MATH 351 Homework 08

Find the maximum likelihood solutions for $\beta_0, \beta_1$ for linear regression under the Normal distribution, which has density function $$f(x, y | \beta_0, \beta_1, \sigma) = (2\pi\sigma^2)^{-1/2} \exp{\left\{-(y - (\beta_0 + \beta_1 * x))^2 / (2 \sigma^2) \right\}}$$ Please type up your solution using $\LaTeX$ and submit a Colab notebook. Don't forget that there might be interdependencies between the solutions for $\hat{\beta}_0$ and $\hat{\beta}_1$.