edu.princeton.cs.algorithms

Class PolynomialRegression

java.lang.Object

edu.princeton.cs.algorithms.PolynomialRegression

public class PolynomialRegression
extends Object

The PolynomialRegression class performs a polynomial regression on an set of N data points (y_i, x_i). That is, it fits a polynomial y = β₀ + β₁ x + β₂ x² + ... + β_d x^d (where y is the response variable, x is the predictor variable, and the β_i are the regression coefficients) that minimizes the sum of squared residuals of the multiple regression model. It also computes associated the coefficient of determination R².

This implementation performs a QR-decomposition of the underlying Vandermonde matrix, so it is not the fastest or most numerically stable way to perform the polynomial regression.

Author:

Robert Sedgewick, Kevin Wayne

Constructor Summary

Constructors

Constructor and Description
PolynomialRegression(double[] x, double[] y, int degree) Performs a polynomial reggression on the data points (y[i], x[i]).

Method Summary

Methods

Modifier and Type	Method and Description
double	beta(int j) Returns the jth regression coefficient
int	degree() Returns the degree of the polynomial to fit
static void	main(String[] args)
double	predict(double x) Returns the expected response y given the value of the predictor variable x.
double	R2() Returns the coefficient of determination R2.
String	toString() Returns a string representation of the polynomial regression model.

Methods inherited from class java.lang.Object

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

Constructor Detail

PolynomialRegression

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

Performs a polynomial reggression on the data points (y[i], x[i]).

Parameters:

x - the values of the predictor variable

y - the corresponding values of the response variable

degree - the degree of the polynomial to fit

Throws:

IllegalArgumentException - if the lengths of the two arrays are not equal

Method Detail

beta

public double beta(int j)

Returns the jth regression coefficient

Returns:

the jth regression coefficient

degree

public int degree()

Returns the degree of the polynomial to fit

Returns:

the degree of the polynomial to fit

R2

public double R2()

Returns the coefficient of determination R².

Returns:

the coefficient of determination R², which is a real number between 0 and 1

predict

public double predict(double x)

Returns the expected response y given the value of the predictor variable x.

Parameters:

x - the value of the predictor variable

Returns:

the expected response y given the value of the predictor variable x

toString

public String toString()

Returns a string representation of the polynomial regression model.

Overrides:

toString in class Object

Returns:

a string representation of the polynomial regression model, including the best-fit polynomial and the coefficient of determination R²

main

public static void main(String[] args)