It is clear that running a regression, the sum of Residuals should equal Zero. I also understand that when running a weighted regression the sum of weighted Residuals should equal Zero.
My model is more complex. The dependent variable (monthly volume) is normalized and it is a pooled regression with many cross sections. Because the observations in certain cross sections and in certain time periods are more valuable we are running a weighted regression to minimize the residuals in the more valuable time periods and cross sections.
After running the regression (with the dependent variable - Model Actual - normalized) the sum of the normalized residuals does not sum to 0. The sum of residuals is 8% off.
However when we weight the normalized residuals by the weighting variable, then the sum of the normalized residuals ends up equaling 0 - as expected.
The problem is that the difference between the Normalized dependent variable and the Model Predicted is the unweighted model residuals, which do not sum to 0. Should the weighting also be applied to the Model Predicted?