Regress.LinRegress Function

Simple linear regression.

Pascal

procedure LinRegress(const X: TVec; const Y: TVec; const B: TVec; Constant: Boolean = True; const Weights: TVec = nil; const YCalc: TVec = nil; const ATA: TMtx = nil);

File

Regress

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). In case constant term is used, the observed values obey the following equation:

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

i.e

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

or if constant term is NOT used:

y(k) = b(0) * x

To calculate additional regression statistical parameters, use RegressTest routine.

See Also

MulLinRegress, RegressTest

Example

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,true,nil,yhat,nil);
  DrawValues(x,y,Series1,false); // draw original data
  DrawValues(x,yhat,Series2,false); // draw fitted data
end;

#include "MtxExpr.hpp"
#include "Regress.hpp"
#include "MtxVecTee.hpp"
void __fastcall Test(TLineSeries* series1, TLineSeries* series2)
{
  sVector x,y,b,yhat;
  x.SetIt(false,OPENARRAY(double,(1.0, 1.5, 2.3, 3.8, 4.2, 5.0, 5.3, 5.9)));
  y.SetIt(false,OPENARRAY(double,(11, 12, 12.5, 14, 14.3, 15.2, 15.3, 17)));
  LinRegress(x,y,b,true,NULL,yhat,NULL);
  DrawValues(x,y,series1,false); // draw original data
  DrawValues(x,yhat,series2,false); // draw fitted data
}

Regress, Functions, Example, See Also

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