The R-squared from the "dummy variable regression" is typically very high. But you shouldn't really get credit for including the dummy variables. As Carlo said, use the within R-squared, as it nets out the dummies. The usual R-squared can be used for pooled OLS without the unit-specific dummies.
There is a way to net out the time effects, too, but that's often less of an issue.
There is a way to net out the time effects, too, but that's often less of an issue.
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