Should I modify x-values for curve fitting with response variable?

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Atanu
Atanu 2024-5-31
评论： John D'Errico 2024-5-31
I am trying to fit concentration (in x-axis) and approach rate (in y-axis) using a logistic equation. The real values of x are [0.5, 2, 5, 9]. Should I fit real_x vs y? I think I saw somewhere that one should use equidistant points (like x = [1,2,3,4]) for fitting. What is your opinion?

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Matt J
Matt J 2024-5-31
编辑：Matt J 2024-5-31
Matlab's fitting solvers do not require the x data to be equidistant.
I'm not sure why it would be a matter of opinion, though. Since you do not have equidistant x, what choice do you have but to use the non-equidistant ones?
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Matt J
Matt J 2024-5-31
You are quite welcome, but please Accept-click the answer if your question has been resolved.
John D'Errico
John D'Errico 2024-5-31
+1 of course, but I would add that spacing/placement can be a significant factor.
For example, given a tight cluster of points, and one point out in the weeds. Now that one point on the edge of tomorrow will often have a high influence on the result.
Another case is the simple one where you have points at exactly 2 levels, with multiple replicates. In this extreme case of a non-uniform sampling, you really only have 2 pieces of information, and a linear fit would pass through the average of the two clusters. This even applies to a case where you have two very tight clusters of points. Again, you have essentially only two pieces of information due to the non-uniform sampling.
All of this gets into things like influence matrices, the hat matrix, and an entire course or book on the subject.

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