As we continue our look into capital appropriations per student from last week, one of the main lessons is that there are a lot of extreme outliers. This can be seen in the histogram and box and whisker charts below. The concentration at the far left of the histogram and the low box in the box and whisker plot demonstrate that most public colleges had no or very small capital appropriations per student (median = $63 and mean = $626). But there were some rather extreme exceptions. (Note that I capped the values for the box and whisker chart, so we can’t see the most extreme ones in that chart.)
Some of these outliers are presumably one-time expenses involved with building a new building or campus. For instance, the University of Hawaii-West Oahu had capital appropriations of more than $54,000 per student and the CUNY School of Law at Queens College more than $46,000 per student; both of these occurred just prior to moving the colleges.
An anonymous reader also suggested we add a squared term to the regression from last week to look for a possible nonlinear relationship. Just as the reader expected, the squared term does improve the fit. The coefficient on the squared term is quite small (-.000000753) and statistically significant (P value < .001).
This nonlinear relationship can be seen with LOESS curve, the red line in the chart below that shows capital appropriations per student tend to increase with regular appropriations per student until regular appropriations reach around $7,000, and then they begin to fall.
Given the long-term nature of most capital investments and the massive one-time jumps in capital appropriations they necessitate, most questions will benefit from taking the average capital appropriations over a number of years, rather than for any single year. Unfortunately, there are only two years of data available at the moment, but this is one of the few instances when time is actually on our side.