Scatterplots of Students vs. Pts per Student by
Division
Broken into public and private schools
2005 Season Only
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Blue Diamonds are Public School
observations
Magenta Squares are Private School observations
Blue Lines are Linear Regressions based on the
Public School Observations in that Division
Magenta Lines are Linear Regressions based on the Private School Observations in
that Division
Summary of Graphs
The six graphs above are scatterplots of each of the divisions. The x-axis represents the enrollment figure for each school and the y-axis represents the computer points per student for that school. For example, Mentor (being the largest school in Ohio) can be seen in Division I. It is the only dot with enrollment over 1300. By looking at how high that dot is on the y-axis, we can see how many points per student this school gained this year. In Mentor's case: just under .01.
There are two lines on each graph. These are regression lines based on public schools and private schools respectively. A regression is a statistical process that attempts to predict the outcome of one observation based on some other observation(s). In this case, the regressions attempt to predict the points per student based on the school's enrollment. By running individual regressions for private and public schools, we can see any differences between the two. For example, in Division I, the public regression line predicts that if a public school has an enrollment of 1100 they will have a points per student score of just over .015. However, the private regression line predicts a private school with an enrollment of 1100 will have a points per student score of over .025.
In those charts that show the private school line above the public school line, we can say that private schools are getting more talent per enrolled student than are the public schools. Divsions I, III, IV, and V demonstrate this situation. To a lesser extent Division II does as well. Division VI tends to show that until enrollment exceeds 75 public schools outperform; in schools larger than that private schools outperform.
The difference between the lines show how great the performance difference is. For example in the Division I example mentioned above, there was a performance difference of just over .01 when the enrollment figure is 1100. The farther the lines are apart, the greater the performace difference.
Interestingly, most graphs have a negative slope. This would indicate that within a division, the larger schools have diminishing returns for each new student enrolled. In Division II, the negative slope is so great for private schools that public schools actually overperform at enrollments greater than 500.
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