Hi!

Congratulations for this forum, is great!

I post this in basic area because i think it's basic for you, however it isnīt for me. I'm doing a project on chemistry and i need some help on analysis of data, if possible. I think i can get more help from a mathematician then a chemist. I'm studying a property (CMC, critical micellar concentration) of a solution, and to treat data i trace a plot of concentration (m) Vs specific conductivity (k), like this:

Then with a linear fit i get two straight lines, and the intersection is the CMC:

The problem begins when the variation is very smooth, like this:

Now, i've found this paper where they did a "complicated" - at least for me - data treatment and get a derivate-like result:

On page 138, in Results and Discussion, they said:

The problem of estimating the derivatives of the regression curve has beenvresolved by implementing the local polynomial regression estimator in the programming language Matlab, using the quartic kernel and plug-in optimal AMSE bandwidth. The calculation of hopt(x0) was achieved by estimating σε2 using a local polynomial regression, with a pilot bandwidth; the Parzen-Rosenblatt kernel estimator for f(x0) was also obtained by using a pilot bandwidth, and a parametric regression and a local polynomial regression were used for m(p+1)(x0). To avoid the problem of choosing an initial value h0, an iterative ap- proach was taken starting with a large h0. This initial pilot bandwidth produces another bandwidth, and this last one produces another, and so on. The iteration is continued to convergence.

paper:

This is chinese for me. I've never work in mathlab,so..it's sound very difficult to me to replicate this method, i just know the basics of math to work. But i would like give it a try. I've done the first and the second dervivative (dk/dm) ant it didn't worked. Its difficult to work with mathlab and this plugin? Is doable to a non-expert? Do you have any sugestion of a method to do the analysis of my data?

Thank you!

PS - Sorry my bad english!