LinearRegression Class Reference

This class offers functions to perform least-squares fits to a straight line model, \( Y(c,x) = c_0 + c_1 x \). More...

#include <OpenMS/ML/REGRESSION/LinearRegression.h>

Collaboration diagram for LinearRegression:

Public Member Functions
	LinearRegression ()
	Constructor.
virtual	~LinearRegression ()=default
	Destructor.
void	computeRegression (double confidence_interval_P, std::vector< double >::const_iterator x_begin, std::vector< double >::const_iterator x_end, std::vector< double >::const_iterator y_begin, bool compute_goodness=true)
	This function computes the best-fit linear regression coefficients \( (c_0,c_1) \) of the model \( Y = c_0 + c_1 X \) for the dataset \( (x, y) \).
void	computeRegressionWeighted (double confidence_interval_P, std::vector< double >::const_iterator x_begin, std::vector< double >::const_iterator x_end, std::vector< double >::const_iterator y_begin, std::vector< double >::const_iterator w_begin, bool compute_goodness=true)
	This function computes the best-fit linear regression coefficients \( (c_0,c_1) \) of the model \( Y = c_0 + c_1 X \) for the weighted dataset \( (x, y) \).
double	getIntercept () const
	Non-mutable access to the y-intercept of the straight line.
double	getSlope () const
	Non-mutable access to the slope of the straight line.
double	getXIntercept () const
	Non-mutable access to the x-intercept of the straight line.
double	getLower () const
	Non-mutable access to the lower border of confidence interval.
double	getUpper () const
	Non-mutable access to the upper border of confidence interval.
double	getTValue () const
	Non-mutable access to the value of the t-distribution.
double	getRSquared () const
	Non-mutable access to the squared Pearson coefficient.
double	getStandDevRes () const
	Non-mutable access to the standard deviation of the residuals.
double	getMeanRes () const
	Non-mutable access to the residual mean.
double	getStandErrSlope () const
	Non-mutable access to the standard error of the slope.
double	getChiSquared () const
	Non-mutable access to the chi squared value.
double	getRSD () const
	Non-mutable access to relative standard deviation.

Static Public Member Functions
static double	computePointY (double x, double slope, double intercept)
	given x compute y = slope * x + intercept

Protected Member Functions
void	computeGoodness_ (const std::vector< double > &X, const std::vector< double > &Y, double confidence_interval_P)
	Computes the goodness of the fitted regression line.
template<typename Iterator >
double	computeChiSquare (Iterator x_begin, Iterator x_end, Iterator y_begin, double slope, double intercept)
	Compute the chi squared of a linear fit.
template<typename Iterator >
double	computeWeightedChiSquare (Iterator x_begin, Iterator x_end, Iterator y_begin, Iterator w_begin, double slope, double intercept)
	Compute the chi squared of a weighted linear fit.

Protected Attributes
double	intercept_
	The intercept of the fitted line with the y-axis.
double	slope_
	The slope of the fitted line.
double	x_intercept_
	The intercept of the fitted line with the x-axis.
double	lower_
	The lower bound of the confidence interval.
double	upper_
	The upper bound of the confidence interval.
double	t_star_
	The value of the t-statistic.
double	r_squared_
	The squared correlation coefficient (Pearson)
double	stand_dev_residuals_
	The standard deviation of the residuals.
double	mean_residuals_
	Mean of residuals.
double	stand_error_slope_
	The standard error of the slope.
double	chi_squared_
	The value of the Chi Squared statistic.
double	rsd_
	the relative standard deviation

Private Member Functions
	LinearRegression (const LinearRegression &arg)
	Not implemented.
LinearRegression &	operator= (const LinearRegression &arg)
	Not implemented.

Detailed Description

This class offers functions to perform least-squares fits to a straight line model, \( Y(c,x) = c_0 + c_1 x \).

Next to the intercept with the y-axis and the slope of the fitted line, this class computes the:

• squared Pearson coefficient
• value of the t-distribution
• standard deviation of the residuals
• standard error of the slope
• intercept with the x-axis (useful for additive series experiments)
• lower border of confidence interval
• higher border of confidence interval
• chi squared value
• x mean

Constructor & Destructor Documentation

LinearRegression() [1/2]

LinearRegression ( )

inline

Constructor.

~LinearRegression()

virtual ~LinearRegression ( )

virtualdefault

Destructor.

LinearRegression() [2/2]

LinearRegression ( const LinearRegression &  arg )

private

Not implemented.

Member Function Documentation

computeChiSquare()

template<typename Iterator >

double computeChiSquare ( Iterator  x_begin, Iterator  x_end, Iterator  y_begin, double  slope, double  intercept  )

protected

Compute the chi squared of a linear fit.

