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 vector y and parameter vector ?. 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

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(Vector y, Vector x, int p) Constructor.

Method Summary

Methods

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 Matrix	xMatrix(Vector 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(Vector y,
                    Vector x,
                    int p)

Constructor.

Parameters:

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

x - the (n x 1)-vector holding the x-values (x1, ..., xn)^T.

p - the order of the polynom.

Method Detail

xMatrix

private static Matrix xMatrix(Vector 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