Collaboration diagram for Regression Analysis:

Enumerations
enum class	JKQTPStatRegressionModelType { JKQTPStatRegressionModelType::Linear , JKQTPStatRegressionModelType::PowerLaw , JKQTPStatRegressionModelType::Exponential , JKQTPStatRegressionModelType::Logarithm }
	when performing linear regression, different target functions can be fitted, if the input data is transformed accordingly. This library provides the options in this enum by default. More...

Functions
template<class InputItX , class InputItY >
double	jkqtpstatCoefficientOfDetermination (InputItX firstX, InputItX lastX, InputItY firstY, InputItY lastY, std::function< double(double)> f)
	calculates the coefficient of determination for a set of measurements with a fit function

jkqtmath_LIB_EXPORT std::pair< std::function< double(double)>, std::function< double(double)> >	jkqtpStatGenerateParameterATransformation (JKQTPStatRegressionModelType type)
	Generates the transformation function for a-parameter (offset, `result.first` : transform, `result.second` : back-transform) for each regression model in JKQTPStatRegressionModelType in type.

jkqtmath_LIB_EXPORT std::pair< std::function< double(double)>, std::function< double(double)> >	jkqtpStatGenerateParameterBTransformation (JKQTPStatRegressionModelType type)
	Generates the transformation function for b-parameter (slope, `result.first` : transform, `result.second` : back-transform) for each regression model in JKQTPStatRegressionModelType in type.

jkqtmath_LIB_EXPORT std::function< double(double, double, double)>	jkqtpStatGenerateRegressionModel (JKQTPStatRegressionModelType type)
	Generates functors `f(x,a,b)` for the models from JKQTPStatRegressionModelType in type.

jkqtmath_LIB_EXPORT std::function< double(double)>	jkqtpStatGenerateRegressionModel (JKQTPStatRegressionModelType type, double a, double b)
	Generates functors `f(x)` for the models from JKQTPStatRegressionModelType in type and binds the parameter values and b to the returned function.

jkqtmath_LIB_EXPORT std::pair< std::function< double(double)>, std::function< double(double)> >	jkqtpStatGenerateTransformation (JKQTPStatRegressionModelType type)
	Generates the transformation function for x-data (`result.first` ) and y-data (`result.second` ) for each regression model in JKQTPStatRegressionModelType in type.

template<class InputItX , class InputItY >
void	jkqtpstatLinearRegression (InputItX firstX, InputItX lastX, InputItY firstY, InputItY lastY, double &coeffA, double &coeffB, bool fixA=false, bool fixB=false)
	calculate the linear regression coefficients for a given data range firstX / firstY ... lastX / lastY where the model is $f(x)=a+b\cdot x$ So this function solves the least-squares optimization problem:

template<class InputItX , class InputItY , class InputItW >
void	jkqtpstatLinearWeightedRegression (InputItX firstX, InputItX lastX, InputItY firstY, InputItY lastY, InputItW firstW, InputItW lastW, double &coeffA, double &coeffB, bool fixA=false, bool fixB=false, std::function< double(double)> fWeightDataToWi=&jkqtp_identity< double >)
	calculate the weighted linear regression coefficients for a given for a given data range firstX / firstY / firstW ... lastX / lastY / lastW where the model is $f(x)=a+b\cdot x$ So this function solves the least-squares optimization problem:

template<class InputItX , class InputItY >
void	jkqtpstatRegression (JKQTPStatRegressionModelType type, InputItX firstX, InputItX lastX, InputItY firstY, InputItY lastY, double &coeffA, double &coeffB, bool fixA=false, bool fixB=false)
	calculate the linear regression coefficients for a given data range firstX / firstY ... lastX / lastY where the model is defined by type So this function solves the least-squares optimization problem:

jkqtmath_LIB_EXPORT QString	jkqtpstatRegressionModel2Latex (JKQTPStatRegressionModelType type, double a, double b)
	Generates a LaTeX string for the models from JKQTPStatRegressionModelType in type.

