Services & Resources / Wolfram Forums / MathGroup Archive
-----

MathGroup Archive 2008

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: Asking NonlinearRegression

  • To: mathgroup at smc.vnet.net
  • Subject: [mg88763] Re: [mg88733] Asking NonlinearRegression
  • From: Darren Glosemeyer <darreng at wolfram.com>
  • Date: Fri, 16 May 2008 05:30:00 -0400 (EDT)
  • References: <200805151050.GAA21764@smc.vnet.net>

Navri Navri Bintang wrote:
> Hi,
>
> I have a problem with nonlinear regression in Mathematica. I want to fit my data (below) to this following equation:
>
> y = Exp[(1-Exp[a*(1-Exp[-b*x])])*(Exp[-b*x])/(1-Exp[-b*x])]
>
> and I would like to find a and b values and also determined r-squared value.
>
> I try to use NonlinearRegression/NonlinearFit code, but its not working, I hope someone could help me
>
> Thanks a lot
>
> DATA:
> x	y
> 1	0.00
> 2	0.00
> 3	0.00
> 4	0.00
> 5	0.00
> 6	0.00
> 7	0.00
> 8	0.00
> 9	0.00
> 10	0.00
> 11	0.00
> 12	0.00
> 13	0.00
> 14	0.00
> 15	0.00
> 16	0.00
> 17	0.00
> 18	0.00
> 19	0.00
> 20	0.00
> 21	0.00
> 22	0.00
> 23	0.00
> 24	0.00
> 25	0.00
> 26	0.00
> 27	0.00
> 28	0.00
> 29	0.00
> 30	0.00
> 31	0.00
> 32	0.00
> 33	0.00
> 34	0.00
> 35	0.00
> 36	0.00
> 37	0.00
> 38	0.00
> 39	0.00
> 40	0.00
> 42	0.00
> 44	0.00
> 46	0.00
> 48	0.00
> 50	0.00
> 52	0.04
> 54	0.06
> 56	0.08
> 58	0.09
> 60	0.16
> 65	0.24
> 70	0.32
> 75	0.43
> 80	0.49
> 85	0.58
> 90	0.80
> 95	0.91
> 100	1.00
> 105	1
>
>
> Rgds,
> Navri
>
>
>       
>
>   

When something is not working, it helps to know what not working means 
(for instance, a function may not be evaluating or there may be 
something undesirable about the result). A couple of possibilities in 
this case are that the package wasn't loaded or that non-default 
starting values are needed for the parameters.

Regardless of whether or not part of the problem was package loading, 
this example will need non-default starting values. By default, 1 is 
used as the starting value for each parameter if no value is specified 
and this is not a good starting point for the parameters in this 
example. Looking at 3D plots as a function of a and b for a couple of 
the larger x values, it looked like 5 would be reasonable for a and .1 
would be reasonable for b and with the sharp nature of the curve it 
would help to give two starting values so the method didn't take too big 
of an initial step. Doing so, it worked fine.

In[1]:= << NonlinearRegression`

In[2]:= data = Import["data.tsv"]

Out[2]= {{1, 0.}, {2, 0.}, {3, 0.}, {4, 0.}, {5, 0.}, {6, 0.}, {7, 0.}, 
{8, 0.}, {9, 0.},
 
 >    {10, 0.}, {11, 0.}, {12, 0.}, {13, 0.}, {14, 0.}, {15, 0.}, {16, 
0.}, {17, 0.},
 
 >    {18, 0.}, {19, 0.}, {20, 0.}, {21, 0.}, {22, 0.}, {23, 0.}, {24, 
0.}, {25, 0.},
 
 >    {26, 0.}, {27, 0.}, {28, 0.}, {29, 0.}, {30, 0.}, {31, 0.}, {32, 
0.}, {33, 0.},
 
 >    {34, 0.}, {35, 0.}, {36, 0.}, {37, 0.}, {38, 0.}, {39, 0.}, {40, 
0.}, {42, 0.},
 
 >    {44, 0.}, {46, 0.}, {48, 0.}, {50, 0.}, {52, 0.04}, {54, 0.06}, 
{56, 0.08},
 
 >    {58, 0.09}, {60, 0.16}, {65, 0.24}, {70, 0.32}, {75, 0.43}, {80, 
0.49}, {85, 0.58},
 
 >    {90, 0.8}, {95, 0.91}, {100, 1.}, {105, 1}}

In[3]:= NonlinearRegress[data,
         Exp[(1 - Exp[a*(1 - Exp[-b*x])])*(Exp[-b*x])/(1 - Exp[-b*x])], 
{{a,
           5, 5.1}, {b, .1, .11}}, x]

Out[3]= {BestFitParameters -> {a -> 5.2052, b -> 0.0724853},
 
 >    ParameterCITable ->     Estimate    Asymptotic SE   
CI                    ,
                         a   5.2052      0.209949        {4.78478, 5.62561}

                         b   0.0724853   0.00290763      {0.0666629, 
0.0783077}
 
 >    EstimatedVariance -> 0.000964242,
 
 >    ANOVATable ->                     DF   SumOfSq     MeanSq     ,
                   Model               2    4.37984     2.18992

                   Error               57   0.0549618   0.000964242

                   Uncorrected Total   59   4.4348

                   Corrected Total     58   3.78327
 
 >    AsymptoticCorrelationMatrix -> 1.         0.985653,

                                    0.985653   1.
 
 >    FitCurvatureTable ->                           Curvature}
                          Max Intrinsic             0.105066

                          Max Parameter-Effects     0.130725

                          95. % Confidence Region   0.562647


If you are using a version prior to 6.0, instead load 
Statistics`NonlinearFit` and flip the parameter and variable arguments 
in NonlinearRegress.

Darren Glosemeyer
Wolfram Research


  • Prev by Date: Re: DSolve question
  • Next by Date: Re: DSolve question
  • Previous by thread: Asking NonlinearRegression
  • Next by thread: Re: Asking NonlinearRegression