I'm hoping to get some intuition on what is happening. My R-squared in the full sample is 10%. When I split my sample into two subsets, my R-squared in each subset is about 1%. I thought the R-squareds in subsets would average to about 10%.
More about my regression model and subsample construction: in the full sample, i have about 40,000 observations. My dependent variable is a dummy variable equal to 1 if a large event occurred and they occur about 32% of the time. I split my sample based on whether the event occurs in large cities, which are more likely to have large events. I have about 10,000 observations in large cities and the large event occurrence increases to 83%. I have about 30,000 observations in small cities and the large event occurrence falls to 15%.