template<class InputItX , class InputItY >
void	jkqtpstatRobustIRLSLinearRegression (InputItX firstX, InputItX lastX, InputItY firstY, InputItY lastY, double &coeffA, double &coeffB, bool fixA=false, bool fixB=false, double p=1.1, int iterations=100)
	calculate the (robust) iteratively reweighted least-squares (IRLS) estimate for the parameters of the model $f(x)=a+b\cdot x$ for a given data range firstX / firstY ... lastX / lastY So this function finds an outlier-robust solution to the optimization problem:

template<class InputItX , class InputItY >
void	jkqtpstatRobustIRLSRegression (JKQTPStatRegressionModelType type, InputItX firstX, InputItX lastX, InputItY firstY, InputItY lastY, double &coeffA, double &coeffB, bool fixA=false, bool fixB=false, double p=1.1, int iterations=100)
	calculate the robust linear regression coefficients for a given data range firstX / firstY ... lastX / lastY where the model is defined by type So this function solves the Lp-norm optimization problem:

template<class InputItX , class InputItY >
double	jkqtpstatSumOfDeviations (InputItX firstX, InputItX lastX, InputItY firstY, InputItY lastY, std::function< double(double)> f)
	calculates the sum of deviations $\chi^2$ for a set of measurements with a fit function

template<class InputItX , class InputItY , class InputItW >
double	jkqtpstatWeightedCoefficientOfDetermination (InputItX firstX, InputItX lastX, InputItY firstY, InputItY lastY, InputItW firstW, InputItW lastW, std::function< double(double)> f, std::function< double(double)> fWeightDataToWi=&jkqtp_identity< double >)
	calculates the weightedcoefficient of determination for a set of measurements with a fit function

template<class InputItX , class InputItY , class InputItW >
void	jkqtpstatWeightedRegression (JKQTPStatRegressionModelType type, InputItX firstX, InputItX lastX, InputItY firstY, InputItY lastY, InputItW firstW, InputItW lastW, double &coeffA, double &coeffB, bool fixA=false, bool fixB=false, std::function< double(double)> fWeightDataToWi=&jkqtp_identity< double >)
	calculate the robust linear regression coefficients for a given data range firstX / firstY ... lastX / lastY where the model is defined by type So this function solves the Lp-norm optimization problem:

template<class InputItX , class InputItY , class InputItW >
double	jkqtpstatWeightedSumOfDeviations (InputItX firstX, InputItX lastX, InputItY firstY, InputItY lastY, InputItW firstW, InputItW lastW, std::function< double(double)> f, std::function< double(double)> fWeightDataToWi=&jkqtp_identity< double >)
	calculates the weighted sum of deviations $\chi^2$ for a set of measurements with a fit function

Detailed Description

Enumeration Type Documentation

◆ JKQTPStatRegressionModelType

enum class JKQTPStatRegressionModelType

strong

when performing linear regression, different target functions can be fitted, if the input data is transformed accordingly. This library provides the options in this enum by default.

Enumerator
Linear	linear model $f(x)=a+b\cdot x$
PowerLaw	power law model $f(x)=a\cdot x^b$
Exponential	exponential model $f(x)=a\cdot \exp(b\cdot x)$
Logarithm	exponential model $f(x)=a+b\cdot \ln(x)$

Function Documentation

◆ jkqtpstatCoefficientOfDetermination()

template<class InputItX , class InputItY >

double jkqtpstatCoefficientOfDetermination	(	InputItX	firstX,
		InputItX	lastX,
		InputItY	firstY,
		InputItY	lastY,
		std::function< double(double)>	f
	)

inline

calculates the coefficient of determination for a set of measurements with a fit function

Template Parameters

InputItX	standard iterator type of firstX and lastX.
InputItY	standard iterator type of firstY and lastY.

