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

java.lang.Object
  de.lmu.ifi.dbs.elki.math.statistics.MultipleLinearRegression

Direct Known Subclasses:

PolynomialRegression

public class MultipleLinearRegression
extends Object

Multiple linear regression attempts to model the relationship between two or more explanatory variables and a response variable by fitting a linear equation to observed data. Every value of the independent variable x is associated with a value of the dependent variable y.

The population regression line for p explanatory variables x1, x2, ... , xp is defined to be y = b0 + b1*x1 + b2*x2 + ... + bp*xp + e.

Field Summary

private Vector	b The (p+1 x 1) - vector holding the estimated b-values (b0, b1, ..., bp)^T.
private Vector	e The (n x 1) - vector holding the estimated residuals (e1, ..., en)^T.
private double	ssr The sum of square residuals
private double	sst The sum of square totals
private double	variance The error variance.
private Matrix	x The (n x p+1)-matrix holding the x-values, where the i-th row has the form (1 x1i ... x1p).
private Matrix	xx_inverse Holds the matrix (x'x)^-1.
private Vector	y The (n x 1) - vector holding the y-values (y1, ..., yn)^T.
private double	y_mean Holds the mean value of the y-values.

Constructor Summary

MultipleLinearRegression(Vector y, Matrix x)
Provides a new multiple linear regression model with the specified parameters.

Method Summary

double	coefficientOfDetermination() Returns the coefficient of determination
double	estimateY(Matrix x) Perform an estimation of y on the specified matrix.
Vector	getEstimatedCoefficients() Returns the estimated coefficients
Vector	getEstimatedResiduals() Returns the estimated residuals
double	getSumOfSquareResiduals() Returns the sum of square residuals.
double	getSumOfSquaresTotal() Returns the sum of squares total.
double	getVariance() Returns the error variance.
String	toString() Returns a string representation of the object.

Methods inherited from class java.lang.Object

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

Field Detail

y

private final Vector y

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

y_mean

private final double y_mean

Holds the mean value of the y-values.

x

private final Matrix x

The (n x p+1)-matrix holding the x-values, where the i-th row has the form (1 x1i ... x1p).

b

private final Vector b

The (p+1 x 1) - vector holding the estimated b-values (b0, b1, ..., bp)^T.

e

private final Vector e

The (n x 1) - vector holding the estimated residuals (e1, ..., en)^T.

variance

private final double variance

The error variance.

xx_inverse

private final Matrix xx_inverse

Holds the matrix (x'x)^-1.

ssr

private final double ssr

The sum of square residuals

sst

private final double sst

The sum of square totals

Constructor Detail

MultipleLinearRegression

public MultipleLinearRegression(Vector y,
                                Matrix x)

Provides a new multiple linear regression model with the specified parameters.

Parameters:

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

x - the (n x p+1)-matrix holding the explanatory values, where the i-th row has the form (1 x1i ... x1p).

Method Detail

toString

public String toString()

Returns a string representation of the object.

Overrides:

toString in class Object

Returns:

a string representation of the object.

getSumOfSquaresTotal

public double getSumOfSquaresTotal()

Returns the sum of squares total.

Returns:

the sum of squares total

getSumOfSquareResiduals

public double getSumOfSquareResiduals()

Returns the sum of square residuals.

Returns:

the sum of square residuals

getEstimatedCoefficients

public Vector getEstimatedCoefficients()

Returns the estimated coefficients

Returns:

the estimated coefficients

getEstimatedResiduals

public Vector getEstimatedResiduals()

Returns the estimated residuals

Returns:

the estimated residuals

coefficientOfDetermination

public double coefficientOfDetermination()

Returns the coefficient of determination

Returns:

the coefficient of determination

estimateY

public double estimateY(Matrix x)

Perform an estimation of y on the specified matrix.

Parameters:

x - the matrix for which y is estimated

Returns:

the estimation of y

getVariance

public double getVariance()

Returns the error variance.

Returns:

the error variance