I have been trying to fit my data to a logistic equation, and it turns out that my data fits well with a Hill-Equation equivalent.
(Attached to this post is an image of the equation and the nature of the curve).
y = A2 + (A1-A2)/(1 + (x/x0)^p)
In origin help files they have drawn the tangent at this mysterious point x1. Where x1 is defined as:
(x1/x0)^p = (p -1 )/ (p+1)
I understand that the n value is for the Hill Coefficient and x0 is the IC50 or EC50, basically, the point where the response is 50% of the maximum. What I don't understand is, what is this x1 where the tangent has been drawn? While I can see the expression for it, I don't get by what it means? Is it the point of infliction? I am kind of clueless with the math.
That's an inflection point where the sign of the sign of the curve's derivative changes. See a Calculus book for details Best, D. Booth
X1 is the abscissa of the inflection point of the curve.
The curve you show is the one of logistics regression (or Verlhust equation). You can obtain the inflection point values by solving this equation :
(If f is a logistic function) :
f''(x)=0
Finally, I would recommend you to have a look here :
https://en.m.wikipedia.org/wiki/Logistic_function
And here :
https://socratic.org/questions/how-do-you-find-the-inflection-point-of-a-logistic-function
Regards
PS : Every inflection points coordinates of every models can be found by solving this equation "f''(x)=0".
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