- Consider a linear regression model on a set of N samples, where each sample has D features, i.e., {(xn,yn)}n=1N,xnRD. We already know a popular loss function, known as Mean Squared Error or MSE, J=N1n=1N(ynxnT)2 where RD. Let us slightly modify the loss function by adding Gaussian noise to each input vector. To be formal, we add zero-mean Gaussian noise of known vairance 2 from the distribution N(0D,2IDD). Hence, the modified loss function takes the form of M=N1n=1N(yn(xn+n)T)2 where nRD are i.i.d. Gaussian noise vectors. (a) [25 points] Find the expectation of M over the Gaussian noise. The final solution should be in the form of the original loss function J plus term that does not depend on the input-output pairs