# linear regression with gaussian distribution

I am reading the book Machine Learning - A Probabilistic Perspective by Kevin P. Murphy.

In the chapter about linear regression he introduces a method where you estimate the parameters for the Gaussian distribution via maximum likelihood estimation:

Instead of maximizing the maximum likelihood he minimizes the negative log-likelihood:

This formula can be transformed to:

Which I can still follow.

However, afterwards he writes:

First, we rewrite the objective in a form that is more amenable to differentiation:

followed by this equation:

I don't understand how this equation equals NLL(theta) (from above). Were are all the sigma, pi etc.?

I understand that he derives the function in order to retrieve optimal parameters but I don't understand the transformation.

I hope this is enough to answer the question, I don't think that I am allowed to post the whole chapter here so I hope that someone has read the book.