MultipleLinearRegression (ELKI: Environment for DeveLoping KDD-Applications Supported by Index-Structures)

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.

Author:

Elke Achtert

Field Summary

Fields
Modifier and Type	Field and Description
`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

Constructors
Constructor and Description

MultipleLinearRegression(Vector y, Matrix x)
Constructor.

Constructors
Constructor and Description
`MultipleLinearRegression(Vector y, Matrix x)` Constructor.

Method Summary

Methods
Modifier and Type	Method and Description
`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)
```
    Constructor.
    
    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

Class MultipleLinearRegression

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

y

y_mean

x

b

e

variance

xx_inverse

ssr

sst

Constructor Detail

MultipleLinearRegression

Method Detail

toString

getSumOfSquaresTotal

getSumOfSquareResiduals

getEstimatedCoefficients

getEstimatedResiduals

coefficientOfDetermination

estimateY

getVariance