# 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 general, you should care most about the within R^2. Feb 28 '20 at 8:19

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.

The ANOVA results indicate 53.11% of dependent variable is explained - which you should check whether it is significant (or insignificant). Moreover, you may ascertain the chi-square with the help of between and within sum of squares. This could help you to test the significance level at which the effect on dependent variable is significant.