// y=b0*x*x + b1*x + b2 i.e. parabola
procedure SimpleParabola(const B: TVec; const X: TVecList; const Y: TVec): double;
begin
    //        SimpleParabola := b[0]*Sqr(x) + b[1]*x + b[2];

    y.Sqr(x[0]);
    y.Scale(b[0));
    y.AddScaled(x[0], b[1]);
    y.Add(b[2]);
end;
// procedure for derivatives
procedure SimplePabolaDeriv(const RegressFun: TRegressFun; const X: TVecList const Y: TVec; const Pars: TVec; const Grad: TVecList);
begin
  Grad[0].Sqr(x[0]);        //  Grad[0] := Sqr(x);
  Grad[1].Copy(x[0]);       //  Grad[1] := x;

  Grad[2].Size(x[0]);       //  Grad[2] := 1;
  Grad[2].SetVal(1);
end;
begin
  // ...
  MtxNonLinReg1.RegressFunction := SimpleParabola;
  MtxNonLinReg1.DeriveProcedure := SimpleParabolaDeriv;
end;