Regress.PCRegress Method (TVec, TMtx, TVec, TVec, TVec, Integer)

Principal Component Regression.

public PCRegress(TVec y, TMtx A, TVec b, TVec YCalc, TVec Bse, int NumOmmit);

Parameters

Parameters	Description
y	Defines vector of dependant variable.
A	Defines matrix of independant variables.
b	Returns calculated regression coefficiens.
YCalc	Returns vector of calculated dependant variable, where YCalc = A*b + constant term.
Bse	Returns principal component b coefficient standard error.
NumOmmit	Defines the number of variables to ommit from initial model.

Remarks

Performs unweighted Principal Component Regression (PCR). PCR is a technique for analyzing multiple regression data that suffer from multicollinearity. When multicollinearity occurs, least squares estimates are unbiased, but their variances are large so they may be far from the true value. By adding a degree of bias to the regression estimates, principal components regression reduces the standard errors. The algorithm first standardizes A matrix and performs PC regression on standardized matrix.

Related Topics

RidgeRegress

C# Example

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 ycalc = new Vector(0);
    Vector b = new Vector(0);
    Vector error = new Vector(0);
    double mse;
    // Load data
    A.SetIt(18,3,false, new double[] {1,  2,  1,
      2,  4,  2,
      3,  6,  4,
      4,  7,  3,
      5, 7,   2,
      6,  7,  1,
      7,  8,  1,
      8,  10, 2,
      9,  12, 4,
      10, 13, 3,
      11, 13, 2,
      12, 13, 1,
      13, 14, 1,
      14, 16, 2,
      15, 18, 4,
      16, 19, 3,
      17, 19, 2,
      18, 19, 1});
    Y.SetIt(false, new double[] {3,9,11,15,13,13,17,21,25,27,25,27,29,33,35,37,37,39});
    // Perform Principal Component Regression
    Regress.PCRegress(y,A,b,ycalc,null,1);
    // Errors
    error.Sub(ycalc,y);
  }
}