RWLinearRegressionANOVA

Does not inherit

• Local Index
• Synopsis
• Description
• Example
• Public Constructors
• Public Member Functions
• Public Member Operator

Members

adjRSquare() FStatistic() FStatisticCriticalValue() FStatisticPValue()

meanSquareRegression() meanSquareResidual() operator=() regressionDegreesOfFreedom()

regressionSumOfSquares() residualDegreesOfFreedom() residualSumOfSquares() RSquare()

RWLinearRegressionANOVA() setLinearRegression()

#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);

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.

#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;
}

RWLinearRegressionANOVA();

Constructs an empty ANOVA object. Behavior undefined.

RWLinearRegressionANOVA(const RWLinearRegressionANOVA& a);

Constructs a copy of a.

RWLinearRegressionANOVA(const RWLinearRegression& lr);

Constructs an ANOVA object for the linear regression lr.

double 
adjRSquare() const;

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

double 
FStatistic() const;

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 
FStatisticCriticalValue(double alpha=.05) const;

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

double 
FStatisticPValue() const;

Returns the P-value for the overall F statistic.

double 
meanSquareRegression() const;

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

double 
meanSquareResidual() const;

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

int 
residualDegreesOfFreedom() const;

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

void 
setLinearRegression(const RWLinearRegression& lr);

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

int 
regressionDegreesOfFreedom() const;

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

double 
residualSumOfSquares() const;

Returns the quantity RSS as defined by

double 
regressionSumOfSquares() const;

Returns the quantity , where

double 
RSquare() const;

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

RWLinearRegressionANOVA&
operator=(const RWLinearRegressionANOVA& lra);

Copies the contents of lra to self.

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