There are many statistical software can use to find the nonlinear correlation for any data. I was use the minitap and spss but the equation form still not wide as I want.
Matlab is also a good choice but R is very powerfull
I use R to run my statistical analyses--it's free for download (http://www.r-project.org/) and easy to use, especially if you use the RStudio GUI (http://www.rstudio.com/).
There are many packages that have been written and are up for free download, one of which will probably do what you are looking to do. If one does not exist, you can write your own code (it's similar to Matlab). There are also tons of free tutorials available to help.
R is the better choice for me but also SPSS, Splus or even excell (for some simple cases)
I think MatLab is better option because all other packages(Minitab, SPSS, DesignExpert, Sigma Plot, etc.) have their own limitation and are shorter than MatLab. MatLab has many more option for linear, non-linear, multi-linear analysis and it provides all result related to statistics.
Are you checking the correlation between experimental data and a fitting model?
In case you have two series of data, the original points and the ones of the fitting equation, you may simply calculate the Pearson coeficient with Excel, i. e. use the two columns of Ymeasured and Ycalculated in the Pearson coeficient function. Even, if Y=F(X) is not linear, Ycalc = F(Ymeas) is intrinsically linear and the Pearson Coeficient may be applied.
Excel is also a good possibility to find fitting equations. Besides using the available trendline equations, you may mount a least square method with any type of equation using the Solver Add-in
Excel is useful for doing simple correlations, but it doesn't give all the information you need (i.e. p-values). If you know the math behind the statistics, you can easily write a code in Matlab (I'm unsure if there are any built in functions for running the statistics you are looking to do.
I know Minitab, SPSS, and R will give you the necessary information and help you find a correlation when y is f(x,z), but outside of free trials you will have to pay for Minitab and SPSS. This tutorial isn't exactly what you're looking for (http://www.youtube.com/watch?v=62EY_9TtbUM) but it gives the basics about R, and teaches you how to do basic linear correlations. I'm sure with a little investigating you could find a tutorial more specific to your needs on youtube.
An excellent software is StatGraphics where regression model adjusted and determines among other factors the correlation model obtained.
The most popular software used by biologists seems to be PRISM (GraphPad Software). It enables to calculate all common statistical indicators (and many more). However, I use MATLAB so that I can perform all my numerical treatments (filters, modelling, fitting...) and check the statistical relevance with the same software. See for instance : http://www.sciencedirect.com/science/article/pii/S1751616113002993
You can use powerfull functions as "corr" and "matrixplot" or program yourself the tools you need ! If you need more functions, a special toolbox is also available.
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