What's going on?

Here's why you shouldn't jump to conclusions about the cadence-power relationship. These data were collected during a ride with a series of hill intervals. Here's a plot showing the data collected on the flat (in black) and the data collected on the hill (in red).

Flat is black, Hill is red

And, just to make clearer the relationship between cadence and power during those two parts of the ride, I've superimposed two smooth lines that show the average power at each cadence level, a red line to show the power on the hill and a black line to show the power on the flat. The relationships are opposite.

Avg power by cadence on flats and hill

Are you now willing to say what the relationship between cadence and power is?