de.lmu.ifi.dbs.elki.math.statistics

Class PolynomialRegression

java.lang.Object

de.lmu.ifi.dbs.elki.math.statistics.MultipleLinearRegression

de.lmu.ifi.dbs.elki.math.statistics.PolynomialRegression

public class PolynomialRegression
extends MultipleLinearRegression

A polynomial fit is a specific type of multiple regression. The simple regression model (a first-order polynomial) can be trivially extended to higher orders.

The regression model y = b0 + b1*x + b2*x^2 + ... + bp*x^p + e is a system of polynomial equations of order p with polynomial coefficients { b0 ... bp}. The model can be expressed using data matrix x, target double[] y and parameter double[] ?. The ith row of X and Y will contain the x and y value for the ith data sample.

The variables will be transformed in the following way: x => x1, ..., x^p => xp Then the model can be written as a multiple linear equation model: y = b0 + b1*x1 + b2*x2 + ... + bp*xp + e

Since:

0.1

Author:

Elke Achtert

Field Summary

Fields

Modifier and Type	Field and Description
int	p The order of the polynom.

Constructor Summary

Constructors

Constructor and Description
PolynomialRegression(double[] y, double[] x, int p) Constructor.

Method Summary

Modifier and Type	Method and Description
double	adaptedCoefficientOfDetermination() Returns the adapted coefficient of determination
double	estimateY(double x) Performs an estimation of y on the specified x value.
private static double[][]	xMatrix(double[] x, int p)

Methods inherited from class de.lmu.ifi.dbs.elki.math.statistics.MultipleLinearRegression

coefficientOfDetermination, estimateY, getEstimatedCoefficients, getEstimatedResiduals, getSumOfSquareResiduals, getSumOfSquaresTotal, getVariance, toString

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Field Detail

p

public final int p

The order of the polynom.

Constructor Detail

PolynomialRegression

public PolynomialRegression(double[] y,
                            double[] x,
                            int p)

Constructor.

Parameters:

y - the (n x 1) - double[] holding the response values (y1, ..., yn)^T.

x - the (n x 1)-double[] holding the x-values (x1, ..., xn)^T.

p - the order of the polynom.

Method Detail

xMatrix

private static double[][] xMatrix(double[] x,
                                  int p)

adaptedCoefficientOfDetermination

public double adaptedCoefficientOfDetermination()

Returns the adapted coefficient of determination

Returns:

the adapted coefficient of determination

estimateY

public double estimateY(double x)

Performs an estimation of y on the specified x value.

Parameters:

x - the x-value for which y is estimated

Returns:

the estimation of y