Consider a dataset of 100 observations, where each observation is a pair of input features x and corresponding output y. Assume that the output y is generated from a linear regression model with Gaussian noise. The model is defined as y = w*x b , where is the Gaussian noise with zero mean and variance ^2. Your task is to estimate the parameters w, b, and ^2 using maximum likelihood estimation. a) Write down the likelihood function for this linear regression model. b) Derive the log-likelihood function based on the likelihood function you wrote in part (a). c) Find the values of w, b, and ^2 that maximize the log-likelihood function. Show your steps in the derivation. d) Explain how you would assess the goodness of fit of your estimated model