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

## Class 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

All 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 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)

public double adaptedCoefficientOfDetermination()
Returns the adapted coefficient of determination
Returns:
public double estimateY(double x)
x - the x-value for which y is estimated