In multiple regression, a coefficient gets opposite sign in subsample than in the full sample In a multiple regression, the regression coefficient of the two subsamples is opposite to that of the full sample. Both coefficients are significant. The sum of the number of obs in the two subsamples is equal to that of the full sample. Is this normal? What are the possible causes? Thanks.
 A: Consider the following data (low noise, so you can see it with small sample size)
 x    y   g
 1  16.1  1
 2  16.9  1
 3  17.9  1
 4  19.1  1
10   5.9  2
11   7.1  2
12   8.1  2
13   8.9  2

If $g$ represented the before vs the after, then each could have a line with slope coefficient of one sign, while the overall data (ignoring the variable $g$) had a line with slope coefficient of the opposite sign:

The red and black lines are individual regression lines, the blue line the overall line. The right thing to do in this data is to add the factor $g$ as a predictor in the regression model (e.g. to add an indicator variable that is "1" when in the second group and "0" otherwise), either as main effect only (for parallel lines) or with interaction (for two lines of different slope).
This is an example of Simpson's paradox - though it's not particularly paradoxical, since it's really just failing to account for an important variable.
So yes, it's possible for example, for the level to change between the two periods, which could result in flipping the sign when you ignore the time variable, as in the diagram  above. Since it's quite easy for this to happen, my guess would be Simpson's paradox.
