>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.
Well, in this contrived scenario, you can't tell what would happen if the driver _didn't_ push down on the gas pedal while going up the hill. The relationship between the gas pedal and the speed of the car is entirely obscured.
However, in a real world system, the chance that there is zero imbalance is also nearly infinitesimal. You could take the most skilled driver in the world and you would still be able to pull out the relationship between gas pedal and speed out of his driving pattern. Similarly, with the right variables and enough data, you could pull a relationship like the one described here out of economic data.
(As a side note, I think the way in which this article is written is pretty obnoxious. The first 500 words are dedicated to the author congratulating himself for being aware of an idea that he hasn't even explained yet.)
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.