# Regression on multiple datasets with a per-dataset variable

I have 10 datasets, each with the same variables (e.g., age and income) but different numbers of observations.

Let us now consider a categorical variable $$X$$ that can only take values $$0$$ and $$1$$ per dataset, meaning that it keeps the same value for all observations. For 5 datasets, $$X=0$$; for the other 5, $$X=1$$.

How do I create a regression model for a variable of these datasets (e.g., age) that takes into account this "meta-variable" $$X$$?

A simple solution would be to append a new column for $$X$$ to each dataset, where the same value is repeated for all observations, and then concatenate the datasets. However, I think there are better ways.