I decided to write a short piece, based on the questions and reasoning I saw here. I mean no offense of course, but I think this is an important point: https://medium.com/@dgoldman0/bad-science-and-modeling-data-c2c13c305c8e

You can try to fit a polynomial equation OR you may try the neural network toolbox in MATLAB. There are also freely available functions to fit a kriging model.

Be sure you will not get perfect match. Out of the two fit you tried y= ax^b + c and y=ax^b , the second will be possible only when the curve passes or very near to the origin else c in first is nothing but the value at x=0. Fit in log(y-c) = log a + b log x .

From the attached figure, as y axis is tangent you may try y^b = ax or in log-log

b log y = log a + log x

Dear Ebrahim Sangsefidi ,

It seems that y = a√x is a good curve that fits your data,

where a is a constant to be determined.

We minimize f(a)=∑(a√xi-yi)² , the summation runs over

all values (xi, yi ). Solving df / da = 0,

we obtain a∑(√xi)- ∑yi = 0,

then a = ∑yi /∑(√xi)

consequently, the suggested curve is

y = (∑yi /∑(√xi))sqrt(x).

Best regards

So, you're going about this all wrong. While you can find an infinite number of different models which can fit a given data set, you should pick your model based on what makes sense. What kind of data are X and Y? What do they represent? Why should they even have a relationship?

Additionally, do you have any more data, beyond the data you've just analyzed to guess on a shape, in order to test the model?

It is possible to use the logarithmic function, because the data distribution takes the form of the logarithmic function. It is possible to use MATLAB to create a polynomial function

Hi Daniel Goldman

Thank you for your answer.

The Y data is the water absorption of my materials and X is the time. The literature has confirmed that there is a relationship between these two parameters.

I have 36 water absorption curves for my materials and I can send some of them through if it can help to solve the problem.

Kind regards,

Ebrahim

Dear Mercedes Orús-Lacort

I went through your suggested equation. I used curve fitting toolbox of MATLAB and the regression results was not quite significant.

Thank you for your time.

Cheers,

Well okay Ebrahim Sangsefidi, can you absorb as much as you want? Or would it make sense that the more you absorb, the harder it is to absorb more?

Dear Daniel Goldman

The latter case happens in reality for my materials. I mean after a while, which can be affected by the quality of materials, the potential absorption will fulfill. However, due to shortage of time I let the test run for only two days.

Cheers,

Okay, so Mercedes Orús-Lacort suggestion seems reasonable. Why? We can say that dY/dX = k(1-Y), right? The absorption rate is a function of how much is absorbed, in comparison to its total absorption capacity. If you solve the differential equation you get

Y = 1 - Ce^{kX}. That's probably the actual form that I'd fit the data to. And I'd imagine there's already discussion out there about absorption rates.

I decided to write a short piece, based on the questions and reasoning I saw here. I mean no offense of course, but I think this is an important point: https://medium.com/@dgoldman0/bad-science-and-modeling-data-c2c13c305c8e

I usually use a computer program called TableCurve 2D (there's also a 3D one). This program is very easy to use and analyzes the data by thousands of equations in a few minutes. You can also restrict the type of equation or the level of error allowed, sort them by correlation or by standard error, etc. It allows you to make smoothies, ....

I have an old version and I'm doing very well. Surely there are more modern versions. Try to get it. Good luck!

Dear Sangsefidi,

I agree with Dr. Felipe , you can use a computer program "TableCurve 2D"

Regards,

I'm tapping out of this discussion. Going on a hunt to find a model that happens to fit a given data set "the best" is bad science. It shows analysis without understanding of what's going on.

Obviously the use of a software such as Table Curve 2D or other, is only one way to start the analysis. It's not a "blind test". It's just to see the trend, the type of equation that best fits, the dispersion of the data, and so on. Then, with that preliminary information, is when we get closer to the problem and its solution. You can look for a model with similar equations and go deeper into the subject!

The best "science" is the one that allows us to solve a problem using all the tools that are in our hand.

Felipe, that's useful if you have some data, and want to try to figure out what's going on, before you gather more data. But if you've already performed your experiment, and then you start figuring out what your model might be, then you've done things completely backwards. Experiment must follow theory.

That's a Langmuir adsorption isotherm. Its time evolution is described by:

Gamma(t)=GammaMax-exp(-K*t)

being Gamma the already adsorbed sites & GammaMax the total adsorption sites. The constant K>0 is an equilibrium constant and can be obtained by fitting the slope of the plot ln(Y) vs X. Remove both ends for more accuracy: the process is not linear at these regions.

I've borrowed the notation from: http://alfisol.com/IFS/IFS-003/LMMpro-Langmuir.php

I withdraw from the discussion! I don't understand anything (it must be a language problem). I don't know what the problem is, I don't know what the doubt is and "I just know I don't know anything". Good luck.

Hello working on logistic data fitting i try with my new method to fit your data .

I will send you back pdf with deterministic caos function map , as possible interpolation. I can reduce the error using my new method wich is under optimization. Regards. Y is normalized to its maximum value.

Giuseppe, what makes you think that a logistic model is a proper fit for the data?

When the trend of the function is monotonic and limited between a minimum and a maximum value you can normalize between 0 and 1 and try t interpolate with generatic functions of logistic type . For example f(p* inverse(f)|computed in x0 )

If p is >1 you have forward continuous map if p

I can't believe it... Could you all stop trying to fit an adsorption process with a polynomial function or 1-sin(exp(ax^6+...))^2 please?

Escuse me i didnt't understand exatly your answer . I made a data fitting throught a generating function of a map . The parameters are recovered by a procedure that is in progress but not in electronic word format. If of interest i can send some Excel sheets with a lot of other function test . Regards.

I agree with you that there are infinite models for the some number of data. Infact i made some important analysis of train motion where the data come from bodies that follows the newton laws . These data can also come from other differential equation of the first order but the simultaneous matching of data and its first and second derivative semmes to much difficukt. And what happen when you want an intermediate value. If the data are monotonic and normalized i find that logistic maps can help and give results in good agreements up to higher order derivative . I am not a matematics i am an application engineering . Regards

Giuseppe Figlia, the full discussion that I give in the linked article that I provided before might help explain my concern better. The point is that knowing the type of data we have, I was able to develop a proposed model for that data, which fit the actual data, before even needing to look at it. Just searching for a model that seems to fit well is not the way to do things. R-squared is not a very good measure of whether a model has been properly chosen. We must always think about what the data represents.

Only if we have no idea what kind of relationship we should expect between two variables should we go off searching in the way that has been suggested above. A number of models also make no sense. For instance, sqrt(x) is unbounded. Absorption is clearly bounded. That should have been a clue right there to exclude sqrt(x) from the options.

Brother use Minitab software

Dear Ebrahim

You can use a software called curve expert 1.4. There are a number of models & equations in this software those can be used to fit your data. This is a free download. Hope this is helpful.

I think this is a good fit to your data.

y=(a*b+c*x^d)/(b+x^d) Coefficient Data: a = 7.75E-05 b = 2.50E-01 c = 1.44E-02 d = 6.15E-01

This is still going? Once again, you have to think about what you're modeling. You can't just look for the best fit model.

Dear all, as a rule of thumb, etiquette and respect for the limited time/availability of the RG community members, I kindly suggest please do read the previous messages before posting your own!

Have a nice day (and readings),

Kinde regards Luis