# Normalization and hypothesis testing under system equations

Hypothesis testing under single equation linear regression is robust to simple data normalization (for example dividing all variables by their respective mean). I see that the same is true for systems of equations estimated by SUR without any constraint. However, that is not the case when constraints are involved. Can anyone explain why? and if normalization has to be done in such cases, how should it be done?

• Normalization usually means fixing the range of your data to the $[0,\ 1]$ interval. I think you mean centering, which is setting the mean to $0$ (see my answer here: how-to-verify-a-distribution-is-normalized). What does "SUR" stand for? What constraints are involved in your situation & where did you hear that they have this effect? Also, why would normalization have to be done? (Cf: When should you center your data & when should you standardize?) – gung - Reinstate Monica Dec 4 '13 at 14:49
• @gung Thanks. I read the links you suggested and what I want is to scale the data because my variables are in different units. To do so I divided all variables by their respective mean. SUR stands for seemingly unrelated regression, a method used to estimate parameters of a system of equations. I have some cross equation restrictions on the parameters. However, I noticed that the p-values do not change because of the scaling when the system is estimated without constraints. I think this is the expected behavior. But they do change when constraints are imposed and I wonder why. – Daniel Dec 5 '13 at 11:25