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I was trying to fit a powerlaw to some data and noticed some inconsistency in the behaviour of mathematica.

This works

{1, 2, 3, 4, 5} // Fit[#, {1, Log[r]}, Log[r]] & // Exp

(* r *)

whereas this does not

{1, 2, 3, 4, 5} // Fit[#, {1, Log10[r]}, Log10[r]] & // 10^# &

enter image description here

While I understand the logic, it seems it represents some level of inconsistency between the way the variables are handled by Fit?

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  • $\begingroup$ Wow, it's a bit surprising to me the first sample works. $\endgroup$
    – xzczd ♦
    Commented Aug 21, 2022 at 8:06
  • $\begingroup$ @xzczd I agree, but its also unfortunate both do not behave the same way (?) $\endgroup$
    – chris
    Commented Aug 21, 2022 at 8:11
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    $\begingroup$ To be on the safe side, you should fit relative to a variable not an expression. That the first example works is really a surprise. $\endgroup$
    – Daniel Huber
    Commented Aug 21, 2022 at 8:14
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    $\begingroup$ I think the first one only works for the same reason that e.g. a[1] is generally allowed to be considered a "variable" in functions like these—Log[r] just happens to be of the same form. Its "meaning" as a logarithm isn't seen by Fit. (However, Log10[r] immediately evaluates to Log[r]/Log[10], and so is not recognized as a variable.) $\endgroup$
    – thorimur
    Commented Aug 22, 2022 at 20:34

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