Apache Commons Math 3.6.1 · org.apache.commons.math3.stat.regression.AbstractMultipleLinearRegression

Modifier and Type	Field and Description
private boolean	noIntercept Whether or not the regression model includes an intercept.
private RealMatrix	xMatrix X sample data.
private RealVector	yVector Y sample data.

Access	Constructor and Description
public	AbstractMultipleLinearRegression()

Method Summary

Modifier and Type	Method and Description
protected abstract RealVector	Returns: beta calculateBeta() Calculates the beta of multiple linear regression in matrix notation.
protected abstract RealMatrix	Returns: beta variance calculateBetaVariance() Calculates the beta variance of multiple linear regression in matrix notation.
protected double	Returns: error variance estimate calculateErrorVariance() Calculates the variance of the error term.
protected RealVector	Returns: The residuals [n,1] matrix calculateResiduals() Calculates the residuals of multiple linear regression in matrix notation.
protected double	Returns: Y variance calculateYVariance() Calculates the variance of the y values.
public double	Returns: estimate of the error variance estimateErrorVariance() Estimates the variance of the error.
public double	estimateRegressandVariance() Implements org.apache.commons.math3.stat.regression.MultipleLinearRegression.estimateRegressandVariance. Returns the variance of the regressand, ie Var(y).
public double[]	estimateRegressionParameters() Implements org.apache.commons.math3.stat.regression.MultipleLinearRegression.estimateRegressionParameters. Estimates the regression parameters b.
public double[]	estimateRegressionParametersStandardErrors() Implements org.apache.commons.math3.stat.regression.MultipleLinearRegression.estimateRegressionParametersStandardErrors. Returns the standard errors of the regression parameters.
public double[][]	estimateRegressionParametersVariance() Implements org.apache.commons.math3.stat.regression.MultipleLinearRegression.estimateRegressionParametersVariance. Estimates the variance of the regression parameters, ie Var(b).
public double	Returns: regression standard error estimateRegressionStandardError() Estimates the standard error of the regression.
public double[]	estimateResiduals() Implements org.apache.commons.math3.stat.regression.MultipleLinearRegression.estimateResiduals. Estimates the residuals, ie u = y - X*b.
protected RealMatrix	Returns: the X sample data. getX()
protected RealVector	Returns: the Y sample data. getY()
public boolean	Returns: true if the model has no intercept term; false otherwise isNoIntercept()
public void	newSampleData(double[] input data array data, int number of observations (rows) nobs, int number of independent variables (columns, not counting y) nvars) Loads model x and y sample data from a flat input array, overriding any previous sample.
protected void	newXSampleData(double[][] the rectangular array representing the x sample x) Loads new x sample data, overriding any previous data.
protected void	newYSampleData(double[] the array representing the y sample y) Loads new y sample data, overriding any previous data.
public void	setNoIntercept(boolean true means the model is to be estimated without an intercept term noIntercept)
protected void	validateCovarianceData(double[][] the [n,k] array representing the x sample x, double[][] the [n,n] array representing the covariance matrix covariance) Validates that the x data and covariance matrix have the same number of rows and that the covariance matrix is square.
protected void	validateSampleData(double[][] the [n,k] array representing the x data x, double[] the [n,1] array representing the y data y) Validates sample data.

Inherited from java.lang.Object:: clone equals finalize getClass hashCode notify notifyAll toString wait wait wait

noIntercept	back to summary
private boolean noIntercept Whether or not the regression model includes an intercept. True means no intercept.

xMatrix	back to summary
private RealMatrix xMatrix X sample data.

yVector	back to summary
private RealVector yVector Y sample data.

AbstractMultipleLinearRegression	back to summary
public AbstractMultipleLinearRegression()

Method Detail

calculateBeta	back to summary
protected abstract RealVector calculateBeta() Calculates the beta of multiple linear regression in matrix notation. Returns:RealVector beta

calculateBeta

back to summary

protected abstract RealVector calculateBeta()

Calculates the beta of multiple linear regression in matrix notation.

Returns:RealVector: beta

calculateBetaVariance	back to summary
protected abstract RealMatrix calculateBetaVariance() Calculates the beta variance of multiple linear regression in matrix notation. Returns:RealMatrix beta variance

calculateBetaVariance

back to summary

protected abstract RealMatrix calculateBetaVariance()

Calculates the beta variance of multiple linear regression in matrix notation.

