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Suppose X is a random vector in R6d and Y is a random variable with mean E(Y ) = and variance Var(Y )] = ^2

Suppose X is a random vector in R6d and Y is a random variable with mean E(Y ) = and variance Var(Y )] = ^2 . Suppose that X and Y are independent. Find a simple expression for the regression function f : R^d R that minimizes the EPE E((Y f(X))^2 ). Rigorously justify your answer, but also give an intuitive explanation.

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