I'm not sure what this is called but I remember seeing a colleague of mine doing a multivariate regression much like
$$Y \sim X_1 + X_2 + X_3$$
and then he said he would "orthogonalize" so he regressed each of the IVs against the other ones, and took the residuals..as in:
$$Z_1 = residuals(X_1 \sim X_2 + X_3)$$ $$Z_2 = residuals(X_2 \sim X_1 + X_3)$$ $$Z_3 = residuals(X_3 \sim X_1 + X_2)$$
after which he redid the regression:
$$Y \sim Z_1 + Z_2 + Z_3$$
I have never seen this before, is there a reference or name under which I can search read more about this and why/when would one want to do something like this?