 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 java.lang.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.

Since:
0.1
Author:
Elke Achtert
• ### Field Summary

Fields
Modifier and Type Field and Description
private double[] b
The (p+1 x 1) - double[] holding the estimated b-values (b0, b1, ..., bp)^T.
private double[] e
The (n x 1) - double[] 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 double[][] x
The (n x p+1)-matrix holding the x-values, where the i-th row has the form (1 x1i ... x1p).
private double[][] xx_inverse
Holds the matrix (x'x)^-1.
private double[] y
The (n x 1) - double[] holding the y-values (y1, ..., yn)^T.
private double y_mean
Holds the mean value of the y-values.
• ### Constructor Summary

Constructors
Constructor and Description
MultipleLinearRegression(double[] y, double[][] x)
Constructor.
• ### Method Summary

All Methods
Modifier and Type Method and Description
double coefficientOfDetermination()
Returns the coefficient of determination
double estimateY(double[][] x)
Perform an estimation of y on the specified matrix.
double[] getEstimatedCoefficients()
Returns the estimated coefficients
double[] 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.
java.lang.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 double[] y
The (n x 1) - double[] 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 double[][] 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 double[] b
The (p+1 x 1) - double[] holding the estimated b-values (b0, b1, ..., bp)^T.
• #### e

private final double[] e
The (n x 1) - double[] holding the estimated residuals (e1, ..., en)^T.
• #### variance

private final double variance
The error variance.
• #### xx_inverse

private final double[][] 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(double[] y,
double[][] x)
Constructor.
Parameters:
y - the (n x 1) - double[] 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 java.lang.String toString()
Returns a string representation of the object.
Overrides:
toString in class java.lang.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 double[] getEstimatedCoefficients()
Returns the estimated coefficients
Returns:
the estimated coefficients
• #### getEstimatedResiduals

public double[] 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(double[][] 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