TGraph Fit

ROOT
1

Hi,
I think I need to open a new thread about TGraph Fit.

I have a very simple example:

test_fit_err() {

  gROOT->SetStyle("Plain");
  gStyle->SetOptFit(11111);
  
  double x[5] = {1, 2, 3, 4, 5};
  double y[5] = {1.3, 1.4, 1.2, 1.25, 1.35};

  TGraph * g = new TGraph(5, x, y);

  g->SetMarkerStyle(20);
  g->SetMarkerColor(2);
  g->Draw("ap");

  TF1 * f = new TF1("func", "[0]", 0, 6);
  f->SetLineStyle(2);
  f->SetLineColor(8);
  g->Fit(f);

  TGraphErrors * ge = new TGraphErrors(5);
  (TVirtualFitter::GetFitter())->GetConfidenceIntervals(ge, 0.99);
  ge->SetFillColor(17);
  ge->Draw("e3");
  g->Draw("psame");
  
}

The fit returns:
chi2/ndf: 0.025/4
Prob: 0.9999
p0: 1.3 ±0.002795

This result confused me so much. As you know, using a straight level line to fit data points is not proper, the result should give a larger error on p0. However, this error is very small. As Rene pointed out, a correction

errorp *= sqrt(chisquare/(ndf-1))

is applied when TGraph points don’t have errors. I don’t know why and whether or not the correction is proper to this case. In the meantime, I tried QtiPlot to do the similar fitting, the result gives me:

Chi^2/doF = 6.25e-03
R^2 = -3.469446951953614e-17
p0: 1.3±0.035

The difference is the error of p0. I think the error from QtiPlot makes sense for me. Please give me some hints. Because ROOT is designed for the more complicated problems?

Cheers,
Zhiyi.

2

when running your script with 5.22 I get the following result.

Rene

c1.gif696×472 5.86 KB

3

Unfortunately, I cannot re-produce your fitting results with the same root version. Here is the summary table that have been done. I don’t know why.

===========================================================
RootVersion                 OS                       p0err 
-----------------------------------------------------------
v5.22(binary)   linux 2.6.24-23-generic(Ubuntu)     0.00279
v5.22(compiled) linux 2.6.24-23-generic(Ubuntu)     0.00279
v5.22(compiled) Linux-2-4 GCC_3_4_3 (D0 release)    0.00279
v5.20(compiled) linux 2.6.24-23-generic(Ubuntu)     0.04082
v5.18(compiled) Linux-2-4 gcc343-opt (D0 release)   0.04082
v5.22           Test from Rene                      0.03536
------------------------------------------------------------
QtiPlot         Ubuntu                              0.035
4

Hi,

there was a bug in 5.22 in the scaling of the errors.
This is fixed in the trunk or in the patch version 5.22a, by scaling
with sqrt( chi2/ ndf), and the result is 0.035 (the same obtained with this other package).

Best Regards

Lorenzo