Multiple linear regression in cross-country analysis with small sample size


While conducting small student’s research project I’ve faced a little problem. I’m using aggregated country data (not in individual, but national level), where a dependent variable is the prevalence of social entrepreneurships (proportion of working-age individuals who are starting or operating “social” business), independent variables are theoretically justified factors that might explain the cross country prevalence of such entities (for example GDP per capita).

I wanted to run multiple linear regression with this data, but my analysis is limited to eastern European countries, so sample size is quite small (n=6) – amount (as far as I know) too small for 4 independent variables.

So my idea is to conduct such regression with a bigger sample size (for example all European Union countries), and then in the next regression step, to add interaction effects of independent variables and dummies for a set of eastern European countries.

I’m (yet) not familiar with interaction effects so I have to ask you: if such operation have any sense? Will I be able to overcome small sample problem and, thanks to that, use beta coefficient to interpret what factors are responsible for cross country differences?

I would be very grateful for any help with this amateurish problem.