MulLinRegress Routines

Summary

Multivariante linear regression.

Declaration

Procedure MulLinRegress(y: TVec; A: TMtx; b: TVec; Constant: boolean = true; YCalc: TVec = nil; ATA: TMtx = nil; Method: TRegSolveMethod = regSolveLQR);

Declaration

Procedure MulLinRegress(y: TVec; A: TMtx; b: TVec; Weights: TVec; Constant: boolean = true; YCalc: TVec = nil; ATA: TMtx = nil; Method: TRegSolveMethod = regSolveLQR);

Parameter	Description
Y	Defines vector of dependant variable.
X	Defines matrix of independant variables.
b	Returns calculated regression coefficiens.
Weights	Defines weights (optional).
Constant	If true then include intercept term b(0) in calculations. If false, set intercept term b(0) to 0.0.
YCalc	Returns vector of calculated dependant variable, where YCalc = A*b.
ATA	Returns inverse matrix of normal equations i.e [A(T)*A]^-1.

Description

Multivariante linear regression. Routine fits equations to data by minimizing the sum of squared residuals:

SS = Sum [y(k) - ycalc(k)]^2 ,

where y(k) and ycalc(k) are respectively the observed and calculated value of the dependent variable for observation k. ycalc(k) is a function of the regression parameters b(0), b(1) ... Here the observed values obey the following equation:

y(k) = b(0) + b(1) * x(1,k) + b(2) * x(2,k) + ...

i.e

y = A * b.

To calculate additional regression statistical values, use RegressTest routine.

See Also
RegressTest
LinRegress
NLinRegress

Example 1

The following example performs multiple linear regression.

  Uses Regress, MtxExpr;
  procedure Example;
  var y,b,w,yhat: Vector;
    A, ATA : Matrix;
    RegStat : TRegStats;
  begin
    A.SetIt(4,2,false,[1.0, 2.0,
                      -3.2, 2.5,
                       8.0,	-0.5,
                       -2.2, 1.8]); // independent variables
    w.SetIt(false,[1,2,2,1]); // weights
    y.SetIt(false,[-3.0, 0.25, 8.0, 5.5]); // dependent variables
    MulLinRegress(y,A,b,w,true,yhat,ATA); //do regression
    // b=(19.093757944, -2.0141843616, -10.082487055)
    RegressTest(y,yhat,V,RegStat,w); // do basic regression stats
    // RegStat = (ResidualVar:0.037230395108; R2:0.99965713428;
    // AdjustedR2:0.99897140285; F:1457.7968725; SignifProb: 0.01851663347)
  end;

  #include "MtxVecCpp.h"
  #include "Regress.hpp"
  void _fastcall Example()
  {
    Matrix A,ATA:
    Vector y,b,w,yhat;
    TRegStats rs;
    // independent variables
    A->SetIt(4,2,false,OPENARRAY(TSample,(1.0, 2.0,
                      -3.2, 2.5,
                       8.0,	-0.5,
                       -2.2, 1.8)));
    w->SetIt(false,OPENARRAY(TSample,(1,2,2,1))); // weights
    y->SetIt(false,OPENARRAY(TSample,(-3.0, 0.25, 8.0, 5.5))); // dependent variables
    MulLinRegress(y,A,b,w,true,yhat,ATA); //do regression
    // b=(19.093757944, -2.0141843616, -10.082487055)
    RegressTest(y,yhat,ATA,RegStat,w); // do basic regression stats
    // RegStat = (ResidualVar:0.037230395108; R2:0.99965713428;
    // AdjustedR2:0.99897140285; F:1457.7968725; SignifProb: 0.01851663347)
  }

  using Dew.Math;
  using Dew.Stats.Units;
  using Dew.Stats;
  namespace Dew.Examples
  {
    private void Example()
    {
      Matrix A = new Matrix(0,0);
      Matrix ATA = new Matrix(0,0);
      Vector y = new Vector(0);
      Vector b = new Vector(0);
      Vector w = new Vector(0);
      Vector b = new Vector(0);
      // independent variables
      A.SetIt(4,2,false, new double[] {1.0, 2.0,
                      -3.2, 2.5,
                       8.0,	-0.5,
                       -2.2, 1.8});
      w.SetIt(false, new double[] {1,2,2,1}); // weights
      y.SetIt(false, new double[] {-3.0, 0.25, 8.0, 5.5}); // dependent variables
      TRegStats rs = MulLinRegress(y,A,b,w,true,yhat,ATA); //do regression
      // b=(19.093757944, -2.0141843616, -10.082487055)
      RegressTest(y,yhat,ATA,RegStat,w); // do basic regression stats
      // RegStat = (ResidualVar:0.037230395108; R2:0.99965713428;
      // AdjustedR2:0.99897140285; F:1457.7968725; SignifProb: 0.01851663347)
    }
  }