That brings up an interesting issue, which is that many systems do have more noise in y than in x. For instance, time series data from an analog-to-digital converter, where time is based on a crystal oscillator.

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jjk166 3 days ago | parent | next [-]

Well yeah, x is specifically the thing you control, y is the thing you don't. For all but the most trivial systems, y will be influenced by something besides x which will be a source of noise no matter how accurately you measure. Noise in x is purely due to setup error. If your x noise was greater than your y noise, you generally wouldn't bother taking the measurement in the first place.

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bravura 3 days ago | parent [-]

“ If your x noise was greater than your y noise, you generally wouldn't bother taking the measurement in the first place.”

Why not? You could still do inference in this case.

	▲	jjk166 3 days ago \| parent [-]
		You could, and maybe sometimes you would, but generally you won't. If at all possible, it makes a lot more sense to improve your setup to reduce the x noise, either with a better setup or changing your x to be something you can better control.

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GardenLetter27 3 days ago | parent | prev [-]

This fact underlies a lot of causal inference.

	▲	randrus 3 days ago \| parent [-]
		I’m not an SME here and would love to hear more about this.