RWLinearRegressionFTest Class Reference

Tests that the estimated parameters in a linear regression model are equal to a hypothesized vector of values. More...

#include <rw/analytics/lrftest.h>

Public Member Functions
	RWLinearRegressionFTest ()
	RWLinearRegressionFTest (const RWLinearRegressionFTest &t)
	RWLinearRegressionFTest (const RWLinearRegression &lr)
	RWLinearRegressionFTest (const RWLinearRegression &lr, const RWGenMat< double > &A, const RWMathVec< double > &c)
double	criticalValue (double alpha) const
double	FStatisticPValue () const
double	FStatisticValue () const
RWLinearRegressionFTest &	operator= (const RWLinearRegressionFTest &ft)
bool	reject (double alpha=.05) const
void	setHypothesis (const RWGenMat< double > &A, const RWMathVec< double > &c)
void	setLinearRegression (const RWLinearRegression &lr)

Detailed Description

Class RWLinearRegressionFTest can be used to test that the estimated parameters in a linear regression model are equal to a hypothesized vector of values. For example, it can test the hypothesis that all parameters are equal to 0. To be completely precise, the class tests the hypothesis that the estimated parameters are the solution to some specified system of linear equations. The test is based on the F statistic, described in the section "Multiple Linear Regression," in the Business Analysis Module User's Guide.

Synopsis

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

RWGenMat<double> predictorMatrix;
RWMathVec<double> observationVector;
RWLinearRegression lr(predictorMatrix, observationVector);
RWLinearRegressionFTest ftest(lr);

Example

The following example creates a linear regression object and tests the hypothesis that all parameters are equal to 0 at a confidence level of 99 percent.

#include <rw/analytics/linregress.h>
#include <lrftest.h>
#include <iostream>

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);
 RWLinearRegressionFTest FTest(lr);

 std::cout << "  f statistic value:   " << FTest.FStatisticValue()
      << std::endl;
 std::cout << "  f statistic P-value: " << FTest.FStatisticPValue()
      << std::endl;
 std::cout << "  99% Critical value:  " << FTest.criticalValue(0.01)
      << std::endl;
 if ( FTest.reject(0.01) )
 {
   std::cout << "Reject H0 at significance level 0.01" << std::endl;
 }
 else
 {
   std::cout << "Fail to reject H0 at significance level 0.01"
        << std::endl;
 }
 return 0;
}

Constructor & Destructor Documentation

RWLinearRegressionFTest::RWLinearRegressionFTest

(

)

Constructs an empty F test object. Behavior is undefined.

RWLinearRegressionFTest::RWLinearRegressionFTest

(

const RWLinearRegressionFTest &

t

)

Constructs a copy of t.

RWLinearRegressionFTest::RWLinearRegressionFTest

(

const RWLinearRegression &

lr

)

Constructs an F test for the hypothesis that \(\beta_1 = \beta_2 = ..\beta_p = 0\)

RWLinearRegressionFTest::RWLinearRegressionFTest	(	const RWLinearRegression &	lr,
		const RWGenMat< double > &	A,
		const RWMathVec< double > &	c
	)

Constructs an F test for the hypothesis that \(A\beta = c\)

Member Function Documentation

double RWLinearRegressionFTest::criticalValue ( double  alpha ) const

inline

Returns the critical value for the test at the significance level alpha.

double RWLinearRegressionFTest::FStatisticPValue ( ) const

inline

Returns the P-value for the test.

double RWLinearRegressionFTest::FStatisticValue ( ) const

inline

Returns the value of the F statistic.

RWLinearRegressionFTest& RWLinearRegressionFTest::operator=

(

const RWLinearRegressionFTest &

ft

)

Copies the contents of ft to self.

bool RWLinearRegressionFTest::reject ( double  alpha = .05 ) const

inline

Returns true if the hypothesis being tested will be rejected at the significance level alpha.

void RWLinearRegressionFTest::setHypothesis	(	const RWGenMat< double > &	A,
		const RWMathVec< double > &	c
	)

Sets the hypothesis being tested to \(A\beta = c\)

void RWLinearRegressionFTest::setLinearRegression

(

const RWLinearRegression &

lr

)

Sets the linear regression for which the hypothesis will be tested.