Parameters

firstX	iterator pointing to the first item in the x-dataset to use
lastX	iterator pointing behind the last item in the x-dataset to use
firstY	iterator pointing to the first item in the y-dataset to use
lastY	iterator pointing behind the last item in the y-dataset to use
f	function , result of a fit to the data

Returns

coeffcicient of determination

$R^2=1-\frac{\sum_i\bigl[y_i-f(x_i)\bigr]^2}{\sum_i\bigl[y_i-\overline{y}\bigr]^2}$

where

$\overline{y}=\frac{1}{N}\cdot\sum_iy_i$

See also: https://en.wikipedia.org/wiki/Coefficient_of_determination

◆ jkqtpStatGenerateParameterATransformation()

jkqtmath_LIB_EXPORT std::pair< std::function< double(double)>, std::function< double(double)> > jkqtpStatGenerateParameterATransformation ( JKQTPStatRegressionModelType type )

Generates the transformation function for a-parameter (offset, result.first : transform, result.second : back-transform) for each regression model in JKQTPStatRegressionModelType in type.

◆ jkqtpStatGenerateParameterBTransformation()

jkqtmath_LIB_EXPORT std::pair< std::function< double(double)>, std::function< double(double)> > jkqtpStatGenerateParameterBTransformation ( JKQTPStatRegressionModelType type )

Generates the transformation function for b-parameter (slope, result.first : transform, result.second : back-transform) for each regression model in JKQTPStatRegressionModelType in type.

◆ jkqtpStatGenerateRegressionModel() [1/2]

jkqtmath_LIB_EXPORT std::function< double(double, double, double)> jkqtpStatGenerateRegressionModel ( JKQTPStatRegressionModelType type )

Generates functors f(x,a,b) for the models from JKQTPStatRegressionModelType in type.

◆ jkqtpStatGenerateRegressionModel() [2/2]

jkqtmath_LIB_EXPORT std::function< double(double)> jkqtpStatGenerateRegressionModel	(	JKQTPStatRegressionModelType	type,
		double	a,
		double	b
	)

Generates functors f(x) for the models from JKQTPStatRegressionModelType in type and binds the parameter values and b to the returned function.

◆ jkqtpStatGenerateTransformation()

jkqtmath_LIB_EXPORT std::pair< std::function< double(double)>, std::function< double(double)> > jkqtpStatGenerateTransformation ( JKQTPStatRegressionModelType type )

Generates the transformation function for x-data (result.first ) and y-data (result.second ) for each regression model in JKQTPStatRegressionModelType in type.

◆ jkqtpstatLinearRegression()

template<class InputItX , class InputItY >

void jkqtpstatLinearRegression	(	InputItX	firstX,
		InputItX	lastX,
		InputItY	firstY,
		InputItY	lastY,
		double &	coeffA,
		double &	coeffB,
		bool	fixA = `false`,
		bool	fixB = `false`
	)

inline

calculate the linear regression coefficients for a given data range firstX / firstY ... lastX / lastY where the model is $f(x)=a+b\cdot x$ So this function solves the least-squares optimization problem:

$(a^\ast, b^\ast)=\mathop{\mathrm{arg\;min}}\limits_{a,b}\sum\limits_i\left(y_i-(a+b\cdot x_i)\right)^2$

Template Parameters

InputItX	standard iterator type of firstX and lastX.
InputItY	standard iterator type of firstY and lastY.

Parameters

	firstX	iterator pointing to the first item in the x-dataset to use
	lastX	iterator pointing behind the last item in the x-dataset to use
	firstY	iterator pointing to the first item in the y-dataset to use
	lastY	iterator pointing behind the last item in the y-dataset to use
[in,out]	coeffA	returns the offset of the linear model
[in,out]	coeffB	returns the slope of the linear model
	fixA	if `true`, the offset coefficient is not determined by the fit, but the value provided in coeffA is used
	fixB	if `true`, the slope coefficient is not determined by the fit, but the value provided in coeffB is used

This function computes internally:

