We want to use this dataset to learn the value of

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$($i$.$e$.,$ to predict which TV shows the person would like based on the attributes of the TV show$).$

This is designed to be small enough to do it manually, however you may find the AIPython $($aipython$.$org$)$ code or useful to check your answers.

$($a$)$ Suppose the error is the sum of absolute errors. Give the optimal decision tree with only one node $($i$.$e$.,$ with no splits$).$ What is the error of this tree?

$($b$)$ Do the same as in part $($a$),$ but with the squared error.

$($c$)$ Suppose the error is the sum of absolute errors. Give the optimal decision tree of depth $2($i$.$e$.,$ the root node is the only node with children$).$ For each leaf in the tree, give the examples that are filtered to that node. What is the error of this tree?

$($d$)$ Do the same as in part $($c$)$ but with the squared error.

$($e$)$ What is the smallest tree that correctly classifies all training examples? Does a top$-$down decision tree that optimizes the information gain at each step represent the same function?

$($f$)$ Give two instances not appearing in the examples of Figure $7\mathrm{.}23$ and show how they are classified using the smallest decision tree. Use this to explain the bias inherent in the tree. $($How does the bias give you these particular predictions?$)$

$($g$)$ Is this dataset linearly separable? Explain why or why not.