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I want run kNN analysis to predict Y (continuous variable). I know that it is necessary to normalize all of the Xs. My question: is it also necessary to normalize Y values?

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No, it is not necessary and not needed at all. You just choose the $k$ nearest point to your test point, and average their target values to predict the target value of your test point. The distances are calculated using your features, i.e. $X$ and are sensitive to scale, not the target variables.

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