Comment by tomp
3 days ago
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.
3 days ago
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.
There is an illustration in https://en.wikipedia.org/wiki/Total_least_squares
Yep, to demonstrate, tilt it (swap x and y) and do it again. Maybe this is what TLS does?
>(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.