Question: For a given quantitative response Y and a single predictor X E [3, 5], consider the following regression model: 1' = for) + s where

 For a given quantitative response Y and a single predictor X

For a given quantitative response Y and a single predictor X E [3, 5], consider the following regression model: 1' = for) + s where x) = X3 3X2 6X + 8 is the true underlying curve and s is an unobservable random variable independent of the predictor with mean zero and variance equals 0'2. l_r1_re_a_ljtva_ _t_l1e_ true regression curve f is unknown and hence you need to estimate it by 3* using statistical learning methods. Suppose that the Knearest neighbour (KNN) method is used to estimate the regression curve f. The gure below presents the three terms involved in the decomposition of the test MSE calculated by averaging over all values of the pmdictor and by considering several values of K. I Identify the three terms of the test MSE from the gure. I Identify the optimal K value. 50. XI: If '07 Mt MSE w. 20. 10' a A o- 5 10 t5 20

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