How to interpret fixed effect regression R-sq. results for panel data? I runned a fixed effect regression in Stata (xtreg, fe) for panel data. I obtained below R-sq. results. How should I interpret them? Which one is my main interest(within,below or overall)? How can I derive the exact Adjusted R-sq. by using these 3 values?

R-sq:
     within  = 0.8226
     between = 0.4727
     overall = 0.5311  

Thanks a lot!
In panel regressions you have multiple dimensions and that is why also you have 3 different $R^2$. The within $R^2$ tells you how much variation within your panel variables is on average explained by your model. The between $R^2$, tells you how much variation between your panel variables is explained by the model, and overall $R^2$ gives you the combination of both and tells you how much variation in the whole panel data your model explains.

According to the stata manual you should get adjusted $R^2$ for fixed effects by ereturn list it will be the r2_a scalar. However, there are no simple adjustments for within and between $R^2$, those are most often reported unadjusted.