the relationship between the raw and the orthogonalized data

OK, so we orthogonalized the hald data, including the constant (the column of 1s).

What’s the relationship between the new variables and the old? We might someday get a new observation, and if we were using the fit to the orthogonalized data, we might want to see what it predicts for a new data point.

(In all honesty, I would use the original fit – but I still want to know what the relationship is.)

My notation is a little awkward. I’m going to stay with what is used for this post, in which I first showed how to find….

Let me start fresh. If we have two typical data matrices (i.e. taller than wide), and they are supposed to be the same data, how do we find the relationship?