Returns:RealMatrix: beta variance

calculateErrorVariance	back to summary
protected double calculateErrorVariance() Calculates the variance of the error term. Uses the formula var(u) = u · u / (n - k) where n and k are the row and column dimensions of the design matrix X. Returns:double error variance estimate Since 2.2

calculateErrorVariance

back to summary

protected double calculateErrorVariance()

Calculates the variance of the error term.

Uses the formula

var(u) = u · u / (n - k)

where n and k are the row and column dimensions of the design matrix X.

Returns:double: error variance estimate
Since: 2.2

calculateResiduals	back to summary
protected RealVector calculateResiduals() Calculates the residuals of multiple linear regression in matrix notation. u = y - X * b Returns:RealVector The residuals [n,1] matrix

calculateResiduals

back to summary

protected RealVector calculateResiduals()

Calculates the residuals of multiple linear regression in matrix notation.

u = y - X * b

Returns:RealVector: The residuals [n,1] matrix

calculateYVariance	back to summary
protected double calculateYVariance() Calculates the variance of the y values. Returns:double Y variance

calculateYVariance

back to summary

protected double calculateYVariance()

Calculates the variance of the y values.

Returns:double: Y variance

estimateErrorVariance	back to summary
public double estimateErrorVariance() Estimates the variance of the error. Returns:double estimate of the error variance Since 2.2

estimateErrorVariance

back to summary

public double estimateErrorVariance()

Estimates the variance of the error.

Returns:double: estimate of the error variance
Since: 2.2

estimateRegressandVariance	back to summary
public double estimateRegressandVariance() Implements org.apache.commons.math3.stat.regression.MultipleLinearRegression.estimateRegressandVariance. Doc from org.apache.commons.math3.stat.regression.MultipleLinearRegression.estimateRegressandVariance. Returns the variance of the regressand, ie Var(y). Returns:double The double representing the variance of y

estimateRegressandVariance

back to summary

public double estimateRegressandVariance()

Implements org.apache.commons.math3.stat.regression.MultipleLinearRegression.estimateRegressandVariance.

Doc from org.apache.commons.math3.stat.regression.MultipleLinearRegression.estimateRegressandVariance.

Returns the variance of the regressand, ie Var(y).

Returns:double: The double representing the variance of y

estimateRegressionParameters	back to summary
public double[] estimateRegressionParameters() Implements org.apache.commons.math3.stat.regression.MultipleLinearRegression.estimateRegressionParameters. Doc from org.apache.commons.math3.stat.regression.MultipleLinearRegression.estimateRegressionParameters. Estimates the regression parameters b. Returns:double[] The [k,1] array representing b

estimateRegressionParameters

back to summary

public double[] estimateRegressionParameters()

Implements org.apache.commons.math3.stat.regression.MultipleLinearRegression.estimateRegressionParameters.

Doc from org.apache.commons.math3.stat.regression.MultipleLinearRegression.estimateRegressionParameters.

Estimates the regression parameters b.

Returns:double[]: The [k,1] array representing b

estimateRegressionParametersStandardErrors	back to summary
public double[] estimateRegressionParametersStandardErrors() Implements org.apache.commons.math3.stat.regression.MultipleLinearRegression.estimateRegressionParametersStandardErrors. Doc from org.apache.commons.math3.stat.regression.MultipleLinearRegression.estimateRegressionParametersStandardErrors. Returns the standard errors of the regression parameters. Returns:double[] standard errors of estimated regression parameters

estimateRegressionParametersStandardErrors

back to summary

public double[] estimateRegressionParametersStandardErrors()

Implements org.apache.commons.math3.stat.regression.MultipleLinearRegression.estimateRegressionParametersStandardErrors.

Doc from org.apache.commons.math3.stat.regression.MultipleLinearRegression.estimateRegressionParametersStandardErrors.

Returns the standard errors of the regression parameters.

Returns:double[]: standard errors of estimated regression parameters

estimateRegressionParametersVariance	back to summary
public double[][] estimateRegressionParametersVariance() Implements org.apache.commons.math3.stat.regression.MultipleLinearRegression.estimateRegressionParametersVariance. Doc from org.apache.commons.math3.stat.regression.MultipleLinearRegression.estimateRegressionParametersVariance. Estimates the variance of the regression parameters, ie Var(b). Returns:double[][] The [k,k] array representing the variance of b

estimateRegressionParametersVariance

back to summary

public double[][] estimateRegressionParametersVariance()

Implements org.apache.commons.math3.stat.regression.MultipleLinearRegression.estimateRegressionParametersVariance.

