I have some survey data collected from 15 government organizations. Using this data, I would like to run an OLS regression to estimate the influence of variables x1 and x2 on y. I have run two models: one including 14 dummy variables accounting for potential differences from organizational membership, and one not including any dummy variables. The difference between R-square values between the models is small (less than 0.02), and the adjusted R-square difference much smaller. Moreover, the coefficients for x1 and x2 and significance levels are not substantially different between models, and none of the dummies has a statistically significant relationship with the dependent variable.
I am hoping for some insight into the following questions:
From a theoretical standpoint, is it necessary to include dummy variables for organizational membership (in order to protect against omitted variable bias or some other reason)? In other words, must I include the dummy variables on principle?
If I must include them on principle, is there any post analysis test that I can use to claim that the model without the organizational dummies should be used in the interpretation of the results? (Something similar to the Hausman test for distinguishing between fixed and random effects models, for instance.)
Please let me know if I can provide any more information that will help.