\mathrm{.}4076$ & $-0\mathrm{.}5582$ & $1\mathrm{.}0727$ & $1\mathrm{.}3849$ & $3\mathrm{.}3647\backslash \backslash$

$\backslash$hline $-1\mathrm{.}1091$ & $-3\mathrm{.}0574$ & $1\mathrm{.}8377$ & $3\mathrm{.}8942$ & $-0\mathrm{.}40304$ & $-3\mathrm{.}031\backslash \backslash$

$\backslash$hline $1\mathrm{.}4926$ & $4\mathrm{.}3903$ & $-8\mathrm{.}0782$ & $-1\mathrm{.}9173$ & $0\mathrm{.}23518$ & $-1\mathrm{.}7975\backslash \backslash$

$\backslash$hline $-2\mathrm{.}0426$ & $-3\mathrm{.}1547$ & $-3\mathrm{.}7207$ & $3\mathrm{.}8357$ & $-2\mathrm{.}7892$ & $4\mathrm{.}0201\backslash \backslash$

$\backslash$hline $-2\mathrm{.}4375$ & $-1\mathrm{.}7232$ & $-1\mathrm{.}3583$ & $-3\mathrm{.}3341$ & $-1\mathrm{.}8377$ & $2\mathrm{.}776\backslash \backslash$

$\backslash$hline $1\mathrm{.}026$ & $4\mathrm{.}6824$ & $0\mathrm{.}32008$ & $3\mathrm{.}118$ & $2\mathrm{.}1839$ & $4\mathrm{.}0341\backslash \backslash$

$\backslash$hline $1\mathrm{.}8233$ & $-2\mathrm{.}5876$ & $-4\mathrm{.}4667$ & $-4\mathrm{.}5025$ & $2\mathrm{.}665$ & $3\mathrm{.}613\backslash \backslash$

$\backslash$hline