LinRegress Routine

Summary

Simple linear regression.

Declaration

Procedure LinRegress(X, Y: TVec; b: TVec; Weights: TVec = nil; YCalc: TVec = nil; ATA: TMtx = nil);

Description

The 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) and b(1). Here the observed values obey the following equation:

y(k) = b(0) + b(1) * x

i.e

Y = b(0) + b(1)*X.

To calculate additional regression statistical values, use RegressTest routine.

See Also
MulLinRegress
RegressTest

Example 1

The following example loads data for simple linear regression (line equation) and then extracts line parameters b(0)=n and b(1)=k:

  Uses MtxExpr, MtxVecTee, Regress;
  procedure Example;
    var x,y,b,yhat: Vector;
  begin
    x.SetIt(false,[1.0, 1.5, 2.3, 3.8, 4.2, 5.0, 5.3, 5.9]);
    y.SetIt(false,[11, 12, 12.5, 14, 14.3, 15.2, 15.3, 17]);
    LinRegress(x,y,b,nil,yhat,nil);
    DrawValues(x,y,Series1,false); // draw original data
    DrawValues(x,yhat,Series2,false); // draw fitted data
  end;

  #include "MtxVecCpp.h"
  #include "Regress.hpp"
  #include "MtxVecTee.hpp"
  void __fastcall(TLineSeries* series1, TLineSeries* series2)
  {
    Vector x,y,b,yhat;
    x->SetIt(false,TOPENARRAY(TSample,(1.0, 1.5, 2.3, 3.8, 4.2, 5.0, 5.3, 5.9)));
    y->SetIt(false,TOPENARRAY(TSample,(11, 12, 12.5, 14, 14.3, 15.2, 15.3, 17)));
    LinRegress(x,y,b,NULL,yhat,NULL);
    DrawValues(x,y,series1,false); // draw original data
    DrawValues(x,yhat,series2,false); // draw fitted data
  }

  using Dew.Math;
  using Dew.Stats;
  using Dew.Stats.Units;
  using Steema.TeeChart;
  namespace Dew.Examples
  {
    private void Example(Styles.Line series1, Styles.Line series2)
    {
      Vector x = new Vector(0);
      Vector y = new Vector(0);
      Vector b = new Vector(0);
      Vector yhat = new Vector(0);
      x.SetIt(false,new double[] {1.0, 1.5, 2.3, 3.8, 4.2, 5.0, 5.3, 5.9});
      y.SetIt(false,new double[] {11, 12, 12.5, 14, 14.3, 15.2, 15.3, 17});
      LinRegress(x,y,b,null,yhat,null);
      MtxVecTee.DrawValues(x,y,series1,false); // draw original data
      MtxVecTee.DrawValues(x,yhat,series2,false); // draw fitted data
    }
  }