LinearModelResult¶

class LinearModelResult(*args)¶

Result of a LinearModelAlgorithm.

Parameters:

inputSample2-d sequence of float: The input sample of a model.
basisBasis: Functional basis to estimate the trend.
designMatrix: The design matrix $X$ .
outputSample2-d sequence of float: The output sample of a model.
metaModelFunction: The meta model.
coefficientssequence of float: The trend coefficients associated to the linear model.
formulastr: The formula description.
coefficientsNamessequence of str: The coefficients names of the basis.
sampleResiduals2-d sequence of float: The residual errors.
standardizedSampleResiduals2-d sequence of float: The normalized residual errors.
diagonalGramInversesequence of float: The diagonal of the Gram inverse matrix.
leveragessequence of float: The leverage score.
cookDistancessequence of float: Cook’s distances.
residualsVariancefloat: The unbiased variance estimator of the output observation error.

See also

LinearModelAlgorithm

Methods

`buildMethod`()	Accessor to the least squares method.
`getAdjustedRSquared`()	Accessor to the Adjusted R-squared test.
`getBasis`()	Accessor to the basis.
`getClassName`()	Accessor to the object's name.
`getCoefficients`()	Accessor to the coefficients of the linear model of the trend.
`getCoefficientsNames`()	Accessor to the coefficients names.
`getCoefficientsStandardErrors`()	Accessor to the coefficients of standard error.
`getCookDistances`()	Accessor to the cook's distances.
`getDegreesOfFreedom`()	Accessor to the degrees of freedom.
`getDesign`()	Accessor to the design matrix.
`getDiagonalGramInverse`()	Accessor to the diagonal gram inverse matrix.
`getFittedSample`()	Accessor to the fitted sample.
`getFormula`()	Accessor to the formula.
`getInputSample`()	Accessor to the input sample.
`getLeverages`()	Accessor to the leverages.
`getMetaModel`()	Accessor to the metamodel.
`getName`()	Accessor to the object's name.
`getNoiseDistribution`()	Accessor to the noise distribution, ie the underlying distribution of the residual.
`getOutputSample`()	Accessor to the output sample.
`getRSquared`()	Accessor to the R-squared test.
`getRelativeErrors`()	Accessor to the relative errors.
`getResiduals`()	Accessor to the residuals.
`getResidualsVariance`()	Accessor to the unbiased sample variance of the residuals.
`getSampleResiduals`()	Accessor to the residuals.
`getStandardizedResiduals`()	Accessor to the standardized residuals.
`hasIntercept`()	Returns if intercept is provided in the basis or not.
`hasName`()	Test if the object is named.
`involvesModelSelection`()	Get the model selection flag.
`setInputSample`(sampleX)	Accessor to the input sample.
`setMetaModel`(metaModel)	Accessor to the metamodel.
`setName`(name)	Accessor to the object's name.
`setOutputSample`(sampleY)	Accessor to the output sample.
`setRelativeErrors`(relativeErrors)	Accessor to the relative errors.
`setResiduals`(residuals)	Accessor to the residuals.

setInvolvesModelSelection

__init__(*args)¶

buildMethod()¶

Accessor to the least squares method.

Returns:

leastSquaresMethod: LeastSquaresMethod: The least squares method.

getAdjustedRSquared()¶

Accessor to the Adjusted R-squared test.

Returns:

adjustedRSquaredfloat: Not defined when degrees of freedom is null.

getBasis()¶

Accessor to the basis.

Returns:

basisBasis: The basis.

getClassName()¶

Accessor to the object’s name.

Returns:

class_namestr: The object class name (object.__class__.__name__).

getCoefficients()¶

Accessor to the coefficients of the linear model of the trend.

Returns:

coefficientsPoint

getCoefficientsNames()¶

Accessor to the coefficients names.

Returns:

coefficientsNamesDescription

getCoefficientsStandardErrors()¶

Accessor to the coefficients of standard error.

Returns:

standardErrorsPoint

getCookDistances()¶

Accessor to the cook’s distances.

