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Why is the equation $\mathbb{E} \left[ (Y - \hat{Y})^2 \right] = \left(f(X) - \hat{f}(X) \right)^2 + \operatorname{Var} (\epsilon)$ true?

In the book An Introduction to Statistical Learning, the authors claim (equation 2.3, p. 19, chapter 2) $$\mathbb{E} \left[ (Y - \hat{Y})^2 \right] = \left(f(X) - \hat{f}(X) \right)^2 + \operatorname{...
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