$a=\overline{y}-b\cdot\overline{x}$

$b=\frac{\sum x_iy_i-N\cdot\overline{x}\cdot\overline{y}}{\sum x_i^2-N\cdot(\overline{x})^2}$

◆ jkqtpstatLinearWeightedRegression()

template<class InputItX , class InputItY , class InputItW >

void jkqtpstatLinearWeightedRegression	(	InputItX	firstX,
		InputItX	lastX,
		InputItY	firstY,
		InputItY	lastY,
		InputItW	firstW,
		InputItW	lastW,
		double &	coeffA,
		double &	coeffB,
		bool	fixA = `false`,
		bool	fixB = `false`,
		std::function< double(double)>	fWeightDataToWi = `&jkqtp_identity<double>`
	)

inline

calculate the weighted linear regression coefficients for a given for a given data range firstX / firstY / firstW ... lastX / lastY / lastW where the model is $f(x)=a+b\cdot x$ So this function solves the least-squares optimization problem:

$(a^\ast, b^\ast)=\mathop{\mathrm{arg\;min}}\limits_{a,b}\sum\limits_iw_i^2\cdot\left(y_i-(a+b\cdot x_i)\right)^2$

Template Parameters

InputItX	standard iterator type of firstX and lastX.
InputItY	standard iterator type of firstY and lastY.
InputItW	standard iterator type of firstW and lastW.

Parameters

	firstX	iterator pointing to the first item in the x-dataset to use
	lastX	iterator pointing behind the last item in the x-dataset to use
	firstY	iterator pointing to the first item in the y-dataset to use
	lastY	iterator pointing behind the last item in the y-dataset to use
	firstW	iterator pointing to the first item in the weight-dataset to use
	lastW	iterator pointing behind the last item in the weight-dataset to use
[in,out]	coeffA	returns the offset of the linear model
[in,out]	coeffB	returns the slope of the linear model
	fixA	if `true`, the offset coefficient is not determined by the fit, but the value provided in coeffA is used
	fixB	if `true`, the slope coefficient is not determined by the fit, but the value provided in coeffB is used
	fWeightDataToWi	an optional function, which is applied to the data from firstW ... lastW to convert them to weight, i.e. `wi=fWeightDataToWi(*itW)` e.g. if you use data used to draw error bars, you can use jkqtp_inversePropSaveDefault(). The default is jkqtp_identity(), which just returns the values. In the case of jkqtp_inversePropSaveDefault(), a datapoint x,y, has a large weight, if it's error is small and in the case if jkqtp_identity() it's weight is directly proportional to the given value.

This function internally computes:

$a=\frac{\overline{y}-b\cdot\overline{x}}{\overline{w^2}}$

$b=\frac{\overline{w^2}\cdot\overline{x\cdot y}-\overline{x}\cdot\overline{y}}{\overline{x^2}\cdot\overline{w^2}-\overline{x}^2}$

Here the averages are defined in terms of a weight vector :

$\overline{x}=\sum\limits_iw_i^2\cdot x_i$

$\overline{y}=\sum\limits_iw_i^2\cdot y_i$

$\overline{x\cdot y}=\sum\limits_iw_i^2\cdot x_i\cdot y_i$

$\overline{x^2}=\sum\limits_iw_i^2\cdot x_i^2$

$\overline{w^2}=\sum\limits_iw_i^2$

◆ jkqtpstatRegression()

template<class InputItX , class InputItY >

void jkqtpstatRegression	(	JKQTPStatRegressionModelType	type,
		InputItX	firstX,
		InputItX	lastX,
		InputItY	firstY,
		InputItY	lastY,
		double &	coeffA,
		double &	coeffB,
		bool	fixA = `false`,
		bool	fixB = `false`
	)

inline

calculate the linear regression coefficients for a given data range firstX / firstY ... lastX / lastY where the model is defined by type So this function solves the least-squares optimization problem:

$(a^\ast, b^\ast)=\mathop{\mathrm{arg\;min}}\limits_{a,b}\sum\limits_i\left(y_i-f_{\text{type}}(x_i,a,b)\right)^2$

by reducing it to a linear fit by transforming x- and/or y-data

Template Parameters

InputItX	standard iterator type of firstX and lastX.
InputItY	standard iterator type of firstY and lastY.

