MATLAB: Fitting a sigmoid curve using curve fitting tool box

curve fittingdata

Hi, I am trying to fit a sigmoid function to the underlying data with the goodness of fit. I was using the curve fitting tool box. Unfortunately, i am not getting an idea to how to go forward with this. I tried to write custom function to fit the data, unfortunately, i am not able to get the required fit. Any help to solve this will be appreciated. X and Y data is shown below.

y= [0.70,1.09,0.96,0.37,0.27,0.35,0.16,0.18,0.18,0.02,0.37,0.67,1.26,1.70,1.85,1.73,1.92,1.72,1.47,1.50,1.46,1.43,2.12,1.6,1.8]

x = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25]

Best Answer

Hi, Hair, the quailty of your data seems to be bad for sigmoid type of function. If take the function like:

y = y0+a/(1+exp(-(x-x0)/b))^c

Then the fitting result looks like:

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MATLAB: What is an accurate function for linear regression

Which Toolboxen do you have? There's fit in the Curve Fitting TB and LinearModel.fit in the Statistics Toolbox. polyfit is certainly just as accurate; for such simple fitting and wants, the coefficients are returned directly and Rsq is easily computed from the definition as 1-SSE/SST

ADDENDUM

>> x=1:10; x=x(:); y=randn(size(x));  % sample data
>> b=polyfit(x,y,1)                   % fit....
b =
  0.2412   -0.7021
>> plot(x,y,'-*)
>> yhat=polyval(b,x);      % evaluate
>> hold all
>> plot(x,yhat)
>> mn=mean(y);
>> dot(y-mn,y-mn)  % definition for SST, total sum squares
ans =
 28.1924
>> SST=var(y)*(length(y)-1)  % Use builtin VAR function
SST =
 28.1924
>> SSE=dot(y-yhat,y-yhat)
SSE =
 23.3944
>> Rsq=1-SSE/SST
Rsq =
  0.1702

MATLAB: How to fix the upper asymptote in sigmoid

Your call to mysigmoid has 6 input arguments (b,c,x,xon,xrated,a; the last of which is your "a"), but your defined function only accepts 5 (b,c,xon,xrated,a). you're missing the 'x' input argument in your function definition.

This is likely leading to your issues with manually setting the "height" of the sigmoid function.

Best Answer

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