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Okay I watched this video. https://www.youtube.com/watch?v=PaFPbb66DxQ Guy seems to have based Sheldon vibes, but he just says people don't use abs because its mathematically tricky. Any particular reason for this? Seems like Abs would be easier.

The other thing is, using squares seems less accurate. Seems like it would give disproportionate weight to far away objects instead of just a consistent weight based on a linear distance. And I've shown in another thread that Ordinary Least Squares has flaws (for vertical type lines). Someone said Total Least Squares is better, but I don't know much about that.

Then I started to wonder...what about circles? Wouldn't distance based on some kind of circle method be the most accurate?

Or the other method, that doesn't use circles, somehow gets the perpendicular vector of the line. But the problem with that is first you have to know the line, in order to get the perpendicular vector.

@Lulu I just learned about Least Squares since a few days ago so I'm not sure about any of this.

proj786
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    Advice Nr. 1 : Avoid math videos ! Read wikipedia and pdf-articles ! – Peter Jun 18 '23 at 22:30
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    People use absolute distance all the time. It can be harder to work with analytically but it has some advantages. That said, there's the Gauss Markov Theorem which tells us Ordinary Least Squares minimizes variance (at least under some sensible assumptions). That's a big advantage for the standard method. If it's not to expensive, computation-wise, run both. – lulu Jun 18 '23 at 22:41
  • here is a discussion of some of the differences. – lulu Jun 18 '23 at 22:42
  • Note: should have said, the discussion I linked to concerns the difference between using absolute deviation and squared distance in the definitions of variance and standard deviation, but the issues are similar. – lulu Jun 18 '23 at 23:01
  • @Peter I am a visual learner lol. All of the math I've learned is from teachers, talking to mathematicians, or math websites, I tried wikipedia and its too confusing for me, I don't recall any instance where I learned new math from there – proj786 Jun 19 '23 at 12:56
  • @Lulu Ok thanks I will read that thread. I tried reading the wikipedia but math wikipedias are usually incompatible with my brain – proj786 Jun 19 '23 at 12:57
  • Conceptually: the biggest reason people sometimes prefer absolute difference is that they are a more robust way to handle outliers. That is, if you know that the data you are collecting is prone to significant disruptions of a sort other than what you want to study, then squared differences can give those bad data points more weight than you'd like. But every method has tradeoffs. – lulu Jun 19 '23 at 13:04

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