Linear Regression Linear model prediction: = wo + W1x1 + w2x2 + ... + Wnxn Vectorized form: = hw(x) = w x Mean Square Error (MSE) cost function: (i y(i Normal Equation (closed-form solution): W = (XT X)-1.8T W: the value of that minimizes the cost function X : the training data set y: the vector of target values containing y(1) to y (m) Complexity: 0(n3) os for linear regression, is 1 In lecture above Using MSE the cost function, thon get the norinal equation ce closed-form solution) Prove that the closed-form solution for Ridge Regression W = (1 + X'Xx.y (where I is the identity matrix) X=(x,x tim) is the input data motor x = (1,2,, dz....an) is the ith data sample y = (y2, 413, ., . Assume the hypothesis function how (x) = Wot Wix, twittunt Wnth and gejs is the measurement of hw (x) for gth training sample. The cost function of the Ridge Regression is E(W) = Z (W"-4" - yaistiwi Linear Regression Linear model prediction: = wo + W1x1 + w2x2 + ... + Wnxn Vectorized form: = hw(x) = w x Mean Square Error (MSE) cost function: (i y(i Normal Equation (closed-form solution): W = (XT X)-1.8T W: the value of that minimizes the cost function X : the training data set y: the vector of target values containing y(1) to y (m) Complexity: 0(n3) os for linear regression, is 1 In lecture above Using MSE the cost function, thon get the norinal equation ce closed-form solution) Prove that the closed-form solution for Ridge Regression W = (1 + X'Xx.y (where I is the identity matrix) X=(x,x tim) is the input data motor x = (1,2,, dz....an) is the ith data sample y = (y2, 413, ., . Assume the hypothesis function how (x) = Wot Wix, twittunt Wnth and gejs is the measurement of hw (x) for gth training sample. The cost function of the Ridge Regression is E(W) = Z (W"-4" - yaistiwi