Linear Regression a.k.a. Ordinary Least Squares assumes only Y has noise, and X is correct.

Your "visual inspection" assumes both X and Y have noise. That's called Total Least Squares.

esafak 3 days ago | parent | next [-]

emmelaich 3 days ago | parent | prev [-]

Yep, to demonstrate, tilt it (swap x and y) and do it again. Maybe this is what TLS does?

	▲	srean 3 days ago \| parent [-]
		>(swap x and y) and do it again. This is a great diagnostic check for symmetry. > Maybe this is what TLS does? No, swapping just exchanges the relation. What one needs to do is to put the errors in X and errors in Y in equal footing. That's exactly what TLS does. Another way to think about it is that the error of a point from the line is not measured as a vertical drop parallel to Y axis but in a direction orthogonal to the line (so that the error breaks up in X and Y directions). From this orthogonality you can see that TLS is PCA (principal component analysis) in disguise.