Question 8 Given the Mean Squared Error cost function for a Linear Regression model: where (X, hq) = he is the hypothesi

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Question 8 Given The Mean Squared Error Cost Function For A Linear Regression Model Where X Hq He Is The Hypothesi 1 (90.91 KiB) Viewed 11 times

Question 8 Given the Mean Squared Error cost function for a Linear Regression model: where (X, hq) = he is the hypothesis function using the model parameter 0. m. training examples (xi, yi) n features, X; = [1, il, ..., Lin] X = OB O D O C 1 m = Σ (x(i). 0-y(i)) ² m O A We can put all such x; as rows of a matrix X called a design matrix. Then we augment the design matrix: where, -xf- x- m ⠀ xm the observed target values y = Lin]¹ € R¹ +1 2x¹.( . (X.0- y) = 0 10 = 1 20 = 1 Im0 = 1 A. Ô = (X^ . X).X”.y B. Ô (X^.X)-1.X^.y c. Ô = (XT . X).yT.X D. Ô = (y^ . X)-1.XT ;*11 ;*21 ; ; xml Ym The Normal Equation can be derived from the gradient (a closed-form solution involving no gradient descent) as follows: Yı : .... (1) ERm XT is the transpose of feature vector X. is the model's parameter vector ; x1n ; x2n 3- ; ; xmn Next, we can solve directly for (we use as it is an estimate of used to minimize the cost function). This leads to being which of the following option: 8 €]Rmxn+1 1 pts .... (2)