Part A$.$ Let us have the training dataset consisting of $3$ data points$($with coordinates on the XoY plane in the form of $($x$,$y$))$: $(-2,0),(0,2),$ and $(2,0).$ The test set consists of $1$ point with x $=(1\mathrm{.}9)$ and the ground truth label y $=0\mathrm{.}75.$ We are using the Euclidian $($or$$l$2)$ metric. Select the correct option below and provide detailed explanation.

Note: input features are $1-$dimensional $($x$-$coordinate$),$ while output label is y$-$coordinate on the XoY plane.

$($A$)$ The mean test error of $1-$NN Regression method is greater than it is for $2-$NN method test error

$($B$)$ The mean test error of $1-$NN Regression method is the same as it is for $2-$NN method test error

$($C$)$ The mean test error of $1-$NN Regression method is less than it is for $2-$NN method test error

$($D$)$ None of the above

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Part B$.$ For the examples above, would the results change if we switch$$l$1$metric with$$l$2$and vice versa?

$($A$)$ Yes,$$l$1$metric would give us generally bigger mean error than$$l$2$

$($B$)$ No$,$ the results above would remain the same

$($C$)$ Yes,$$l$2$metric would give us generally bigger mean error than$$l$1$