i need the answers for a, b and c please

Let y, ..., yn be a set of responses and let x1, ...,an be a corresponding set of predictors lying in the interval [a, b]. Recall that a cubic smoothing spline is the function obtained by minimizing 1) + over functions fin the space of all functions C defined on [a, b] for which S/"()da is well defined (where i>o is a smoothing parameter). Write fi(x) for the minimizer. Consider the cubic smoothing spline f '(x) obtained by minimizing 19; (x3)2 + 1 +^ "()?dis (2) over all f e C (that is, consider the smooth obtained when the ith point is deleted). a) let yj, 1 - 1....,, be the sequence with y = y; j , au ). Show that the function minimizing [(y; - $(23)2 +1 /* $"()da i=1 over f e C is f(x). [Hint: You can start by splitting the first term in expression (3) into a sum that includes all terms j =i and the ith term] b) We define e the obtained by setting weight heith obser vation to be zero and increasing the remaining weights in the smoothing matrix so that they sum to one. Deduce that ) - SW + S where Sa = [Si] is the smoothing matrix which satisfies j = SU and where y is the vector of fitted values y = ((11)..., f()). c) Using Part b), show that Please see over... 9-fi (0) = y - f(x) 1 - Su from which the computational formula for the cross-validation criterion CV(X) = => 9 12 * (?:))2 = - (", -fasters) follows you do not need to show that). Let y, ..., yn be a set of responses and let x1, ...,an be a corresponding set of predictors lying in the interval [a, b]. Recall that a cubic smoothing spline is the function obtained by minimizing 1) + over functions fin the space of all functions C defined on [a, b] for which S/"()da is well defined (where i>o is a smoothing parameter). Write fi(x) for the minimizer. Consider the cubic smoothing spline f '(x) obtained by minimizing 19; (x3)2 + 1 +^ "()?dis (2) over all f e C (that is, consider the smooth obtained when the ith point is deleted). a) let yj, 1 - 1....,, be the sequence with y = y; j , au ). Show that the function minimizing [(y; - $(23)2 +1 /* $"()da i=1 over f e C is f(x). [Hint: You can start by splitting the first term in expression (3) into a sum that includes all terms j =i and the ith term] b) We define e the obtained by setting weight heith obser vation to be zero and increasing the remaining weights in the smoothing matrix so that they sum to one. Deduce that ) - SW + S where Sa = [Si] is the smoothing matrix which satisfies j = SU and where y is the vector of fitted values y = ((11)..., f()). c) Using Part b), show that Please see over... 9-fi (0) = y - f(x) 1 - Su from which the computational formula for the cross-validation criterion CV(X) = => 9 12 * (?:))2 = - (", -fasters) follows you do not need to show that)