References LinearRegression::computePointY().

computeGoodness_()

void computeGoodness_ ( const std::vector< double > &  X, const std::vector< double > &  Y, double  confidence_interval_P  )

protected

Computes the goodness of the fitted regression line.

computePointY()

static double computePointY ( double  x, double  slope, double  intercept  )

inlinestatic

given x compute y = slope * x + intercept

Referenced by LinearRegression::computeChiSquare(), and LinearRegression::computeWeightedChiSquare().

computeRegression()

void computeRegression	(	double	confidence_interval_P,
		std::vector< double >::const_iterator	x_begin,
		std::vector< double >::const_iterator	x_end,
		std::vector< double >::const_iterator	y_begin,
		bool	compute_goodness = true
	)

This function computes the best-fit linear regression coefficients \( (c_0,c_1) \) of the model \( Y = c_0 + c_1 X \) for the dataset \( (x, y) \).

The values in x-dimension of the dataset \( (x,y) \) are given by the iterator range [x_begin,x_end) and the corresponding y-values start at position y_begin.

For a "x %" Confidence Interval use confidence_interval_P = x/100. For example the 95% Confidence Interval is supposed to be an interval that has a 95% chance of containing the true value of the parameter.

Parameters

[in]	confidence_interval_P	Value between 0-1 to determine lower and upper CI borders.
[in]	x_begin	Begin iterator of x values
[in]	x_end	End iterator of x values
[in]	y_begin	Begin iterator of y values (same length as x)
[in]	compute_goodness	Compute meta stats about the fit. If this is not done, none of the members (except slope and intercept) are meaningful.

Exceptions

Exception::UnableToFit

is thrown if fitting cannot be performed

computeRegressionWeighted()

void computeRegressionWeighted	(	double	confidence_interval_P,
		std::vector< double >::const_iterator	x_begin,
		std::vector< double >::const_iterator	x_end,
		std::vector< double >::const_iterator	y_begin,
		std::vector< double >::const_iterator	w_begin,
		bool	compute_goodness = true
	)

This function computes the best-fit linear regression coefficients \( (c_0,c_1) \) of the model \( Y = c_0 + c_1 X \) for the weighted dataset \( (x, y) \).

The values in x-dimension of the dataset \( (x, y) \) are given by the iterator range [x_begin,x_end) and the corresponding y-values start at position y_begin. They will be weighted by the values starting at w_begin.

For a "x %" Confidence Interval use confidence_interval_P = x/100. For example the 95% Confidence Interval is supposed to be an interval that has a 95% chance of containing the true value of the parameter.

Parameters

[in]	confidence_interval_P	Value between 0-1 to determine lower and upper CI borders.
[in]	x_begin	Begin iterator of x values
[in]	x_end	End iterator of x values
[in]	y_begin	Begin iterator of y values (same length as x)
[in]	w_begin	Begin iterator of weight values (same length as x)
[in]	compute_goodness	Compute meta stats about the fit. If this is not done, none of the members (except slope and intercept) are meaningful.

Exceptions

Exception::UnableToFit

is thrown if fitting cannot be performed

computeWeightedChiSquare()

template<typename Iterator >

double computeWeightedChiSquare ( Iterator  x_begin, Iterator  x_end, Iterator  y_begin, Iterator  w_begin, double  slope, double  intercept  )

protected

Compute the chi squared of a weighted linear fit.

References LinearRegression::computePointY().

getChiSquared()

double getChiSquared

(

)

const

Non-mutable access to the chi squared value.

getIntercept()

double getIntercept

(

)

const

Non-mutable access to the y-intercept of the straight line.

getLower()

double getLower

(

)

const

Non-mutable access to the lower border of confidence interval.

getMeanRes()

double getMeanRes

(

)

const

Non-mutable access to the residual mean.

getRSD()

double getRSD

(

)

const

Non-mutable access to relative standard deviation.

getRSquared()

double getRSquared

(

)

const

Non-mutable access to the squared Pearson coefficient.

getSlope()

double getSlope

(

)

const

Non-mutable access to the slope of the straight line.

getStandDevRes()

double getStandDevRes

(

)

const

Non-mutable access to the standard deviation of the residuals.

getStandErrSlope()

double getStandErrSlope

(

)

const

Non-mutable access to the standard error of the slope.

getTValue()

double getTValue

(

)

const

Non-mutable access to the value of the t-distribution.

getUpper()

double getUpper

(

)

const

Non-mutable access to the upper border of confidence interval.

getXIntercept()

double getXIntercept

(

)

const

Non-mutable access to the x-intercept of the straight line.

operator=()

LinearRegression & operator= ( const LinearRegression &  arg )

private

Not implemented.

Member Data Documentation

chi_squared_

double chi_squared_

protected

The value of the Chi Squared statistic.

intercept_

double intercept_

protected

The intercept of the fitted line with the y-axis.

lower_

double lower_

protected

The lower bound of the confidence interval.

mean_residuals_

double mean_residuals_

protected

Mean of residuals.

r_squared_

double r_squared_

protected

The squared correlation coefficient (Pearson)

rsd_

double rsd_

protected

the relative standard deviation

slope_

double slope_

protected

The slope of the fitted line.

stand_dev_residuals_

double stand_dev_residuals_

protected

The standard deviation of the residuals.

stand_error_slope_

double stand_error_slope_

protected

The standard error of the slope.

t_star_

double t_star_

protected

The value of the t-statistic.

upper_

double upper_

protected

The upper bound of the confidence interval.

x_intercept_

double x_intercept_

protected

The intercept of the fitted line with the x-axis.