#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 Analytics.h++ 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>
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 3.2.4.
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.
©Copyright 1999, Rogue Wave Software, Inc.
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