 ## 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 MultipleLinearRegressionextends 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

 Release 0.4.0 (2011-09-20_1324)