I'm implementing a linear regression (OLS) on real estate data. I have a lot of dummy variables, where its value 1 indicate the presence of a characteristic, and 0 otherwise. Iteratively, I run the OLS, then check for the biggest statistically insignificant variable, that ones wich P > t are beyond 0.05. I take the greates P > t and remove it from the model.
But, now I realized I haven't removed the observations where the variables dumped in the process above was 1. Let's take as an example the number of rooms. In my model, this data goes from 1 to 4. So, I have three dummy variables, indicating if it has 2, 3 or 4 rooms. Let's say "2 rooms" is not significant, so I remove it from the model. I was letting all the "2 room" observations in the new model, but then I think they are being taken as the "1 room" variable, because the remaining "3 rooms" and "4 rooms" variables are 0.
Shouldn't I remove the observations according to the dummy variable removed?