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Nonlinear fitting question

  • To: mathgroup at smc.vnet.net
  • Subject: [mg111577] Nonlinear fitting question
  • From: eric g <eric.phys at gmail.com>
  • Date: Fri, 6 Aug 2010 06:56:07 -0400 (EDT)

Hello Group,
In the example below I want to do a fitting "exploiting" the correlation 
between y1 and y2 rather than separate them like I did. Like a 2D 
fitting thing.
Also, in NonlinearModelFit, I dont like treating 1/(1+b) like another 
parameter.

how to do it?

best regards,
Eric

(* my model *)
b = 1;
k = 1/2;
y1[t_] = (b + Exp[-k*t])/(1 + b);
y2[t_] = (1 - Exp[-k*t])/(1 + b);

(* my measurements *)
dat1 = Table[{t, y1[t] + RandomReal[{-1, 1}]/20}, {t, 0, 10, .1}];
dat2 = Table[{t, y2[t] + RandomReal[{-1, 1}]/20}, {t, 0, 10, .1}];

Plot[{y1[t], y2[t]}, {t, 0, 10}, Epilog -> {{Red, Point[dat1]}, {Blue, 
Point[dat2]}},  PlotStyle -> {Red, Blue}]

(*FITTING*)
(* results with dat1:   *)
Clear[b, k];
Normal[NonlinearModelFit[dat1, (b + Exp[-k*t])/(1 + b), {b, k}, t]]
0.504916 (0.980528 + E^(-0.492309 t))

(* results with dat2:   *)
Clear[b, k];
Normal[NonlinearModelFit[dat2, (1 - Exp[-k*t])/(1 + b), {b, k}, t]]
0.494348 (1 - E^(-0.524777 t))




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