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Did you account for the difference in the cost of living between regions? $1,000 in Mississippi can probably "buy" a lot more than $1,000 in New Jersey or DC.

I have factored the "cost of living" on other reports and my claim that spending and achievement aren't linked. For one quick example, we can look at the average teacher salary by state. The teachers in states that have a higher cost of living would presumably be paid more, which would cause the amount per student to rise. In this quick case we look at teacher's pay because we can safely assume that 4th graders aren't the ones that need the adjustment (since young kids don't have to pay for their home, utilities, etc.)

The average salary for teachers in DC (last in score, first in spending) in 2001-2002 was $47,049. The average salary for teachers in Nevada (first in score, 43 in spending) was $41,524. That's a difference of $5,525 (13%)per teacher per year. The 13% extra that DC pays teachers does little to explain the astounding 80% extra that DC gets over Nevada per student per year.

http://nces.ed.gov/nationsreportcard/reading/results2003/schsystchar-c.asp