A relatively simple question, but I cannot seem to find anything relevant to this. In fact, I'm not even sure of "unbalanced design" is even the right terminology here, but it was suggested to me.
The problem may be described as follows. Let's say you have a partition of your population into some groups - A, B and C. These groups contain 100, 200 and 500 individuals respectively. You don't know that - you only know the relative sizes (so, B is 2x the size of A, C is 5x the size of A, etc.). Furthermore, you have three random samples, of sizes 50, 20 and 100 from each of these.
How does one construct a linear regression here (nothing fancy) that combines the data from all three samples?