Attaching independent variable values to data for curve fitting

I have a data set of $$10^4$$ entries. I want to plot the last $$2000$$ data with the same argument at $$x$$ axis and fit a curve. That means the range of $$x$$ axis will be $$8001$$ to $$10000$$ incremented by $$1$$.

I wrote code like the following to know the coefficient of fitting curve:

d = Import["ss.dat"];
T = Table[d[[1, i]], {i, 8001, 10000}];
FindFit[T, a*E^(-b*x), {a, b}, x]

FindFit returns the values of $$a$$ and $$b$$ considering $$x$$ to range from $$1$$ to $$2000$$ instead of $$8001$$ to $$10000$$.

If anyone can tell me how to deal with this problem that will be great help.

I am attaching data in the following link:

data as DAT file in Google Drive

• You could try T = Table[{i, d[[1, i]]}, {i, 8001, 10000}];. This will allow you to give FindFit 2D data with the specific x values you want. – MassDefect Mar 18 at 16:11
• Your first problem has been pointed out by @MassDefect. But you should linearize your model with the following: lmf = LinearModelFit[Transpose[{T[[All, 1]], Log[T[[All, 2]]]}], x, x] Show[LogPlot[Exp[lmf[x]], {x, 8001, 10000}, PlotStyle -> {LightGray, Thickness[0.03]}], ListLogPlot[T, PlotStyle -> Red]]. – JimB Mar 18 at 16:33

Generally, you don't need nearly so many points to get a nice fit. Regardless, we can use NonlinearModelFit[] to get what you want:

You can use Drop[list,n] to drop the first n elements of a list.

dir = NotebookDirectory[];
SetDirectory[dir];
file = "ss.dat";

d = Import[file];
T = Drop[Flatten[d], 8000];
St = Drop[Take[T, {1, -1, 1}], 0];
Stt = Table[{i, T[[i]]}, {i, 1, Length[St]}];
e = NonlinearModelFit[Stt, a*E^(-b*x), {a, b}, x]
e["BestFitParameters"]

GraphicsGrid[{{ListPlot[Stt, ImageSize -> Medium, PlotRange -> All, PlotTheme -> "Scientific"], Plot[{Evaluate[a*E^(-b*x) /. e["BestFitParameters"]]}, {x, 0,Length[Stt]}, PlotTheme -> "Scientific", Epilog -> {Red, Point[Stt]}]}}] Using the code will drop every x elements from your entire list, drastically reducing your plot points. 2000, or even 10000 are just not needed.

St = Drop[Take[T, {1, -1, 1}], 0];

and changing to:

St = Drop[Take[T, {1, -1, 40}], 0];

Gives us: A nice visual that the points lay directly on our function, and a good fit for a and b.