Suppose a $7$-nearest-neighbors regression search
returns $ {7, 6, 8, 4, 7, 11, 100} $ as the 7 nearest $y$ values for a
given $x$ value. What is the value of $\hat{y}$ that minimizes the $L_1$
loss function on this data? There is a common name in statistics for
this value as a function of the $y$ values; what is it? Answer the same
two questions for the $L_2$ loss function.