RWLinearRegressionANOVA Class Reference
[Regression]

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

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/math/genmat.h>
 #include <rw/math/mathvec.h>
 #include <rw/analytics/linregress.h>
 #include <rw/analytics/lranova.h>

 RWGenMat<double> predictorMatrix;
 RWMathVec<double> observationVector;
 RWLinearRegression lr(predictorMatrix, observationVector);
 RWLinearRegressionANOVA anova(lr);

Examples

 #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::RWLinearRegressionANOVA ( )

Constructs an empty ANOVA object. Behavior undefined.

RWLinearRegressionANOVA::RWLinearRegressionANOVA ( const RWLinearRegressionANOVA & a )

Constructs a copy of a.

RWLinearRegressionANOVA::RWLinearRegressionANOVA ( const RWLinearRegression & lr )

Constructs an ANOVA object for the linear regression lr.

Member Function Documentation

double RWLinearRegressionANOVA::adjRSquare ( ) const [inline]

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

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

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.

double RWLinearRegressionANOVA::FStatisticCriticalValue ( double alpha = .05 ) const [inline]

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

double RWLinearRegressionANOVA::FStatisticPValue ( ) const [inline]

Returns the P-value for the overall F statistic.

double RWLinearRegressionANOVA::meanSquareRegression ( ) const [inline]

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

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.

RWLinearRegressionANOVA& RWLinearRegressionANOVA::operator= ( const RWLinearRegressionANOVA & lra )

Copies the contents of lra to self.

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.

double RWLinearRegressionANOVA::regressionSumOfSquares ( ) const [inline]

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

int RWLinearRegressionANOVA::residualDegreesOfFreedom ( ) const [inline]

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

double RWLinearRegressionANOVA::residualSumOfSquares ( ) const [inline]

Returns the quantity RSS as defined by

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

double RWLinearRegressionANOVA::RSquare ( ) const [inline]

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

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

void RWLinearRegressionANOVA::setLinearRegression ( const RWLinearRegression & lr )

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

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