MATLAB: Fminsearch for ligistic fit

fminsearch

I'm trying to use fminsearch to fit a logistic model to my data. My problem is that I'm rreally confused about how to define the input for the fminsearch function.
My data:
x = [0.5 2.7 6 8.8 9.7 12.8 16 20 23];
y = [0.8 1.1 3.4 7 9 13 13.4 13.2 18.8];
I want to fit the parameters of following function to my data:
Now I don't know how to define the right functions for the optimization.
What I've tried so far:
f = @(p,x)p(1)*(0.5-(1./(1+exp(p(2)*(x-p(3))))))+p(4)*x+p(5);
f2 = @(p)f(p,x);   
p0 = [0.1 0.1 0.1 0.0001 0.1];
p = fminsearch(f2,p0);
But this is not the right way.

Best Answer

f2 = @(p)f(p,x);
That relies on x existing in your workspace. If you are going to do that you might as well assume it on the previous line, and use cleaner code.
But your bigger problem is that you are failing to calculate a sum-of-squared errors
f = @(p) p(1) * (0.5 - (1 ./ (1 + exp(p(2)*(x-p(3)))))) + p(4) .* x + p(5);
f2 = @(p) sum((f(p) - y).^2);
p0 = [0.1 0.1 0.1 0.0001 0.1];
p = fminsearch(f2, p0);
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