- #1

Malamala

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Can I just replace ##\sigma_y^2## with ##\sigma_x^2+\sigma_y^2##? The errors on x and y are not correlated. Thank you!

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- Thread starter Malamala
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- #1

Malamala

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Can I just replace ##\sigma_y^2## with ##\sigma_x^2+\sigma_y^2##? The errors on x and y are not correlated. Thank you!

- #2

Vanadium 50

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- #3

Dale

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It is also called orthogonal distance regression.

- #4

Vanadium 50

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It is also called orthogonal distance regression.

Yes. You start with the obvious thing - a line y = mx + b, and you try and do a least-squares fit using the perpendicular distances between the points and the candidate line instead of the y-distances. Problem is that doesn't always get you a unique unbiased solution.

That's why you need to specify what you are looking for very carefully.

- #5

Stephen Tashi

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Vanadium 50

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If you minimize a function of Δy only, it's clear what you are doing. If you minimize something like Δx

To get a well-defined answer, one needs to pose a much, much better defined question. And even then it may not exist.

- #7

WWGD

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Maybe if you standardize your variables you can avoid the issue with units? I understand that is one if the reasons for standardization.

If you minimize a function of Δy only, it's clear what you are doing. If you minimize something like Δx^{2}+ Δy^{2}it's not even guaranteed that you have a number with consistent dimensions: suppose y is temperature and x is time. What units would Δx^{2}+ Δy^{2}even be in?

To get a well-defined answer, one needs to pose a much, much better defined question. And even then it may not exist.

- #8

Malamala

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What do you mean by this?Maybe if you standardize your variables you can avoid the issue with units? I understand that is one if the reasons for standardization.

- #9

WWGD

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I was replying to @Vanadium 50 regarding his statement on mixed units in the expression ##\sqrt \delta x^2 + \ delta y^2 ##. If you standardize your expression ( assuming normality of data or other) the resulting variable is unitless , from algebra alone ( you're dividing two expressions with the same units ), so that you avoid at least this issue of having mixed units. Seems like something @Stephen Tashi may know about.What do you mean by this?

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