Regress.MulLinRegress Function

Multivariante linear regression.

Pascal

procedure MulLinRegress(const Y: TVec; const A: TMtx; const b: TVec; const Weights: TVec; Constant: boolean = true; const YCalc: TVec = nil; const ATA: TMtx = nil; Method: TRegSolveMethod = regSolveLQR); overload;

File

Regress

Parameters

Parameters	Description
Y	Defines vector of dependant variable.
A	Defines matrix of independant (also X) variables.
b	Returns calculated regression coefficiens.
Weights	Defines weights (optional).
Constant	If true then intercept term b(0) will be included 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.
Method	Use QR, SVD, or LU solver. Typically QR will yield best compromise between stability and performance.

Description

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

The following example performs multiple linear regression.

Uses Regress, MtxExpr;
procedure Example;
var y,b,w,yhat, resid, bstd: 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,ATA,RegStat,resid, bstd, true,w); // do basic regression stats
  // RegStat = (ResidualVar:0.037230395108; R2:0.99965713428;
  // AdjustedR2:0.99897140285; F:1457.7968725; SignifProb: 0.01851663347)
end;

#include "MtxExpr.hpp"
#include "Regress.hpp"
void _fastcall Example()
{
    sMatrix A,ATA;
    sVector y,b,w,yhat,residuals,bstdev;
    TRegStats rs;
    // independent variables
    A.SetIt(4,2,false,OPENARRAY(double,(1.0, 2.0,
              -3.2, 2.5,
               8.0,   -0.5,
               -2.2, 1.8)));
    w.SetIt(false,OPENARRAY(double,(1,2,2,1))); // weights
    y.SetIt(false,OPENARRAY(double,(-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,rs,residuals,bstdev,true,w); // do basic regression stats
      // RegStat = (ResidualVar:0.037230395108; R2:0.99965713428;
      // AdjustedR2:0.99897140285; F:1457.7968725; SignifProb: 0.01851663347)
}

Regress, Functions, Example, See Also

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