Doc from org.apache.commons.math3.stat.regression.MultipleLinearRegression.estimateRegressionParametersVariance.

Estimates the variance of the regression parameters, ie Var(b).

Returns:double[][]: The [k,k] array representing the variance of b

estimateRegressionStandardError	back to summary
public double estimateRegressionStandardError() Estimates the standard error of the regression. Returns:double regression standard error Since 2.2

estimateRegressionStandardError

back to summary

public double estimateRegressionStandardError()

Estimates the standard error of the regression.

Returns:double: regression standard error
Since: 2.2

estimateResiduals	back to summary
public double[] estimateResiduals() Implements org.apache.commons.math3.stat.regression.MultipleLinearRegression.estimateResiduals. Doc from org.apache.commons.math3.stat.regression.MultipleLinearRegression.estimateResiduals. Estimates the residuals, ie u = y - X*b. Returns:double[] The [n,1] array representing the residuals

estimateResiduals

back to summary

public double[] estimateResiduals()

Implements org.apache.commons.math3.stat.regression.MultipleLinearRegression.estimateResiduals.

Doc from org.apache.commons.math3.stat.regression.MultipleLinearRegression.estimateResiduals.

Estimates the residuals, ie u = y - X*b.

Returns:double[]: The [n,1] array representing the residuals

getX	back to summary
protected RealMatrix getX() Returns:RealMatrix the X sample data.

getY	back to summary
protected RealVector getY() Returns:RealVector the Y sample data.

isNoIntercept	back to summary
public boolean isNoIntercept() Returns:boolean true if the model has no intercept term; false otherwise Since 2.2

newSampleData back to summary

newSampleData	back to summary
public void newSampleData(double[] data, int nobs, int nvars) Loads model x and y sample data from a flat input array, overriding any previous sample. Assumes that rows are concatenated with y values first in each row. For example, an input `data` array containing the sequence of values (1, 2, 3, 4, 5, 6, 7, 8, 9) with `nobs = 3` and `nvars = 2` creates a regression dataset with two independent variables, as below: y x[0] x[1] -------------- 1 2 3 4 5 6 7 8 9 Note that there is no need to add an initial unitary column (column of 1's) when specifying a model including an intercept term. If `isNoIntercept()` is `true`, the X matrix will be created without an initial column of "1"s; otherwise this column will be added. Throws IllegalArgumentException if any of the following preconditions fail: `data` cannot be null `data.length = nobs * (nvars + 1)` `nobs > nvars` `Parameters data:double[] input data array nobs:int number of observations (rows) nvars:int number of independent variables (columns, not counting y) Exceptions NullArgumentException: if the data array is null DimensionMismatchException: if the length of the data array is not equal to nobs * (nvars + 1) InsufficientDataException: if nobs is less than nvars + 1`

public void newSampleData(double[] data, int nobs, int nvars)

Loads model x and y sample data from a flat input array, overriding any previous sample.

Assumes that rows are concatenated with y values first in each row. For example, an input data array containing the sequence of values (1, 2, 3, 4, 5, 6, 7, 8, 9) with nobs = 3 and nvars = 2 creates a regression dataset with two independent variables, as below:

  y   x[0]  x[1]
  --------------
  1     2     3
  4     5     6
  7     8     9

Note that there is no need to add an initial unitary column (column of 1's) when specifying a model including an intercept term. If isNoIntercept() is true, the X matrix will be created without an initial column of "1"s; otherwise this column will be added.

Throws IllegalArgumentException if any of the following preconditions fail:

data cannot be null
data.length = nobs * (nvars + 1)


nobs > nvars




Parameters

data:double[]
input data array
nobs:int
number of observations (rows)
nvars:int
number of independent variables (columns, not counting y)

Exceptions

NullArgumentException:
if the data array is null
DimensionMismatchException:
if the length of the data array is not equal to nobs * (nvars + 1)
InsufficientDataException:
if nobs is less than nvars + 1

newXSampleData back to summary

newXSampleData	back to summary
protected void newXSampleData(double[][] x) Loads new x sample data, overriding any previous data. The input `x` array should have one row for each sample observation, with columns corresponding to independent variables. For example, if `x = new double[][] {{1, 2}, {3, 4}, {5, 6}}` then `setXSampleData(x)` results in a model with two independent variables and 3 observations: x[0] x[1] ---------- 1 2 3 4 5 6 Note that there is no need to add an initial unitary column (column of 1's) when specifying a model including an intercept term. Parameters x:double[][] the rectangular array representing the x sample Exceptions NullArgumentException: if x is null NoDataException: if x is empty DimensionMismatchException: if x is not rectangular

protected void newXSampleData(double[][] x)

Loads new x sample data, overriding any previous data.

