Regress.MulLinRegress Method (TVec, TMtx, TVec, TVec, boolean, TVec, TMtx, TRegSolveMethod)

Multivariante linear regression.

public MulLinRegress(TVec y, TMtx A, TVec b, TVec Weights, bool Constant, TVec YCalc, TMtx ATA, TRegSolveMethod Method);

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 = Ab<c>.
ATA	Returns inverse matrix of normal equations i.e [A(T)*A]^-1 .

Remarks

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.

Related Topics

RegressTest, LinRegress, NLinRegress

C# Example

The following example performs multiple linear regression.

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)
  }
}