# Formula for B values in Multiple Regression [duplicate]

I am curious what the formula for B values is when you have more than two variables. While I know any software can easily tell me the answer, I do not want to use it to figure out the B values, I want the actual equation. Everywhere I look I get equations like the following:

I cannot find any images or information on equations for the b values when there is more than two variables. I am also interested in how the formulas change between amount of variables. If anyone can tell me or point me to where I can find this information I would be grateful.

$\hat{\beta} = (X^TX)^{-1}X^Ty$
where $X$ is the matrix of predictors and $y$ is the vector of observed values of the dependent variable. See https://en.wikipedia.org/wiki/Ordinary_least_squares#Estimation for a discussion.