The input x array should have one row for each sample observation, with columns corresponding to independent variables. For example, if

 x = new double[][] {{1, 2}, {3, 4}, {5, 6}}

then setXSampleData(x) results in a model with two independent variables and 3 observations:

  x[0]  x[1]
  ----------
    1    2
    3    4
    5    6

Note that there is no need to add an initial unitary column (column of 1's) when specifying a model including an intercept term.

Parameters

x:double[][]: the rectangular array representing the x sample

Exceptions

NullArgumentException:: if x is null
NoDataException:: if x is empty
DimensionMismatchException:: if x is not rectangular

newYSampleData	back to summary
protected void newYSampleData(double[] y) Loads new y sample data, overriding any previous data. Parameters y:double[] the array representing the y sample Exceptions NullArgumentException: if y is null NoDataException: if y is empty

newYSampleData

back to summary

protected void newYSampleData(double[] y)

Loads new y sample data, overriding any previous data.

Parameters

y:double[]: the array representing the y sample

Exceptions

NullArgumentException:: if y is null
NoDataException:: if y is empty

setNoIntercept	back to summary
public void setNoIntercept(boolean noIntercept) Parameters noIntercept:boolean true means the model is to be estimated without an intercept term Since 2.2

validateCovarianceData	back to summary
protected void validateCovarianceData(double[][] x, double[][] covariance) Validates that the x data and covariance matrix have the same number of rows and that the covariance matrix is square. Parameters x:double[][] the [n,k] array representing the x sample covariance:double[][] the [n,n] array representing the covariance matrix Exceptions DimensionMismatchException: if the number of rows in x is not equal to the number of rows in covariance NonSquareMatrixException: if the covariance matrix is not square

validateCovarianceData

back to summary

protected void validateCovarianceData(double[][] x, double[][] covariance)

Validates that the x data and covariance matrix have the same number of rows and that the covariance matrix is square.

Parameters

x:double[][]: the [n,k] array representing the x sample
covariance:double[][]: the [n,n] array representing the covariance matrix

Exceptions

DimensionMismatchException:: if the number of rows in x is not equal to the number of rows in covariance
NonSquareMatrixException:: if the covariance matrix is not square

validateSampleData back to summary

validateSampleData	back to summary
protected void validateSampleData(double[][] x, double[] y) throws MathIllegalArgumentException Validates sample data. Checks that Neither x nor y is null or empty; The length (i.e. number of rows) of x equals the length of y x has at least one more row than it has columns (i.e. there is sufficient data to estimate regression coefficients for each of the columns in x plus an intercept. Parameters x:double[][] the [n,k] array representing the x data y:double[] the [n,1] array representing the y data Exceptions MathIllegalArgumentException: if the number of rows of `x` is not larger than the number of columns + 1 NullArgumentException: if `x` or `y` is null DimensionMismatchException: if `x` and `y` do not have the same length NoDataException: if `x` or `y` are zero-length

protected void validateSampleData(double[][] x, double[] y) throws MathIllegalArgumentException

Validates sample data. Checks that

Neither x nor y is null or empty;
The length (i.e. number of rows) of x equals the length of y
x has at least one more row than it has columns (i.e. there is sufficient data to estimate regression coefficients for each of the columns in x plus an intercept.

Parameters

x:double[][]: the [n,k] array representing the x data
y:double[]: the [n,1] array representing the y data

Exceptions

MathIllegalArgumentException:: if the number of rows of x is not larger than the number of columns + 1
NullArgumentException:: if x or y is null
DimensionMismatchException:: if x and y do not have the same length
NoDataException:: if x or y are zero-length

public abstract Class AbstractMultipleLinearRegression

Field Summary

Constructor Summary

Method Summary

Field Detail

Constructor Detail

Method Detail