Parameters

	type	model to be fitted
	firstX	iterator pointing to the first item in the x-dataset to use
	lastX	iterator pointing behind the last item in the x-dataset to use
	firstY	iterator pointing to the first item in the y-dataset to use
	lastY	iterator pointing behind the last item in the y-dataset to use
[in,out]	coeffA	returns the offset of the linear model
[in,out]	coeffB	returns the slope of the linear model
	fixA	if `true`, the offset coefficient is not determined by the fit, but the value provided in coeffA is used
	fixB	if `true`, the slope coefficient is not determined by the fit, but the value provided in coeffB is used

This function computes internally first transforms the data, as appropriate to fit the model defined by type and then calls jkqtpstatLinearRegression() to obtain the parameters. The output parameters are transformed, so they can be used with jkqtpStatGenerateRegressionModel() to generate a functor that evaluates the model

See also: JKQTPStatRegressionModelType, jkqtpStatGenerateRegressionModel(), jkqtpstatLinearRegression(), jkqtpStatGenerateTransformation()

◆ jkqtpstatRegressionModel2Latex()

jkqtmath_LIB_EXPORT QString jkqtpstatRegressionModel2Latex	(	JKQTPStatRegressionModelType	type,
		double	a,
		double	b
	)

Generates a LaTeX string for the models from JKQTPStatRegressionModelType in type.

◆ jkqtpstatRobustIRLSLinearRegression()

template<class InputItX , class InputItY >

void jkqtpstatRobustIRLSLinearRegression	(	InputItX	firstX,
		InputItX	lastX,
		InputItY	firstY,
		InputItY	lastY,
		double &	coeffA,
		double &	coeffB,
		bool	fixA = `false`,
		bool	fixB = `false`,
		double	p = `1.1`,
		int	iterations = `100`
	)

inline

calculate the (robust) iteratively reweighted least-squares (IRLS) estimate for the parameters of the model $f(x)=a+b\cdot x$ for a given data range firstX / firstY ... lastX / lastY So this function finds an outlier-robust solution to the optimization problem:

$(a^\ast,b^\ast)=\mathop{\mathrm{arg\;min}}\limits_{a,b}\sum\limits_i|a+b\cdot x_i-y_i|^p$

Template Parameters

InputItX	standard iterator type of firstX and lastX.
InputItY	standard iterator type of firstY and lastY.

Parameters

	firstX	iterator pointing to the first item in the x-dataset to use
	lastX	iterator pointing behind the last item in the x-dataset to use
	firstY	iterator pointing to the first item in the y-dataset to use
	lastY	iterator pointing behind the last item in the y-dataset to use
[in,out]	coeffA	returns the offset of the linear model
[in,out]	coeffB	returns the slope of the linear model
	fixA	if `true`, the offset coefficient is not determined by the fit, but the value provided in coeffA is used
	fixB	if `true`, the slope coefficient is not determined by the fit, but the value provided in coeffB is used
	p	regularization parameter, the optimization problem is formulated in the norm, using this p (see image below for an example)
	iterations	the number of iterations the IRLS algorithm performs

This is a simple form of the IRLS algorithm to estimate the parameters a and b in a linear model $f(x)=a+b\cdot x$ . This algorithm solves the optimization problem for a -norm:

$(a^\ast,b^\ast)=\mathop{\mathrm{arg\;min}}\limits_{a,b}\sum\limits_i|a+b\cdot x_i-y_i|^p$

by iteratively optimization weights $\vec{w}$ and solving a weighted least squares problem in each iteration:

$(a_n,b_n)=\mathop{\mathrm{arg\;min}}\limits_{a,b}\sum\limits_i|a+b\cdot x_i-y_i|^{(p-2)}\cdot|a+b\cdot x_i-y_i|^2$

