Decision Trees.

$($a$)$ Consider the data in Table $1.$ Draw the associated Decision Tree showing all the intermediate computations. Use $lo{g}_2$ for your calculations.

$(16$ marks$)$

$\backslash$table$[[$Attributes$,$Classes$],[$Gender$,$Car Ownership,Travel Cost,Income Level,Transportation$],[$Male$,0,$Cheap,Low,Bus$],[$Male$,1,$Cheap,Medium,Bus$],[$Female$,1,$Cheap,Medium,Train$],[$Female$,0,$Cheap,Low,Bus$],[$Male$,1,$Cheap,Medium,Bus$],[$Male$,0,$Standard,Medium,Train$],[$Female$,1,$Standard,Medium,Train$],[$Female$,1,$Expensive,High,Car$],[$Male$,2,$Expensive,Medium,Car$],[$Female$,2,$Expensive,High,Car$]]$

Table $1$

$($b$)$ Use the obtained Decision Tree to classify the cases in Table $2$ filling in the 'Transportation' column.

$(4$ marks$)$

$\backslash$table$[[$Name$,$Gender,$\backslash$table$[[$Car$],[$Ownership$]],$Travel cost,$\backslash$table$[[$Income$],[$Level$]],$Transportation$],[$Alex$,$Male,$1,$Standard,High,$],[$Buddy$,$Male,$0,$Cheap,Medium,$],[$Cherry$,$Female,$1,$Cheap,High,$],[$Tom$,$Male,$1,$Standard,Low,$]]$

Table $2$