I wanted to understand the relationship between particulate matter measurements (PM2.5) and the U.S. air quality index (AQI).

The formula is on wikipedia, defined as a piecewise linear function. But it's weird that the slope isn't monotonic! It starts at 4.2, then drops to 2.1, but goes up to 2.5, then drops to 0.5, then goes up to 1.0, then back down to 0.66. Weird!