$$ spent per student and SAT scores

This is very surprising! I wonder how it might tie into other traditional factors for education, e.g. class size and use of computers in the classroom. If, for example, we imagine that computers don't actually enhance the classroom experience much and happen to be absent in most Utah schools (or alternatively that Utah teachers are underpaid) and imagine those explaining Utah's low costs per student, and further imagine that Utah classroom sizes average significantly smaller than the rest of the nation, we can more easily understand how they have both a lower cost per student and a higher SAT achievement.

Alternatively and more cynically, we could imagine Utah's school systems teaching to the SAT test rather than providing a more generic education.

I would love to see class size and SAT scores analysed on a per-state basis (maybe that's on there?)

The simple average combined SAT score is a highly biased measure of statewide performance. States like Alabama, Mississippi and Arkansas have significantly fewer students choose to take the SAT at all. Many opt for the ACT and military or fail to graduate high school at all, thus the students who do choose to take the SAT are a highly selective group and simply can not be compared to other State populations where significantly higher proportions of the student body take the SAT to begin with.

This got me curious, so I went and looked up the percent of high school graduates who take the SAT from each state:

http://nces.ed.gov/programs/digest/d05/tables/dt05_129.asp

I ran a multiple regression with the data and found that for every 1% increase in the percent of graduates taking the SAT in a state, the average score declines by 2.63 points. That means the state with the highest percentage (NY - 90%) compared to the state with the lowest percentage (SD - 5%) will have average SAT scores that are 221+/-18 points lower for this reason alone.

In comparison, the correlation between average SAT score and expenditure per pupil actually turned POSITIVE when the percentage taking the SAT was held constant - a 0.842 point increase for every extra $100 spent. That means the state with the highest expenditure (NJ) compared to the state with the lowest expenditure (UT) will have average SAT scores that are 75+/-28 points higher for this reason alone.

The conclusions that can be drawn from this, however, are murky at best. First of all, since educated people tend to move to states like NY and MA, the schools in these states could be starting with smarter kids in the first place. Also, how much of that extra money goes toward SAT prep classes? (Maryland, for example, gives SAT prep classes to ALL 10th graders). If UT spent an extra $1,000 per student to give SAT prep classes to all 10th graders, how much of that 75-point gap with NJ be filled? That extra $8,000 that NJ spends could have no discernible effect at all.