MATLAB: How to do curve fitting on data with inflection point

curve fittinginflection point

Hello
Dear experts,
I have a scatter plot of data of x and y and I need to fit a curve on them. However, it is obvious that there is no function that can fit the whole range of these data (blue line of the attached picture). So, I need to fit two curves (dashed red line): one is on the data that are less than the inflection point (yellow point), and one for data that are larger than the inflection point. The inflection point can visually be guessed as 0.25, but is there any way that I can calculate the inflection point from the original scatter plot?
Note that I know how to do the curve fitting, and my question is only regarding the inflection point.
Hope this is the appropriate forum to ask this question.
Thank you very much.

Best Answer

Why do you think there is no equation that can fit this data? This looks like a sigmoid E max model to me. A similar shape is obtained from the Hill equation, too.
Here's a simple example using the Hill equation and trying to match your curve.
mx = 0;
mn = 1;
ec50 = 0.25;
n=5;
x=0:.01:1;
y = mn + (mx-mn)*ec50^n./(ec50^n+x.^n);
plot(x,y)
grid on
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