LinearRegression Class Reference

This class offers functions to perform least-squares fits to a straight line model, . More...

#include <OpenMS/MATH/STATISTICS/LinearRegression.h>

Collaboration diagram for LinearRegression:

Public Member Functions
	LinearRegression ()
	Constructor. More...
virtual	~LinearRegression ()=default
	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...

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

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()

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().

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().

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,
		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 .

The values in x-dimension of the dataset 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 of the model for the weighted dataset .

The values in x-dimension of the dataset 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.

References LinearRegression::computePointY().

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.