Chisquare fit to multiple data sets

[CAF123]

I am looking to perform a $\chi^2$ fit to more than one data set in mathematica, I just wondered how one would set this up?

Given some non-linear ansatz function $F$ depending on some parameters $a,b,c$ to describe all sets of data, i.e $F = F_z(x,a,b,c)$ I want to do a $\chi^2$ fit that will take all sets of data into account to get the best fit values of the parameters. So I just wondered how to do this in mathematica?

In the plot attached, the x argument above corresponds to the x-axis and F is the predicted value along the y axis. The upper most band of data corresponds to some value of z and the lower band of data corresponds to another value of z. a,b,c are my parameters that I would like the best estimate for. So essentially I'm looking for some simultaneous non-linear minimisation routine.

I am fairly new to mathematica so still getting to grips with it so apologies if my question is too simple from the outset.

Thanks!

 

[NateD]

The best way to go about this task is to use Mathematica's NonlinearModelFit function. This function allows you to fit nonlinear models to data sets. You can specify the model as a function of your parameters, then pass in your data sets as an argument. The function will then return the best fit values for each of your parameters, along with some additional useful information like the chi-squared value and the covariance matrix.Here is an example of how to use this function:model[x_,a_,b_,c_] := F[x,a,b,c]; data1 = {{x1,y1},{x2,y2},...};data2 = {{x3,y3},{x4,y4},...};fit = NonlinearModelFit[Join[data1,data2],model[x,a,b,c],{a,b,c},x];fit["BestFitParameters"]This should give you the best fit values for your parameters, as well as other useful information.