The IRLS-algorithm works as follows:

calculate initial and with unweighted regression from x and y
perform a number of iterations (parameter iterations ). In each iteration :
- calculate the error vector $\vec{e}$ :
  $e_i = a+b\cdot x_i -y_i$
- estimate new weights $\vec{w}$ :
  $w_i=|e_i|^{(p-2)/2}$
- calculate new estimates and with weighted regression from $\vec{x}$ and $\vec{y}$ and $\vec{w}$

return the last estimates and

See also: https://en.wikipedia.org/wiki/Iteratively_reweighted_least_squares, C. Sidney Burrus: "Iterative Reweighted Least Squares", http://cnx.org/content/m45285/latest/

◆ jkqtpstatRobustIRLSRegression()

template<class InputItX , class InputItY >

void jkqtpstatRobustIRLSRegression	(	JKQTPStatRegressionModelType	type,
		InputItX	firstX,
		InputItX	lastX,
		InputItY	firstY,
		InputItY	lastY,
		double &	coeffA,
		double &	coeffB,
		bool	fixA = `false`,
		bool	fixB = `false`,
		double	p = `1.1`,
		int	iterations = `100`
	)

inline

calculate the robust linear regression coefficients for a given data range firstX / firstY ... lastX / lastY where the model is defined by type So this function solves the Lp-norm optimization problem:

$(a^\ast, b^\ast)=\mathop{\mathrm{arg\;min}}\limits_{a,b}\sum\limits_i|y_i-f_{\text{type}}(x_i,a,b)|^p$

by reducing it to a linear fit by transforming x- and/or y-data

Template Parameters

InputItX	standard iterator type of firstX and lastX.
InputItY	standard iterator type of firstY and lastY.

Parameters

	type	model to be fitted
	firstX	iterator pointing to the first item in the x-dataset to use
	lastX	iterator pointing behind the last item in the x-dataset to use
	firstY	iterator pointing to the first item in the y-dataset to use
	lastY	iterator pointing behind the last item in the y-dataset to use
[in,out]	coeffA	returns the offset of the linear model
[in,out]	coeffB	returns the slope of the linear model
	fixA	if `true`, the offset coefficient is not determined by the fit, but the value provided in coeffA is used
	fixB	if `true`, the slope coefficient is not determined by the fit, but the value provided in coeffB is used
	p	regularization parameter, the optimization problem is formulated in the norm, using this p (see image below for an example)
	iterations	the number of iterations the IRLS algorithm performs

This function computes internally first transforms the data, as appropriate to fit the model defined by type and then calls jkqtpstatRobustIRLSLinearRegression() to obtain the parameters. The output parameters are transformed, so they can be used with jkqtpStatGenerateRegressionModel() to generate a functor that evaluates the model

See also: JKQTPStatRegressionModelType, jkqtpStatGenerateRegressionModel(), jkqtpstatRobustIRLSLinearRegression(), jkqtpStatGenerateTransformation()

◆ jkqtpstatSumOfDeviations()

template<class InputItX , class InputItY >

double jkqtpstatSumOfDeviations	(	InputItX	firstX,
		InputItX	lastX,
		InputItY	firstY,
		InputItY	lastY,
		std::function< double(double)>	f
	)

inline

calculates the sum of deviations $\chi^2$ for a set of measurements with a fit function

Template Parameters

InputItX	standard iterator type of firstX and lastX.
InputItY	standard iterator type of firstY and lastY.

