RWLinearRegressionANOVA Class Reference

Provides information on the variance of residual errors for a linear regression model. More...

#include <rw/analytics/lranova.h>

Public Member Functions
	RWLinearRegressionANOVA ()
	RWLinearRegressionANOVA (const RWLinearRegression &lr)
	RWLinearRegressionANOVA (const RWLinearRegressionANOVA &a)
double	adjRSquare () const
double	FStatistic () const
double	FStatisticCriticalValue (double alpha=.05) const
double	FStatisticPValue () const
double	meanSquareRegression () const
double	meanSquareResidual () const
RWLinearRegressionANOVA &	operator= (const RWLinearRegressionANOVA &lra)
int	regressionDegreesOfFreedom () const
double	regressionSumOfSquares () const
int	residualDegreesOfFreedom () const
double	residualSumOfSquares () const
double	RSquare () const
void	setLinearRegression (const RWLinearRegression &lr)

Detailed Description

ANOVA stands for analysis of variance. For the Linear Algebra Module class RWLinearRegressionANOVA, the analyzed variance is the variance of residual errors in a linear regression model, also known as the regression's goodness of fit.

Once an instance of RWLinearRegressionANOVA is constructed with a linear regression model, it can be queried for values related to goodness of fit, including the residual sum of squares, the coefficient of determination, and the F statistic.

Synopsis

#include <rw/analytics/linregress.h>
#include <rw/analytics/lranova.h>
#include <rw/math/genmat.h>
#include <rw/math/mathvec.h>
 
RWGenMat<double> predictorMatrix;
RWMathVec<double> observationVector;
RWLinearRegression lr(predictorMatrix, observationVector);
RWLinearRegressionANOVA anova(lr);

Example

#include <rw/analytics/linregress.h>
#include <rw/analytics/lranova.h>
 
int main() {
  RWGenMat<double> predictorMatrix =
      "5x2 [1.2 2.1 8 7 3 3.2 6.4 4.6 2 2.3]";
  RWMathVec<double> observationVector = "[2.5 3.7 1.4 2.3 5.6]";
 
  RWLinearRegression lr(predictorMatrix, observationVector);
  RWLinearRegressionANOVA lranova(lr);
 
  cout << "f statistic:           " << lranova.FStatistic() << endl;
  cout << "f statistic P-value:   " << lranova.FStatisticPValue()
       << endl;
  cout << "mean square residual   " << lranova.meanSquareResidual()
       << endl;
  cout << "mean square regression " << lranova.meanSquareRegression()
       << endl;
  cout << "Rsquare:               " << lranova.RSquare() << endl;
  cout << "adjusted Rsquare:      " << lranova.adjRSquare() << endl;
  return 0;
}

Constructor & Destructor Documentation

RWLinearRegressionANOVA() [1/3]

RWLinearRegressionANOVA::RWLinearRegressionANOVA

(

)

Constructs an empty ANOVA object. Behavior undefined.

RWLinearRegressionANOVA() [2/3]

RWLinearRegressionANOVA::RWLinearRegressionANOVA

(

const RWLinearRegressionANOVA &

a

)

Constructs a copy of a.

RWLinearRegressionANOVA() [3/3]

RWLinearRegressionANOVA::RWLinearRegressionANOVA

(

const RWLinearRegression &

lr

)

Constructs an ANOVA object for the linear regression lr.

Member Function Documentation

adjRSquare()

double RWLinearRegressionANOVA::adjRSquare ( ) const

inline

Returns the adjusted coefficient of determination as defined by the following formula:

\[ R_{adj}^2 = 1.0 - \frac{\displaystyle\sum_{i=1}^{n}(Y_i - \hat{Y}_i)^2 / (n - p - 2)}{\displaystyle\sum_{i=1}^{n}(Y_i - \overline{Y})^2 / (n - 1)} \]

FStatistic()

double RWLinearRegressionANOVA::FStatistic ( ) const

inline

Returns the overall F statistic for the model as defined in Section 3.2, "Multiple Linear Regression," in the Business Analysis Module User's Guide.

FStatisticCriticalValue()

double RWLinearRegressionANOVA::FStatisticCriticalValue ( double alpha = .05 ) const

inline

Returns the alpha level critical value for the overall F statistic.

FStatisticPValue()

double RWLinearRegressionANOVA::FStatisticPValue ( ) const

inline

Returns the P-value for the overall F statistic.

meanSquareRegression()

double RWLinearRegressionANOVA::meanSquareRegression ( ) const

inline

Returns the quotient of the regression sum of squares and the number of degrees of freedom for the regression.

meanSquareResidual()

double RWLinearRegressionANOVA::meanSquareResidual ( ) const

inline

Returns the quotient of the residual sum of squares, RSS, and the number of degrees of freedom for the model.

operator=()

RWLinearRegressionANOVA & RWLinearRegressionANOVA::operator=

(

const RWLinearRegressionANOVA &

lra

)

Copies the contents of lra to self.

regressionDegreesOfFreedom()

int RWLinearRegressionANOVA::regressionDegreesOfFreedom ( ) const

inline

Returns the number of degrees of freedom for the model, defined as 1 less than the number of parameters in the model.

regressionSumOfSquares()

double RWLinearRegressionANOVA::regressionSumOfSquares ( ) const

inline

Returns the quantity \(\displaystyle\sum_{i=1}^{n}(\hat{Y}_i - \overline{Y})^2\) , where \(\overline{Y} = \frac{1}{n}\displaystyle\sum_{i=1}^{n}(Y_i)\)

residualDegreesOfFreedom()

int RWLinearRegressionANOVA::residualDegreesOfFreedom ( ) const

inline

Returns the residual degrees of freedom, defined as the number of observations minus the number of parameters.

residualSumOfSquares()

double RWLinearRegressionANOVA::residualSumOfSquares ( ) const

inline

Returns the quantity RSS as defined by

\[ RSS = \displaystyle\sum_{i=1}^{n}(Y_i - \hat{Y}_i)^2 \]

RSquare()

double RWLinearRegressionANOVA::RSquare ( ) const

inline

Returns the coefficient of determination as defined by the following formula:

\[ R^2 = 1.0 - \frac{\displaystyle\sum_{i=1}^{n}(Y_i - \hat{Y}_i)^2} {\displaystyle\sum_{i=1}^{n}(Y_i - \overline{Y})^2} \]

setLinearRegression()

void RWLinearRegressionANOVA::setLinearRegression

(

const RWLinearRegression &

lr

)

Sets the linear regression for which the analysis of variance is to be performed.