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/MATH/STATISTICS/LinearRegression.h>

Collaboration diagram for LinearRegression:

Public Member Functions
	LinearRegression ()
	Constructor. More...

virtual	~LinearRegression ()
	Destructor. More...

template<typename Iterator >
void	computeRegression (double confidence_interval_P, Iterator x_begin, Iterator x_end, Iterator y_begin, bool compute_goodness=true)
	This function computes the best-fit linear regression coefficients of the model for the dataset . More...

template<typename Iterator >
void	computeRegressionWeighted (double confidence_interval_P, Iterator x_begin, Iterator x_end, Iterator y_begin, Iterator w_begin, bool compute_goodness=true)
	This function computes the best-fit linear regression coefficients of the model for the weighted dataset . More...

double	getIntercept () const
	Non-mutable access to the y-intercept of the straight line. More...

double	getSlope () const
	Non-mutable access to the slope of the straight line. More...

double	getXIntercept () const
	Non-mutable access to the x-intercept of the straight line. More...

double	getLower () const
	Non-mutable access to the lower border of confidence interval. More...

double	getUpper () const
	Non-mutable access to the upper border of confidence interval. More...

double	getTValue () const
	Non-mutable access to the value of the t-distribution. More...

double	getRSquared () const
	Non-mutable access to the squared Pearson coefficient. More...

double	getStandDevRes () const
	Non-mutable access to the standard deviation of the residuals. More...

double	getMeanRes () const
	Non-mutable access to the residual mean. More...

double	getStandErrSlope () const
	Non-mutable access to the standard error of the slope. More...

double	getChiSquared () const
	Non-mutable access to the chi squared value. More...

double	getRSD () const
	Non-mutable access to relative standard deviation. More...

Protected Member Functions
void	computeGoodness_ (const std::vector< Wm5::Vector2d > &points, double confidence_interval_P)
	Computes the goodness of the fitted regression line. More...

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. More...

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. More...

Protected Attributes
double	intercept_
	The intercept of the fitted line with the y-axis. More...

double	slope_
	The slope of the fitted line. More...

double	x_intercept_
	The intercept of the fitted line with the x-axis. More...

double	lower_
	The lower bound of the confidence interval. More...

double	upper_
	The upper bound of the confidence interval. More...

double	t_star_
	The value of the t-statistic. More...

double	r_squared_
	The squared correlation coefficient (Pearson) More...

double	stand_dev_residuals_
	The standard deviation of the residuals. More...

double	mean_residuals_
	Mean of residuals. More...

double	stand_error_slope_
	The standard error of the slope. More...

double	chi_squared_
	The value of the Chi Squared statistic. More...

double	rsd_
	the relative standard deviation More...

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

LinearRegression &	operator= (const LinearRegression &arg)
	Not implemented. More...

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 ( )

inlinevirtual

Destructor.

◆ LinearRegression() [2/2]

LinearRegression ( const LinearRegression & arg )

private

Not implemented.

Member Function Documentation

◆ computeChiSquare()

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

protected

Compute the chi squared of a linear fit.

Referenced by LinearRegression::computeRegression().

◆ computeGoodness_()

void computeGoodness_	(	const std::vector< Wm5::Vector2d > &	points,
		double	confidence_interval_P
	)

protected

Computes the goodness of the fitted regression line.

Referenced by LinearRegression::computeRegression(), and LinearRegression::computeRegressionWeighted().

◆ computeRegression()

void computeRegression	(	double	confidence_interval_P,
		Iterator	x_begin,
		Iterator	x_end,
		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

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

Returns: If an error occurred during the fit.

Exceptions

Exception::UnableToFit is thrown if fitting cannot be performed

References LinearRegression::chi_squared_, LinearRegression::computeChiSquare(), LinearRegression::computeGoodness_(), LinearRegression::intercept_, OpenMS::Math::iteratorRange2Wm5Vectors(), and LinearRegression::slope_.

◆ computeRegressionWeighted()

void computeRegressionWeighted	(	double	confidence_interval_P,
		Iterator	x_begin,
		Iterator	x_end,
		Iterator	y_begin,
		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

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

Returns: If an error occurred during the fit.

Exceptions

Exception::UnableToFit is thrown if fitting cannot be performed

References LinearRegression::chi_squared_, LinearRegression::computeGoodness_(), LinearRegression::computeWeightedChiSquare(), LinearRegression::intercept_, OpenMS::Math::iteratorRange2Wm5Vectors(), and LinearRegression::slope_.

◆ computeWeightedChiSquare()

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.

Referenced by LinearRegression::computeRegressionWeighted().

◆ 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.

Referenced by LinearRegression::computeRegression(), and LinearRegression::computeRegressionWeighted().

◆ intercept_

double intercept_

protected

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

Referenced by LinearRegression::computeRegression(), and LinearRegression::computeRegressionWeighted().

◆ 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.

Referenced by LinearRegression::computeRegression(), and LinearRegression::computeRegressionWeighted().

◆ 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.

Public Member Functions

Protected Member Functions

Protected Attributes

Private Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ LinearRegression() [1/2]

◆ ~LinearRegression()

◆ LinearRegression() [2/2]

Member Function Documentation

◆ computeChiSquare()

◆ computeGoodness_()

◆ computeRegression()

◆ computeRegressionWeighted()

◆ computeWeightedChiSquare()

◆ getChiSquared()

◆ getIntercept()

◆ getLower()

◆ getMeanRes()

◆ getRSD()

◆ getRSquared()

◆ getSlope()

◆ getStandDevRes()

◆ getStandErrSlope()

◆ getTValue()

◆ getUpper()

◆ getXIntercept()

◆ operator=()

Member Data Documentation

◆ chi_squared_

◆ intercept_

◆ lower_

◆ mean_residuals_

◆ r_squared_

◆ rsd_

◆ slope_

◆ stand_dev_residuals_

◆ stand_error_slope_

◆ t_star_

◆ upper_

◆ x_intercept_