Parameters

firstX	iterator pointing to the first item in the x-dataset to use
lastX	iterator pointing behind the last item in the x-dataset to use
firstY	iterator pointing to the first item in the y-dataset to use
lastY	iterator pointing behind the last item in the y-dataset to use
f	function , result of a fit to the data

Returns: sum of deviations
$\chi^2=\sum_i\bigl[y_i-f(x_i)\bigr]^2$

See also: https://en.wikipedia.org/wiki/Coefficient_of_determination

◆ jkqtpstatWeightedCoefficientOfDetermination()

template<class InputItX , class InputItY , class InputItW >

double jkqtpstatWeightedCoefficientOfDetermination	(	InputItX	firstX,
		InputItX	lastX,
		InputItY	firstY,
		InputItY	lastY,
		InputItW	firstW,
		InputItW	lastW,
		std::function< double(double)>	f,
		std::function< double(double)>	fWeightDataToWi = `&jkqtp_identity<double>`
	)

inline

calculates the weightedcoefficient of determination for a set of measurements with a fit function

Template Parameters

InputItX	standard iterator type of firstX and lastX.
InputItY	standard iterator type of firstY and lastY.
InputItW	standard iterator type of firstW and lastW.

Parameters

firstX	iterator pointing to the first item in the x-dataset to use
lastX	iterator pointing behind the last item in the x-dataset to use
firstY	iterator pointing to the first item in the y-dataset to use
lastY	iterator pointing behind the last item in the y-dataset to use
firstW	iterator pointing to the first item in the weight-dataset to use
lastW	iterator pointing behind the last item in the weight-dataset to use
f	function , result of a fit to the data
fWeightDataToWi	an optional function, which is applied to the data from firstW ... lastW to convert them to weight, i.e. `wi=fWeightDataToWi(*itW)` e.g. if you use data used to draw error bars, you can use jkqtp_inversePropSaveDefault(). The default is jkqtp_identity(), which just returns the values. In the case of jkqtp_inversePropSaveDefault(), a datapoint x,y, has a large weight, if it's error is small and in the case if jkqtp_identity() it's weight is directly proportional to the given value.

Returns

weighted coeffcicient of determination

$R^2=1-\frac{\sum_iw_i^2\bigl[y_i-f(x_i)\bigr]^2}{\sum_iw_i^2\bigl[y_i-\overline{y}\bigr]^2}$

where

$\overline{y}=\frac{1}{N}\cdot\sum_iw_iy_i$

with

$\sum_iw_i=1$

See also: https://en.wikipedia.org/wiki/Coefficient_of_determination

◆ jkqtpstatWeightedRegression()

template<class InputItX , class InputItY , class InputItW >

void jkqtpstatWeightedRegression	(	JKQTPStatRegressionModelType	type,
		InputItX	firstX,
		InputItX	lastX,
		InputItY	firstY,
		InputItY	lastY,
		InputItW	firstW,
		InputItW	lastW,
		double &	coeffA,
		double &	coeffB,
		bool	fixA = `false`,
		bool	fixB = `false`,
		std::function< double(double)>	fWeightDataToWi = `&jkqtp_identity<double>`
	)

inline

calculate the robust linear regression coefficients for a given data range firstX / firstY ... lastX / lastY where the model is defined by type So this function solves the Lp-norm optimization problem:

$(a^\ast, b^\ast)=\mathop{\mathrm{arg\;min}}\limits_{a,b}\sum\limits_iw_i^2\left(y_i-f_{\text{type}}(x_i,a,b)\right)^2$

by reducing it to a linear fit by transforming x- and/or y-data

Template Parameters

InputItX	standard iterator type of firstX and lastX.
InputItY	standard iterator type of firstY and lastY.
InputItW	standard iterator type of firstW and lastW.

Parameters

	type	model to be fitted
	firstX	iterator pointing to the first item in the x-dataset to use
	lastX	iterator pointing behind the last item in the x-dataset to use
	firstY	iterator pointing to the first item in the y-dataset to use
	lastY	iterator pointing behind the last item in the y-dataset to use
	firstW	iterator pointing to the first item in the weight-dataset to use
	lastW	iterator pointing behind the last item in the weight-dataset to use
[in,out]	coeffA	returns the offset of the linear model
[in,out]	coeffB	returns the slope of the linear model
	fixA	if `true`, the offset coefficient is not determined by the fit, but the value provided in coeffA is used
	fixB	if `true`, the slope coefficient is not determined by the fit, but the value provided in coeffB is used
	fWeightDataToWi	an optional function, which is applied to the data from firstW ... lastW to convert them to weight, i.e. `wi=fWeightDataToWi(*itW)` e.g. if you use data used to draw error bars, you can use jkqtp_inversePropSaveDefault(). The default is jkqtp_identity(), which just returns the values. In the case of jkqtp_inversePropSaveDefault(), a datapoint x,y, has a large weight, if it's error is small and in the case if jkqtp_identity() it's weight is directly proportional to the given value.

