Curve fitting / Nonlinear regression

After inspecting the data given in the files you just downloaded with grace and gnuplot we return to grace for the next task of fitting a function to the data provided.

Open the menu entry Data/Transformations/Non-linear curve fitting. Select your dataset in the left half of the window (Source). Enter a polynome of the variable $x$ with parameters $A_0, \dotsc, A_N$ in the Formula field of the Main tab. Type in a non-linear function (formula) like this:

y = A0 + A1 * cos(A2 * x)

Then select the number of variables you've introduced in the drop-down menue and provide good estimates for these variables if possible.

You can use as many parameters as you want and make the functions as complicated as possible. Mathematical operators you may use inside you non-linear polynome are:

+: addition,       e.g.: (a + b)
*: multiplication, e.g.: (a*b)
^: power of,       e.g.: (x^2)

It is also possible to use trigonometric functions like sin(), cos(), the logarithm log() or the exponential exp()

Be aware of the fact that you should first have a look at the data curve itself to get a good guess of the underlying function. If you can't find any function that fits your data or if the data does look too strange try other ways to find out properties of the underlying data. Grace provides you with tools for analyzing the distribution of the values (you can make histograms, Fourier transformations, etc.). You can find the appropriate menu entries under Data/Transformations. After examining certain properties of the distribution of your data you might be able to get an idea of the underlying function that produced the data