RegressTest Routines

Summary

Regression tests.

Declaration

Procedure RegressTest(Y, YCalc: TVec; NumPars: Integer; out RegStat: TRegStats; Constant: boolean = True; Weights: TVec = nil);

Parameter	Description
Y	Dependant variables.
YCalc	Estimated (calculated) dependant variables.
Weights	Model weights (optional).
MumPars	Number of variables (parameters) in ML model A*b=y (number of columns in A matrix or number of rows in b).
Constant	If true then include intercept term b(0) in calculations. If false, set intercept term b(0) to 0.0.
RegStat	Returns regression statistics parameters.

Description

Use regression results to calculate basic regression statistics for model:

  A*b=Y

Declaration

Procedure RegressTest(Y, YCalc: TVec; ATA: TMtx; out RegStat: TRegStats; Residuals: TVec; BStdDev: TVec; Constant: boolean = True; Weights: TVec = nil);

Parameter	Description
Y	Dependant variables.
YCalc	Estimated (calculated) dependant variables.
ATA	Inverse matrix of normal equations i.e [A(T)*A]^-1.
Weights	Model weights (optional).
Constant	If true then include intercept term b(0) in calculations. If false, set intercept term b(0) to 0.0.
RegStat	Returns regression statistics parameters.

Description

Using regression results the routine calculates additional regression statistical parameters, together with model coefficients standard errors and model errors.

Example 1

Perform MLR and use results to calculate additional statistical parameters.

  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,res,bse;
    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,res,bse,true,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);
      Vector res = new Vector(0);
      Vector bse = 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,out RegStat,res,bse,true,w); // do basic regression stats
      // RegStat = (ResidualVar:0.037230395108; R2:0.99965713428;
      // AdjustedR2:0.99897140285; F:1457.7968725; SignifProb: 0.01851663347)
    }
  }