MulLinFit Routine

Summary

Fits multiple linear equations to data.

Declaration

Procedure MulLinFit(B: TVec; X: TMtx; Y: TVec; Constant: boolean = false; Weights: TVec = nil);

Parameter	Description
X	Vector of independent variable.
Y	Vector of dependent variable.
Weights	Weights (optional). Weights are used only if they are set.
B	Returns regression coefficients for multiple linear function.

Description

The routine fits equations to data by minimizing the sum of squared residuals. The observed values obey the following equation:

where X is matrix, Y, B are vectors.

See Also
MulLinEval

Example 1

In the following example we generate some data. Then we fit multiple linear function to this data and retreive it's regression coefficients.

  Uses MathExpr, RegModels;
  procedure Example);
  var Y,B: Vector;
    X: Matrix;
  begin
    X.SetIt(3,2,false,[1.0, 2.0,
                      -3.2, 2.5,
                      8.0, -0.5]);
    Y.SetIt(false, [-3.0, 0.25, 8.0]);
    MulLinFit(B,X,Y,true);
    // B = (18.646428571, -1.9464285714, -9.85 )
  end;

  #include "MtxVecCpp.h"
  #include "Math387.hpp"
  #include "RegModels.hpp"
  #include "MtxVecTee.hpp"
  void __fastcall Example();
  {
    Matrix X;
    Vector Y,B;
    X->SetIt(3,2,false,OPENARRAY(TSample,(1.0, 2.0,
                      -3.2, 2.5,
                      8.0, -0.5)));
    Y->SetIt(3,false, OPENARRAY(TSample,(-3.0, 0.25, 9.0)));
    MulLineFit(B,X,Y,true,NULL);
    // B = (18.646428571, -1.9464285714, -9.85 )
  }

  using Dew.Math;
  using Dew.Stats.Units;
  namespace Dew.Examples
  {
    private void Example()
    {
      Matrix X = new Matrix(0,0);
      Vector Y = new Vector(0);
      Vector B = new Vector(0);
      X.SetIt(3,2,false,new double[]{1.0, 2.0,
                      -3.2, 2.5,
                      8.0, -0.5});
      Y.SetIt(3,false,new double[] {-3.0, 0.25, 9.0});
      RegModels.MulLineFit(B,X,Y,true,null);
      // B = (18.646428571, -1.9464285714, -9.85 )
    }
  }