# Confusion related to data normalization

I am trying to learn a linear regression model. However, I have some confusion related to the normalization of the data. I have normalized the features/predictors to zero mean and unit variance. Do I need to do the same for the target. If so why?

• Why did you normalize the features/predictors? – Peter Flom Apr 20 '13 at 21:39
• BTW I think 'standardize' is a better term for that. – Scortchi - Reinstate Monica Apr 21 '13 at 0:56

Normalizing the target in linear regression doesn't matter. In linear regression, your fit will be of the form $$\hat{y}_i = a_0 + a \cdot x_i.$$ When you predictors $x_i$ are centered, the constant term $a_0$ will always be the mean of the $y_i$. So if you center the $y_i$ before running a regression, you will just get $a_0 = 0$, but all your other coefficients will remain unchanged.
• @Stefan. Yeah, when I center the predictors, I get the constant term $a_0$ to be the mean of y. But I didn't get how come it becomes the mean. Can you tell me the maths behind it? – user34790 Apr 21 '13 at 12:40