Overload List
| # | Signature | Description |
|---|---|---|
| 1 | void PCRegress(TVec Y, TMtx A, TVec b, TVec Weights, TVec YCalc, TVec Bse, Int32 NumOmmit) | Weighted PC regression. |
| 2 | void PCRegress(TVec Y, TMtx A, TVec b, TVec YCalc, TVec Bse, Int32 NumOmmit) | Principal Component Regression. |
Overload 1: void PCRegress(TVec Y, TMtx A, TVec b, TVec Weights, TVec YCalc, TVec Bse, Int32 NumOmmit)
Weighted PC regression.
| # | Name | Description |
|---|---|---|
| 1 | Y | Defines vector of dependant variable. |
| 2 | A | Defines matrix of independant variables. |
| 3 | b | Returns calculated regression coefficiens. |
| 4 | Weights | Defines weights for PC regression. |
| 5 | YCalc | Returns vector of calculated dependant variable, where YCalc = A*b + constant term. |
| 6 | Bse | Returns principal component b coefficient standard error. |
| 7 | NumOmmit | Defines the number of variables to ommit from initial model. |
Result: stored in self (calling object)
Overload 2: void PCRegress(TVec Y, TMtx A, TVec b, TVec YCalc, TVec Bse, Int32 NumOmmit)
Principal Component Regression.
| # | Name | Description |
|---|---|---|
| 1 | Y | Defines vector of dependant variable. |
| 2 | A | Defines matrix of independant variables. |
| 3 | NumOmmit | Defines the number of variables to ommit from initial model. |
| 4 | b | Returns calculated regression coefficiens. |
| 5 | YCalc | Returns vector of calculated dependant variable, where YCalc = A*b + constant term. |
| 6 | Bse | Returns principal component b coefficient standard error. |
Result: stored in self (calling object)
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.
Examples
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);
}
}See Also: Regress.RidgeRegress