I definitely appreciate the simple approach in the article. If the OP is like myself, perhaps he's posting this to better his understanding and leaving artifacts for others to follow as they learn. I have to point out, there's so much more happening in regression. To do it well, read further on it.
As a concrete example of why- The author mentions the R^2 value but doesn't seem to warn that adding more variables to your model will artificially increase it. For this reason, a better value is the "Adjusted R^2" which adjusts for that. Also testing the validity of your model, building it up from scratch, understanding you can't predict outside of the domain of your independent variables, etc.
With that out of the way, I very much enjoyed seeing some of the math behind this. My class was entirely focused on just learning to use a statistical package to run regression. That's perfectly adequate, fine, and all I'll use on a day to day basis. Understanding what's going on beneath the covers has always just enabled me to be more powerful at the given task.
Thanks!