I have a model Y = A(1-EXP(-AX)) and I want to get the value of A so the Y vs X model and Y vs X experiment has a minimum deviation (R-squared value = 1). I think I can fitting that curve by using goal seek method but the problem is how to calculate the R-squared value manually.
You could use the function nlinfit.
[A] = nlinfit(X,Y,@(X,A)(A.*(1-exp(-A.*X)),[A_ini])
where A_ini is an initial value for your parameter A to start the iterations. nlinfit finds a solution for A by iterative least square estimation.
To calculate R^2 manually, use the formula given by any proper statistics manual.
http://www.mathworks.com/help/stats/nlinfit.html
Thank you for the answer, Pierre-Erik and Dashty. I've already tried both of your methods and it was very helpful. Thank you.
Differentiating the model you can obtaine the following equation for Y : dY/dX = A(A-Y), finite-difference approximation of which is (Yn+1)+(A-1)Yn-A*A = (en). By minimizing the sum of (en) squares you will obtain the cubic equation for A. It is known that such equations can be solved manually (http://oeis.org/wiki/Cubic_formula :)
Neural networks are a good choice for fitting non linear functions.
I like to use the Excel Solver Add-In to do nonlinear curve fitting. You can fit a function to any number of independent variables using any number of fitting parameters. Start with a column for each independent variable and a column with your data. Locate your parameters in adjacent cells somewhere on the spread sheet. Calculate your function as a function of the independent variables and the parameters in the column adjacent to the data. In the next column calculate the difference between the data and the calculated value and in the next column calculate the square of the difference. Sum the square of the difference in another cell and use the Solver Add-In located on the Analysis section at the far right of the Data tab to minimize the cell. Note that the default installation of Excel does not load the solver.
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