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I have an x-y data list. The data is here. It looks like below: enter image description here

I want to mark the knee location. I mean I need to find the point of greatest slope change and get the x coordinate of this point. Theoretically, this position is around x=29.2519.

I tried SavitzkyGolayMatrix method and get the below result (x=29.4461). This result is a little deviation from the theoretical result x=29.2519. enter image description here

I read some literature. Find them with a method: a least squares fit method, find the knee by intersecting two straight lines. And they show the below similar pictures: enter image description here

Can someone tell me how to implement this method? Thank you!

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    $\begingroup$ Ummm... what's the "SG" method? $\endgroup$
    – David G. Stork
    Commented Aug 29, 2023 at 5:00
  • $\begingroup$ A result of x=29.4461 seems o.k. considering the noise. $\endgroup$
    – Daniel Huber
    Commented Aug 29, 2023 at 10:05
  • $\begingroup$ I'm confused. The plots show such a big range that the presumed knee at around x=29 isn't visible. If you expect it to be there, why not restrict the data range up to, e.g., x=50? $\endgroup$
    – corey979
    Commented Aug 29, 2023 at 10:54

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