How to do a Four Parameters logistic regression fit without the Curve fitting toolbox?

I have an 'X' and 'Y' vector (see below) which I want to fit to a Four Parameters logistic model: Y=D+(A-D)/(1+(X/C)^B), but I don't have access to any Matlab toolboxes. How can I do this so I end up with the A,B,C and D parameters?

X=[0.000; 0.012; 0.023; 0.047; 0.094; 0.188; 0.375; 0.750; 1.500; 3.000; 6.000; 12.000]
Y=[0.034; 0.018; 0.023; 0.036; 0.051; 0.065; 0.077; 0.128; 0.224; 0.399; 0.660; 1.0350]

Answer 1

[Torsten]

function main
  X = [0.000; 0.012; 0.023; 0.047; 0.094; 0.188; 0.375; 0.750; 1.500; 3.000; 6.000; 12.000];
  Y = [0.034; 0.018; 0.023; 0.036; 0.051; 0.065; 0.077; 0.128; 0.224; 0.399; 0.660; 1.0350];
  p0 = [2 1 1 1];  %Set initial guess for parameter vector
  p = fminsearch(@(p)fun(p,X,Y),p0);  % Call optimizer for fitting
  Ysim = p(4)+(p(1)-p(4))./(1+(X/p(3)).^p(2)); % evaluate final logistic function at measurement points
  plot(X,Y,X,Ysim) %plot measured and fitted values
end

function obj = fun(p,X,Y)
  Ysim = p(4)+(p(1)-p(4))./(1+(X/p(3)).^p(2))  % evaluate logistic function at measurement points
  obj = (Y-Ysim).'*(Y-Ysim)  % calculate sum of squared differences between measured and fitted values
end

[Johnny Birch]

That is brilliant, thanks a lot Torsten.