From $ROOTSYS/tutorials/fit/fitLinear2.C

#include "TLinearFitter.h"
#include "TF1.h"
#include "TRandom.h"

void fitLinear2()
{
   //Fit a 5d hyperplane by n points, using the linear fitter directly

   //This macro shows some features of the TLinearFitter class
   //A 5-d hyperplane is fit, a constant term is assumed in the hyperplane
   //equation (y = a0 + a1*x0 + a2*x1 + a3*x2 + a4*x3 + a5*x4)
   //Author: Anna Kreshuk

   Int_t n=100;
   Int_t i;
   TRandom rand;
   TLinearFitter *lf=new TLinearFitter(5);

   //The predefined "hypN" functions are the fastest to fit
   lf->SetFormula("hyp5");

   Double_t *x=new Double_t[n*10*5];
   Double_t *y=new Double_t[n*10];
   Double_t *e=new Double_t[n*10];

   //Create the points and put them into the fitter
   for (i=0; i<n; i++){
      x[0 + i*5] = rand.Uniform(-10, 10);
      x[1 + i*5] = rand.Uniform(-10, 10);
      x[2 + i*5] = rand.Uniform(-10, 10);
      x[3 + i*5] = rand.Uniform(-10, 10);
      x[4 + i*5] = rand.Uniform(-10, 10);
      e[i] = 0.01;
      y[i] = 4*x[0+i*5] + x[1+i*5] + 2*x[2+i*5] + 3*x[3+i*5] + 0.2*x[4+i*5]  + rand.Gaus()*e[i];
   }

   //To avoid copying the data into the fitter, the following function can be used:
   lf->AssignData(n, 5, x, y, e);
   //A different way to put the points into the fitter would be to use
   //the AddPoint function for each point. This way the points are copied and stored
   //inside the fitter

   //Perform the fitting and look at the results
   lf->Eval();
   TVectorD params;
   TVectorD errors;
   lf->GetParameters(params);
   lf->GetErrors(errors);
   for (Int_t i=0; i<6; i++)
      printf("par[%d]=%f+-%f\n", i, params(i), errors(i));
   Double_t chisquare=lf->GetChisquare();
   printf("chisquare=%f\n", chisquare);


   //Now suppose you want to add some more points and see if the parameters will change
   for (i=n; i<n*2; i++) {
      x[0+i*5] = rand.Uniform(-10, 10);
      x[1+i*5] = rand.Uniform(-10, 10);
      x[2+i*5] = rand.Uniform(-10, 10);
      x[3+i*5] = rand.Uniform(-10, 10);
      x[4+i*5] = rand.Uniform(-10, 10);
      e[i] = 0.01;
      y[i] = 4*x[0+i*5] + x[1+i*5] + 2*x[2+i*5] + 3*x[3+i*5] + 0.2*x[4+i*5]  + rand.Gaus()*e[i];
   }

   //Assign the data the same way as before
   lf->AssignData(n*2, 5, x, y, e);
   lf->Eval();
   lf->GetParameters(params);
   lf->GetErrors(errors);
   printf("\nMore Points:\n");
   for (Int_t i=0; i<6; i++)
      printf("par[%d]=%f+-%f\n", i, params(i), errors(i));
   chisquare=lf->GetChisquare();
   printf("chisquare=%.15f\n", chisquare);


   //Suppose, you are not satisfied with the result and want to try a different formula
   //Without a constant:
   //Since the AssignData() function was used, you don't have to add all points to the fitter again
   lf->SetFormula("x0++x1++x2++x3++x4");

   lf->Eval();
   lf->GetParameters(params);
   lf->GetErrors(errors);
   printf("\nWithout Constant\n");
   for (Int_t i=0; i<5; i++)
     printf("par[%d]=%f+-%f\n", i, params(i), errors(i));
   chisquare=lf->GetChisquare();
   printf("chisquare=%f\n", chisquare);

