# Normalization in weighted least squares regression

I have a question about the normalization in case we use weigthed last squared. By normalization i mean the column of the predictor matrix $X$ have unitary variance. In case of WOLS i weigth each observation $y_i$ and predictor $x_i$ with a weigth $w_i$.

$$\min\sum_{i=1}^n (w_i y_i - \beta w_i x_i))^2$$ $$=\min (Y-\beta X)^t W (Y-\beta X)$$

In this case i have a new regression problem: $$\min (Y'-\beta X')^t(Y'-\beta X')$$

My question is do i normalize $X$ or $X'$ ?

• It depends on your goal with the normalization. What do you want to achieve with the normalization? – Tae-Sung Shin Sep 12 '14 at 19:47