Dummy variable regression with a few observations

#1
Dear all,

I have 26 observations about Italian cities.
I would like to control for regional fixed effects by adding a dummy variable for each Italian region (26 regions).

Given that the coefficient I would like to estimate remains statistically significant, the question is the following: is it accurate to run a regression with 26 observations and 20 dummy variables, or there are not sufficient observations to make conclusions?

Thank you for your time and help

Alice