SUPER IMPORTANT ML Question, If answered I will UPVOTE IMMEDIATELY

You are given a dataset D= {(l'n, Yn)}M=1, where In E X = Rd,d > 1, and yn Y=R. We wish to train a linear regression model, h(x) = b + L Woli = w"X, E Rd+1,2 Rd+1 (3) that fits through our examples. The in-sample error associated with linear regression is, Einw) ER=( w2m - yn)? 2N 1 1 Note that we chose the cocfficient to be This coefficient also sometimes appear as This 2N N docsn't make a difference because positive scaling does not change location of the optimum weight. Let us define the data matrix and the target vector as, 210 : X = 211... Did : : INI 2nd ERNX(d+1) INO 1 1 ERN 1 where x; = [1:01 Bid]', 10 = 1, Vi {1,...,N}. (a) Show and convince yourself that the in-sample crror in (4) is equivalent to the following expression, Bin(w) = ||Xw y 13 = (w'X'Xw 2w'X'y + || | ||3) (5) 2N 1 (b) Find the expressions for the gradient of (4) and (5) with respect to w. (You may wish to start with a low-dimension example, c.g., set d= 2 and N = 2). (c) Convince yourself that the expressions of the gradients of (4) and (5) you have found are equivalent by trying to convert one into the other. You are given a dataset D= {(l'n, Yn)}M=1, where In E X = Rd,d > 1, and yn Y=R. We wish to train a linear regression model, h(x) = b + L Woli = w"X, E Rd+1,2 Rd+1 (3) that fits through our examples. The in-sample error associated with linear regression is, Einw) ER=( w2m - yn)? 2N 1 1 Note that we chose the cocfficient to be This coefficient also sometimes appear as This 2N N docsn't make a difference because positive scaling does not change location of the optimum weight. Let us define the data matrix and the target vector as, 210 : X = 211... Did : : INI 2nd ERNX(d+1) INO 1 1 ERN 1 where x; = [1:01 Bid]', 10 = 1, Vi {1,...,N}. (a) Show and convince yourself that the in-sample crror in (4) is equivalent to the following expression, Bin(w) = ||Xw y 13 = (w'X'Xw 2w'X'y + || | ||3) (5) 2N 1 (b) Find the expressions for the gradient of (4) and (5) with respect to w. (You may wish to start with a low-dimension example, c.g., set d= 2 and N = 2). (c) Convince yourself that the expressions of the gradients of (4) and (5) you have found are equivalent by trying to convert one into the other