Exercise 20.6 [linear-regression-exercise]

Consider $N$ data points $(x_j,y_j)$, where the $y_j$s are generated from the $x_j$s according to the linear Gaussian model in Equation (linear-gaussian-likelihood-equation). Find the values of $\theta_1$, $\theta_2$, and $\sigma$ that maximize the conditional log likelihood of the data.