# Assumptions of weighted least squares regression

I have built a weighted least squares regression model and was about to interpret the results. But before doing that, I wanted to check for assumptions first. However, I couldn't find the assumptions of weighted least squares anywhere. I was going to check for the assumptions of ordinary least squares but because these two models are completely different, I didn't do it.

What are the assumptions of weighted least squares regression?

• if by WLS, you are weighting the diagonals of the covariance matrix by the inverse of the $predictor^2$, then the assumptions are the same as OLS except that $\sigma^2_{i}$ is proportional to $\sigma^2 x_{i}^2$. – mlofton Jun 18 at 14:40
• I used the inverse of residuals^2. Does this mean the assumptions are the same? – Ahmet Atilla Colak Jun 18 at 14:41
• hopefully someone else can comment because it's been too long since I looked at this material but I don't think you should use the residuals because you don't know what they are beforehand. – mlofton Jun 18 at 14:43
• I built a multiple variable model, so I had to use the residuals. – Ahmet Atilla Colak Jun 18 at 14:44
• Note that, in regard to your original question, the assumptions are be the same as those in OLS except that OLS assumes constant variance of the error term and WLS doesn't. – mlofton Jun 19 at 15:26