Why curve fitting options give two diffrent results

I am getting two different solutions and goodness of fitting on using same equation and fitting options in Curve fitting tool.

I am using two terms exponential fitting as a*exp(b*x)+c*exp(d*x) with nonlinear LeastSquare , LAR and Trust region algorithm. I am getting goodness of fit : SSE=902.8; RMSE= 1.456

Same equation if I use in custom equation with similar fit options, neither I get similar coefficient values nor similar goodness of fit:

SSE= 8.55 e+14 RMSE= 1.417e+06

Please let me know why it so??

[Matt J]

I don't understand the difference between the two tests. If the equation is the same in both cases and the data is the same in both cases, and the fitting options are the same, then what did you do differently in each case?

[Neeta]

There is no difference in two tests except (1) I used exponential fitting option and (2) I have used custom equation option. I am surprised to see two different results.

Answer 1

[Shashank Prasanna]

Your results will be sensitive to starting point. As long as you use the same equation and a close enough starting point you must get similar results.

Click on Fit Options and see what the bounds and starting point is for the exponential fitting, and use the same for your custom equation.

[Neeta]

I understand initial guess (starting point) affects the convergence of the algorithm. However, when I use same starting point/s as I have used in exponential, custom equation option gives error as "inf computed model function, fitting cannot continue". I have also used similar maxfuncevals and maxIter. Lower and upper bounds are (-inf) and (inf).

Answer 2

[Matt J]

You might try using instead the custom equation

 a*exp(b*x)+c*exp((b+d^2)*x)

This way, the two exponential terms can be distinguished by the solver.