Should I remove this outlier? I am running a multiple variable regression predicting GDP per capita for U.S. states with a bunch of independent variables. Currently I have included the District of Columbia in the data set which has a much higher GDP per capita. Should I still include D.C. in the dataset?
My reasoning to include it is that D.C. has a higher population than states like Vermont, etc.
 A: The criterion for making this decision should be based on
your purposes, and not influenced by the fact that the GDP per capita is for DC is about twice that of the leading state (NY) [which is in turn about twice that of the trailing state (MS)].
You say you are "... predicting DP per capita for U.S. states....$
If you consider DC as a 'state' for your purposes, then include CD for all useful independent variables. If you don't want to
predict GDP for DC, then what would be the motivation for including DC?
If you were trying to predict GDP for the US, then DC is part of the US and should be included. In that case you'd also have to decide
whether you consider various territories, etc. are "part of the US."
A: As a general rule, you should not remove data from your dataset unless you think it was recorded incorrectly and so it unreliable due to measurement error.  If a data point is correctly measured, but it merely has a value that is substantially different to other values in the data (making it an "outlier" in the sense you describe) then you should keep it in your data and find a way to model your data in a way that accomodates that value.$^\dagger$  Often this means altering your model to allow higher kurtosis in the "error terms", yielding higher probabilities of large deviations from the mean.
When you remove data from a dataset due to it being an "outlier" with respect to an assumed statistical model, you are effectively banishing parts of reality that do not conform to your statistical assumptions.  The resulting predictions you make will be poor, since they reflect only the cherry-picked part of reality that behaved according to your a priori assumptions.  Since many statistical models are built on an assumption of normally distributed error terms (which are mesokurtic) they may be inadequate to deal with cases where values in the data exhibit higher kurtosis, and therefore more frequent occurrence of values that are far from the mean.

$^\dagger$ The other time that removal of outliers can be justified is when one is doing sensitivity analysis.  In this case it is reasonable to remove outliers and refit a statistical model in order to determine the sensitivity of the inferences to the presence of the outlying values.
