Let us assume that I have data of age and weight of 100 humans between the age of 1 to 15, and also similar data for 100 donkeys between the ages of 1 to 5. I think we could have a pretty decent regression for the impact of age on weight individually for each species. Note that individually the two species have a very different intercept and slope.
Let us say that we combine the data. We use a dummy variable to distinguish between the two species. There seems no way from the joint data to find the relationship between age and weight for the individual animals. We will have a joint slope, joint intercept and coefficient for the dummy. But, we can't find the true individual intercepts or slopes. By combining data we lose our ability to get the real relationship.
The larger questions is that we sometimes combine very different entities and then use multiple regressions with dummy variables. Considering the above example is there a limiting condition to when regression can be used for data with different entities?