   //Now suppose that you want to fix the value of one of the parameters
   //Let's fix the first parameter at 4:
   lf->SetFormula("hyp5");
   lf->FixParameter(1, 4);
   lf->Eval();
   lf->GetParameters(params);
   lf->GetErrors(errors);
   printf("\nFixed Constant:\n");
   for (i=0; i<6; i++)
      printf("par[%d]=%f+-%f\n", i, params(i), errors(i));
   chisquare=lf->GetChisquare();
   printf("chisquare=%.15f\n", chisquare);

   //The fixed parameters can then be released by the ReleaseParameter method
   delete lf;

}

 fitLinear2.C:1
 fitLinear2.C:2
 fitLinear2.C:3
 fitLinear2.C:4
 fitLinear2.C:5
 fitLinear2.C:6
 fitLinear2.C:7
 fitLinear2.C:8
 fitLinear2.C:9
 fitLinear2.C:10
 fitLinear2.C:11
 fitLinear2.C:12
 fitLinear2.C:13
 fitLinear2.C:14
 fitLinear2.C:15
 fitLinear2.C:16
 fitLinear2.C:17
 fitLinear2.C:18
 fitLinear2.C:19
 fitLinear2.C:20
 fitLinear2.C:21
 fitLinear2.C:22
 fitLinear2.C:23
 fitLinear2.C:24
 fitLinear2.C:25
 fitLinear2.C:26
 fitLinear2.C:27
 fitLinear2.C:28
 fitLinear2.C:29
 fitLinear2.C:30
 fitLinear2.C:31
 fitLinear2.C:32
 fitLinear2.C:33
 fitLinear2.C:34
 fitLinear2.C:35
 fitLinear2.C:36
 fitLinear2.C:37
 fitLinear2.C:38
 fitLinear2.C:39
 fitLinear2.C:40
 fitLinear2.C:41
 fitLinear2.C:42
 fitLinear2.C:43
 fitLinear2.C:44
 fitLinear2.C:45
 fitLinear2.C:46
 fitLinear2.C:47
 fitLinear2.C:48
 fitLinear2.C:49
 fitLinear2.C:50
 fitLinear2.C:51
 fitLinear2.C:52
 fitLinear2.C:53
 fitLinear2.C:54
 fitLinear2.C:55
 fitLinear2.C:56
 fitLinear2.C:57
 fitLinear2.C:58
 fitLinear2.C:59
 fitLinear2.C:60
 fitLinear2.C:61
 fitLinear2.C:62
 fitLinear2.C:63
 fitLinear2.C:64
 fitLinear2.C:65
 fitLinear2.C:66
 fitLinear2.C:67
 fitLinear2.C:68
 fitLinear2.C:69
 fitLinear2.C:70
 fitLinear2.C:71
 fitLinear2.C:72
 fitLinear2.C:73
 fitLinear2.C:74
 fitLinear2.C:75
 fitLinear2.C:76
 fitLinear2.C:77
 fitLinear2.C:78
 fitLinear2.C:79
 fitLinear2.C:80
 fitLinear2.C:81
 fitLinear2.C:82
 fitLinear2.C:83
 fitLinear2.C:84
 fitLinear2.C:85
 fitLinear2.C:86
 fitLinear2.C:87
 fitLinear2.C:88
 fitLinear2.C:89
 fitLinear2.C:90
 fitLinear2.C:91
 fitLinear2.C:92
 fitLinear2.C:93
 fitLinear2.C:94
 fitLinear2.C:95
 fitLinear2.C:96
 fitLinear2.C:97
 fitLinear2.C:98
 fitLinear2.C:99
 fitLinear2.C:100
 fitLinear2.C:101
 fitLinear2.C:102
 fitLinear2.C:103
 fitLinear2.C:104
 fitLinear2.C:105
 fitLinear2.C:106
 fitLinear2.C:107
 fitLinear2.C:108
 fitLinear2.C:109
 fitLinear2.C:110