$(63$ marks$)$ Assume you have the table below containing information about the Golden Gophers

soccer games. For every game recorded, there is an entry $($e$.$g$.$ row$)$ for whether it took place on a

Friday, Saturday, or Sunday, whether the team's star, Whirling Willie, started the game or came in

off the bench later, whether the defenseman Donnie played on the left or right of the field, whether

the offensive player Otto played on the left or right of the field, whether the opponent's team was

on average young $($below $22$ years of age$)$ or old, and, finally, whether the Golden Gophers won

or lost. Suppose "Outcome" is the target$/$label attribute with "Won" labeling positive $(+)$ and

"Lost" labeling negative $(-).$ Use ID$3$ to learn a decision tree. You are required to show how you

calculate the information entropy for selecting attributes in every step in detail. For the selection

of attribute at each node of the tree, show:

the calculation of conditional information entropy for each candidate attribute $($including the

cases of all its possible values$)$;

the selection of attribute based on the conditional information entropy;

the partial$/$final decision tree once the attribute is selected;

the rule$($s$)$ if any.

Note: ID is not a conditional attribute.

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

$\backslash$hline ID & When & WW Starts & Donnie & Otto & OppAge & Outcome $\backslash \backslash$

$\backslash$hline $\backslash$hline $1$ & Sat & Yes & Left & Left & Young & Won $(+)\backslash \backslash$

$2$ & Sat & Yes & Left & Left & Old & Won $(+)\backslash \backslash$

$3$ & Sat & Yes & Left & Left & Old & Won $(+)\backslash \backslash$

$4$ & Sat & Yes & Left & Right & Young & Won $(+)\backslash \backslash$

$5$ & Sat & Yes & Left & Right & Young & Won $(+)\backslash \backslash$

$6$ & Sat & Yes & Left & Right & Old & Won $(+)\backslash \backslash$

$7$ & Sat & Yes & Right & Left & Old & Won $(+)\backslash \backslash$

$8$ & Sat & Yes & Right & Right & Young & Won $(+)\backslash \backslash$

$9$ & Sat & No & Left & Right & Young & Won $(+)\backslash \backslash$

$10$ & Sun & No & Left & Left & Young & Won $(+)\backslash \backslash$

$11$ & Sun & No & Left & Right & Young & Won $(+)\backslash \backslash$

& & & & & & $\backslash \backslash$

$12$ & Fri & Yes & Left & Right & Old & Lost $(-)\backslash \backslash$

$13$ & Fri & Yes & Right & Right & Old & Lost $(-)\backslash \backslash$

$14$ & Fri & No & Right & Left & Old & Lost $(-)\backslash \backslash$

$15$ & Fri & No & Right & Right & Old & Lost $(-)\backslash \backslash$

$16$ & Sat & No & Left & Left & Young & Lost $(-)\backslash \backslash$

$17$ & Sat & No & Right & Left & Young & Lost $(-)\backslash \backslash$

$18$ & Sat & No & Right & Right & Old & Lost $(-)\backslash \backslash$

$19$ & Sun & No & Right & Left & Young & Lost $(-)\backslash \backslash$

$20$ & Sun & No & Right & Left & Old & Lost $(-)\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$