# Plotting confidence bands from data fitted using Levenberg–Marquardt algorithm.

Good Morning!

I have some experimental data which are fitted using different equations.
For example y=a[1-exp(-x+c)/b] +gx
The program uses the Levenberg–Marquardt algorithm and the results are given as
a ± std error
b ± std error
c ± std error
g ± std error
I can plot from the best fitted line but do not know how I could plot the confidence band.
From this fitted equation, I can then interpolate but need to estimate the error of the interpolation on the confidence band.
The confidence band will vary for the same fitted curve on the choice of data point and x values, and position of those x values with respect to the interpolating value. I would like therefore to be able to plot that confidence band with the fitted curve.
I have no idea whatsoever how to proceed from the results, nor that the confidence band is what I need.
I would greatly appreciate any help!
I am joining a file with some data and results.
pseudo-data-to-be-fitted.xlsx
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Commented:
Would the confidence ban be the Sum(Abs(std errors))  down to -Sum(Abs(std errors)) ?
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Research associateAuthor Commented:
Thank you!

Thank you for referring  me the minpack R package. I am a novice at R ( but great fan of it!) and  will give it a go!
this will definitely be of great help as i have at present no idea how to evaluate how good is the fit.

I saw that the minpack is a modification of the Levenberg-Marquardt algorithm, rather than the actual Levenberg-Marquardt algorithm? I will try and figure out what are those modifications though if the fit is good, that should not really be an issue.

I was not very clear as to what I was expecting, and your reply fitted my written question but not what I had been wanting to know, but did not write down clearly!

I was hoping that using that algorithm or any other fitting algorithm for that matter (Simplex etc.), I could then use the fitting equation and the factors with their std errors and calculate an Upper and Lower limits.
I was hoping  they could somehow be obtained with a simple package like say excel? I was hoping you could give me more insight on how the calculations for the U and L bounds were actually obtained from the fitting equation and the parameters and their errors or whether indeed you need to evaluate those separately?
Rereading my question, there was no way you could have guessed that is what i had hoped for.

I will post these extra questions separately, but am truly grateful for your help as it will be used, and is a major improvement tool for my data analysis!

Many thanks!

Danièle
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Research associateAuthor Commented:
Thanks!
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Commented:
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Research associateAuthor Commented:
Hi gheist,

Thanks for the course tip!

Danièle
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