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

Field Summary

int	p The order of the polynom.

Constructor Summary

PolynomialRegression(Vector y, Vector x, int p)
Provides a new polynomial regression model with the specified parameters.

Method Summary

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)

Provides a new polynomial regression model with the specified parameters.

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