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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 ca
by tomp 9mo 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.
- emmelaich 9mo agoYep, to demonstrate, tilt it (swap x and y) and do it again. Maybe this is what TLS does?
- srean 9mo ago>(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.
- esafak 9mo agoThere is an illustration in https://en.wikipedia.org/wiki/Total_least_squares https://en.wikipedia.org/wiki/Total_least_squares