Consider the penalized least square problems: N f = min{{(x, f(xi)) + 1 [* (r(m) (x)*...

  

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Consider the penalized least square problems: N f = min{{(x, f(xi)) + 1 [* (r(m) (x)* dx] f Li=1 N - 2 a f = min | (y; f(x;)) + 2 f (f{(m +x)(x)* dx] where k is a positive integer. a Part 1: Consider fin the following cases and determine the degree of the polynomial. (1) m = 0 and = (2) m == 1 and = o (3) m = 2 and = o (4) m 3 and = 0 Part2: = (1) Will f or f have the smaller training residual sum of squares as . (2) Will f or f have the smaller test residual sum of squares as 0. (3) Will f or f have the smaller training and test residual sum of squares for = 0. Consider the penalized least square problems: N f = min{{(x, f(xi)) + 1 [* (r(m) (x)* dx] f Li=1 N - 2 a f = min | (y; f(x;)) + 2 f (f{(m +x)(x)* dx] where k is a positive integer. a Part 1: Consider fin the following cases and determine the degree of the polynomial. (1) m = 0 and = (2) m == 1 and = o (3) m = 2 and = o (4) m 3 and = 0 Part2: = (1) Will f or f have the smaller training residual sum of squares as . (2) Will f or f have the smaller test residual sum of squares as 0. (3) Will f or f have the smaller training and test residual sum of squares for = 0.