Hello, so I thought I was doing a multiple linear regression with the command

Code:
reg realgvaperh lifesatisfaction happy anxiety i.regionNum
I thought this was a multiple linear regression, and I was reading the r-adjusted values, f tests, t tests of coefficients etc. as if they were.I think it turns out that that is not what I've been doing, and therefore my entire dissertation is based on this wrong assumption. Is my assumption really that wrong? How hard am I going to fail my dissertation?

My thinking was that the multiple linear regression did lots of mini regressions in my panel by basically doing a regression on each bit of regional data (see picture attached below), instead of just one massive blob of data. If that's not what I've done, is there a way to do this, and what is it called?

Picture : https://i.imgur.com/gRaqPiK.png

Thanks and please help me,
An incredibly stressed, and probably very stupid, student

EDIT : So what I THOUGHT I was doing was fixed effects, so I guess I'll just drink loads of coffee and hardcore edit my dissertation over the next day.