This function computes internally first transforms the data, as appropriate to fit the model defined by type and then calls jkqtpstatLinearWeightedRegression() to obtain the parameters. The output parameters are transformed, so they can be used with jkqtpStatGenerateRegressionModel() to generate a functor that evaluates the model

See also: JKQTPStatRegressionModelType, jkqtpStatGenerateRegressionModel(), jkqtpstatLinearWeightedRegression(), jkqtpStatGenerateTransformation()

◆ jkqtpstatWeightedSumOfDeviations()

template<class InputItX , class InputItY , class InputItW >

double jkqtpstatWeightedSumOfDeviations	(	InputItX	firstX,
		InputItX	lastX,
		InputItY	firstY,
		InputItY	lastY,
		InputItW	firstW,
		InputItW	lastW,
		std::function< double(double)>	f,
		std::function< double(double)>	fWeightDataToWi = `&jkqtp_identity<double>`
	)

inline

calculates the weighted sum of deviations $\chi^2$ for a set of measurements with a fit function

Template Parameters

InputItX	standard iterator type of firstX and lastX.
InputItY	standard iterator type of firstY and lastY.
InputItW	standard iterator type of firstW and lastW.

Parameters

firstX	iterator pointing to the first item in the x-dataset to use
lastX	iterator pointing behind the last item in the x-dataset to use
firstY	iterator pointing to the first item in the y-dataset to use
lastY	iterator pointing behind the last item in the y-dataset to use
firstW	iterator pointing to the first item in the weight-dataset to use
lastW	iterator pointing behind the last item in the weight-dataset to use
f	function , result of a fit to the data
fWeightDataToWi	an optional function, which is applied to the data from firstW ... lastW to convert them to weight, i.e. `wi=fWeightDataToWi(*itW)` e.g. if you use data used to draw error bars, you can use jkqtp_inversePropSaveDefault(). The default is jkqtp_identity(), which just returns the values. In the case of jkqtp_inversePropSaveDefault(), a datapoint x,y, has a large weight, if it's error is small and in the case if jkqtp_identity() it's weight is directly proportional to the given value.

Returns: weighted sum of deviations
$\chi^2=\sum_iw_i^2\cdot\bigl[y_i-f(x_i)\bigr]^2$

See also: https://en.wikipedia.org/wiki/Reduced_chi-squared_statistic

Enumerations

Functions

Detailed Description

Enumeration Type Documentation

◆ JKQTPStatRegressionModelType

Function Documentation

◆ jkqtpstatCoefficientOfDetermination()

◆ jkqtpStatGenerateParameterATransformation()

◆ jkqtpStatGenerateParameterBTransformation()

◆ jkqtpStatGenerateRegressionModel() [1/2]

◆ jkqtpStatGenerateRegressionModel() [2/2]

◆ jkqtpStatGenerateTransformation()

◆ jkqtpstatLinearRegression()

◆ jkqtpstatLinearWeightedRegression()

◆ jkqtpstatRegression()

◆ jkqtpstatRegressionModel2Latex()

◆ jkqtpstatRobustIRLSLinearRegression()

◆ jkqtpstatRobustIRLSRegression()

◆ jkqtpstatSumOfDeviations()

◆ jkqtpstatWeightedCoefficientOfDetermination()

◆ jkqtpstatWeightedRegression()

◆ jkqtpstatWeightedSumOfDeviations()