>And no, you can not get around this problem by doing a multivariate regression of speed on gas pedal and hill.

I'm no expert on statistics, but this seems like a pretty basic scenario for a statistical analysis to provide insight into. These two phenomena would be perfectly correlated in both the time of appearance and the degree.

You wouldn't be able to derive anything about the effect of hills or gas pedals on speed, but you'd be given a powerful clue as to what's going on.

The second there's even a tiny imbalance between the two, you're given the relationship to speed.