Principal Component Regression.
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.
Example 1
Uses MtxExpr, Regress, StatTools, Math387;
procedure Example;
var y,b,ycalc,error: Vector;
A,ATA: Matrix;
mse: TSample;
begin
// Load data
A.SetIt(18,3,false,[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([3,9,11,15,13,13,17,21,25,27,25,27,29,33,35,37,37,39]);
// Perform Principal Component Regression
PCRegress(y,A,b,ycalc,nil,1);
// Errors
error.Sub(ycalc,y);
end;
#include "MtxVecCpp.h"
#include "Regress.hpp"
#include "StatTools.hpp"
#include "Math387.hpp"
void __fastcall Example()
{
Matrix A, ATA;
Vector y,b,ycalc,error;
double mse;
// Load data
A->SetIt(18,3,false,OPENARRAY(TSample,(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,OPENARRAY(TSample,(3,9,11,15,13,13,17,21,25,27,25,27,29,33,35,37,37,39)));
// Perform Principal Component Regression
PCRegress(y,A,b,ycalc,null,1);
// Errors
error->Sub(ycalc,y);
}
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);
}
}
Declaration
Procedure PCRegress(y: TVec; A: TMtx; b: TVec; Weights: TVec; YCalc: TVec = nil; Bse: TVec = nil; NumOmmit: Integer = 1);
Performs weighted PC regression.