My vector multiplication skills have gotten very rusty. I think that the equation 1 shown is wrong, given that the part highlighted in red seems to imply that X==w. I would like to know if the gradient that I wrote down is correct and why. Also, if the circled part is correct, then wouldn't I just have to multiply by X^T * X again to derive equation 1?

We have learned how to solve linear regression numerically using gradient descent. This homework problem will help you to understand how to solve for regression parameters in closed-form. (a) (5 points) Linear regression minimizes the squared error SJ( w) min- _(yi - yi)?, Swu = 2 X Xw - 24 X ASK where y = Xw is the prediction. In vectorized form and assuming a linear model the ABOUT cost function is given by J ( w) = =(Xu - Y)I (Xw - Y). THIS To find the parameters w that minimize the objective J(w), we take the derivative of J(w) with respect to w and set it to 0, specifically, VuJ(w) = =(2XTXw - 2YTW) = 0. (1) Name: Rewriting Eq. (1), 2XTXw = 2YTX. Thus, w = (XX)-lyTx. Please derive Eq. (1). Your