Returns:

cookDistancesPoint

getDegreesOfFreedom()¶

Accessor to the degrees of freedom.

Returns:

dofint: Sample size minus basis size, a null value is allowed.

getDesign()¶

Accessor to the design matrix.

Returns:

design: Matrix: The design matrix.

getDiagonalGramInverse()¶

Accessor to the diagonal gram inverse matrix.

Returns:

diagonalGramInversePoint

getFittedSample()¶

Accessor to the fitted sample.

Returns:

outputSampleSample

getFormula()¶

Accessor to the formula.

Returns:

condensedFormulastr

getInputSample()¶

Accessor to the input sample.

Returns:

inputSampleSample: The input sample.

getLeverages()¶

Accessor to the leverages.

Returns:

leveragesPoint

getMetaModel()¶

Accessor to the metamodel.

Returns:

metaModelFunction: Metamodel.

getName()¶

Accessor to the object’s name.

Returns:

namestr: The name of the object.

getNoiseDistribution()¶

Accessor to the noise distribution, ie the underlying distribution of the residual.

Returns:

noiseDistributionDistribution: Not defined when degrees of freedom is null.

getOutputSample()¶

Accessor to the output sample.

Returns:

outputSampleSample: The output sample.

getRSquared()¶

Accessor to the R-squared test.

Returns:

rSquaredfloat

getRelativeErrors()¶

Accessor to the relative errors.

Returns:

relativeErrorsPoint: The relative errors defined as follows for each output of the model: $\displaystyle \frac{\sum_{i=1}^N (y_i - \hat{y_i})^2}{N \Var{\vect{Y}}}$ with $\vect{Y}$ the vector of the $N$ model’s values $y_i$ and $\hat{y_i}$ the metamodel’s values.

getResiduals()¶

Accessor to the residuals.

Returns:

residualsPoint: The residual values defined as follows for each output of the model: $\displaystyle \frac{\sqrt{\sum_{i=1}^N (y_i - \hat{y_i})^2}}{N}$ with $y_i$ the $N$ model’s values and $\hat{y_i}$ the metamodel’s values.

getResidualsVariance()¶

Accessor to the unbiased sample variance of the residuals.

Returns:

residualsVariancefloat

getSampleResiduals()¶

Accessor to the residuals.

Returns:

sampleResidualsSample

getStandardizedResiduals()¶

Accessor to the standardized residuals.

Returns:

standardizedResidualsSample

hasIntercept()¶

Returns if intercept is provided in the basis or not.

Returns:

interceptBool

hasName()¶

Test if the object is named.

Returns:

hasNamebool: True if the name is not empty.

involvesModelSelection()¶

Get the model selection flag.

A model selection method can be used to select the coefficients to best predict the output. Model selection can lead to a sparse model.

Returns:

involvesModelSelection: bool: True if the method involves a model selection method.

setInputSample(sampleX)¶

Accessor to the input sample.

Parameters:

inputSampleSample: The input sample.

setMetaModel(metaModel)¶

Accessor to the metamodel.

Parameters:

metaModelFunction: Metamodel.

setName(name)¶

Accessor to the object’s name.

Parameters:

namestr: The name of the object.

setOutputSample(sampleY)¶

Accessor to the output sample.

Parameters:

outputSampleSample: The output sample.

setRelativeErrors(relativeErrors)¶

Accessor to the relative errors.

Parameters:

relativeErrorssequence of float: The relative errors defined as follows for each output of the model: $\displaystyle \frac{\sum_{i=1}^N (y_i - \hat{y_i})^2}{N \Var{\vect{Y}}}$ with $\vect{Y}$ the vector of the $N$ model’s values $y_i$ and $\hat{y_i}$ the metamodel’s values.

setResiduals(residuals)¶

Accessor to the residuals.

Parameters:

residualssequence of float: The residual values defined as follows for each output of the model: $\displaystyle \frac{\sqrt{\sum_{i=1}^N (y_i - \hat{y_i})^2}}{N}$ with $y_i$ the $N$ model’s values and $\hat{y_i}$ the metamodel’s values.