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.

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.





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