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In developing an OLS regression equation using cross-sectional data, I obtained an adjusted R^2 of 0.009. On a whim, I added an AR(1) term to the right side of the equation, even though I know of no statistical basis for doing this. The AR(1) increased the adjusted R^2 to 0.91. Does anyone have an idea of whether the higher R^2 was a coincidence or explained by an obscure statistical principle? Thanks.

Coincidence, sort of.


It probably indicates that you have strong correlation between the cross-sections.

Out of interest you should try mixing up the order of the cross-sections, re-estimate and see how the R-squared changes.

To mix up the order, whilst looking at the workfile, click on:
Proc->Sort Current Page.
Then in the "Sort key(s)" box, type nrnd, and hit OK.