MATLAB: Smooth line of semilog plot

curve fittingsemilogsmooth curvespline

Hi all,
Is there any effective and easy-understandable way to make a smoothly best-fitted line to the data on semilogx plot? The plot with spline seems to be effective way, however, it is uneasy to understand for me. Could somebody guide me to know how to smooth the semilogx plot? My data are
x = [5 15 25 35 45 55 65 75 85 95 105 135 155 165];
y = [0 0 7.5 30 47.5 62.5 75 85 90 92.5 95 97.5 100 100];
plot this with the semilogx and find the smooth curve fitting them through.
Thank you so much.

Best Answer

Your data appear to be able to be modeled by a Logistic function (link).
I would simply do the fit:
x = [5 15 25 35 45 55 65 75 85 95 105 135 155 165];
y = [0 0 7.5 30 47.5 62.5 75 85 90 92.5 95 97.5 100 100];
logistic_fcn = @(b,x) b(1) ./ (1 + exp(-b(2).*(x-b(3))));
NRCF = @(b) norm(y - logistic_fcn(b,x));
B = fminsearch(NRCF, [100; 0.1; 50]);
xi = linspace(min(x), max(x));
yi = logistic_fcn(B,xi);
figure(1)
semilogx(x, y, 'pg')
hold on
plot(xi, yi)
hold off
grid
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