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FindFit and squared residuals

  • To: mathgroup at smc.vnet.net
  • Subject: [mg126214] FindFit and squared residuals
  • From: leigh pascoe <leigh at evry.inserm.fr>
  • Date: Wed, 25 Apr 2012 00:36:14 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com

Is there a command to get the sum of the squared residuals after using
FindFit?

Here is an example that fits a function and then plots the data and the
fitted function

inc1[x_, M_, \[Tau]_, \[Phi]_] :=
 M/\[Tau] \[Phi]^M E^(-(x/\[Tau])) (1 - E^(-(x/\[Tau])))^(M - 1)

franceMaleCDdata19882005 = {{2.5,
    0}, {7.5, .000008}, {12.5, .00004}, {17.5, .00012}, {22.5, \
.000142}, {27.5, .00012}, {32.5, .000084}, {37.5,
    0.000060}, {42.5, .000050}, {47.5, .000046}, {52.5, .000039}, \
{57.5, 0.000043}, {62.5, .000022}, {67.5, .000026}, {72.5, .000016}, \
{77.5, 0.000019}, {82.5, .000015}, {87.5, .000017}};
franceMaleCDdata19882005plot =
  ListPlot[franceMaleCDdata19882005,
   PlotStyle -> {Red, Dashed, Thick}, PlotRange -> All,
   Joined -> True];
franceMaleCDdata19882005fit =
 FindFit[franceMaleCDdata19882005,
  inc1[x, M, \[Tau], \[Phi]], {{M, 10}, {\[Tau], 5}, {\[Phi], .6}}, x]
Show[Plot[
  inc1[x, M, \[Tau], \[Phi]] /. franceMaleCDdata19882005fit, {x, 0,
   85}, PlotRange -> All], franceMaleCDdata19882005plot]

What is the minimised value of the squared residuals in this case? I
would like to compare the fit with the more complex function shown below
(the fit is obviously better, but with more parameters used}.

inc4[x_, N1_, N2_, \[Tau]1_, \[Tau]2_, \[Phi]_] := (
  E^(-(x/\[Tau]1)) (1 - E^(-(x/\[Tau]1)))^(-1 +
    N1) (1 - E^(-(x/\[Tau]2)))^N2 N1 \[Phi]^(N1 + N2))/\[Tau]1 + (
  E^(-(x/\[Tau]2)) (1 - E^(-(x/\[Tau]1)))^
   N1 (1 - E^(-(x/\[Tau]2)))^(-1 + N2) N2 \[Phi]^(N1 + N2))/\[Tau]2

franceMaleCDdata19882005fit =
 FindFit[franceMaleCDdata19882005,
  inc4[x, N1,
   N2, \[Tau]1, \[Tau]2, \[Phi]], {{N1, 8}, {N2, 2}, {\[Tau]1,
    7}, {\[Tau]2, 23}, {\[Phi], .6}}, x]
Show[Plot[
  inc4[x, N1, N2, \[Tau]1, \[Tau]2, \[Phi]] /.
   franceMaleCDdata19882005fit, {x, 0, 85},
  PlotRange -> All], franceMaleCDdata19882005plot]

Thanks for any help.

Leigh



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