## From \$ROOTSYS/tutorials/fit/fitLinearRobust.C

```#include "TRandom.h"
#include "TGraphErrors.h"
#include "TF1.h"
#include "TCanvas.h"
#include "TLegend.h"

void fitLinearRobust()
{
//This tutorial shows how the least trimmed squares regression,
//included in the TLinearFitter class, can be used for fitting
//in cases when the data contains outliers.
//Here the fitting is done via the TGraph::Fit function with option "rob":
//If you want to use the linear fitter directly for computing
//the robust fitting coefficients, just use the TLinearFitter::EvalRobust
//Author: Anna Kreshuk

//First generate a dataset, where 20% of points are spoiled by large
//errors
Int_t npoints = 250;
Int_t fraction = Int_t(0.8*npoints);
Double_t *x = new Double_t[npoints];
Double_t *y = new Double_t[npoints];
Double_t *e = new Double_t[npoints];
TRandom r;
Int_t i;
for (i=0; i<fraction; i++){
//the good part of the sample
x[i]=r.Uniform(-2, 2);
e[i]=1;
y[i]=1 + 2*x[i] + 3*x[i]*x[i] + 4*x[i]*x[i]*x[i] + e[i]*r.Gaus();
}
for (i=fraction; i<npoints; i++){
//the bad part of the sample
x[i]=r.Uniform(-1, 1);
e[i]=1;
y[i] = 1 + 2*x[i] + 3*x[i]*x[i] + 4*x[i]*x[i]*x[i] + r.Landau(10, 5);
}

TGraphErrors *grr = new TGraphErrors(npoints, x, y, 0, e);
grr->SetMinimum(-30);
grr->SetMaximum(80);
TF1 *ffit1 = new TF1("ffit1", "pol3", -5, 5);
TF1 *ffit2 = new TF1("ffit2", "pol3", -5, 5);
ffit1->SetLineColor(kBlue);
ffit2->SetLineColor(kRed);
TCanvas *myc = new TCanvas("myc", "Linear and robust linear fitting");
myc->SetFillColor(42);
myc->SetGrid();
grr->Draw("ap");
//first, let's try to see the result sof ordinary least-squares fit:
printf("Ordinary least squares:\n");
grr->Fit(ffit1);
//the fitted function doesn't really follow the pattern of the data
//and the coefficients are far from the real ones

printf("Resistant Least trimmed squares fit:\n");
//Now let's try the resistant regression
//The option "rob=0.75" means that we want to use robust fitting and
//we know that at least 75% of data is good points (at least 50% of points
//should be good to use this algorithm). If you don't specify any number
//and just use "rob" for the option, default value of (npoints+nparameters+1)/2
//will be taken
grr->Fit(ffit2, "+rob=0.75");
//
TLegend *leg = new TLegend(0.6, 0.8, 0.89, 0.89);
leg->SetFillColor(42);
leg->Draw();

delete [] x;
delete [] y;
delete [] e;

}
```
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