public void MultivariateLinearRegressionAgreement()
{
Random rng = new Random(1);
MultivariateSample SA = new MultivariateSample(2);
for (int i = 0; i < 10; i++)
{
SA.Add(rng.NextDouble(), rng.NextDouble());
}
GeneralLinearRegressionResult RA = SA.LinearRegression(0);
ColumnVector PA = RA.Parameters.ValuesVector;
SymmetricMatrix CA = RA.Parameters.CovarianceMatrix;
MultivariateSample SB = SA.Columns(1, 0);
GeneralLinearRegressionResult RB = SB.LinearRegression(1);
ColumnVector PB = RB.Parameters.ValuesVector;
SymmetricMatrix CB = RB.Parameters.CovarianceMatrix;
Assert.IsTrue(TestUtilities.IsNearlyEqual(PA[0], PB[1])); Assert.IsTrue(TestUtilities.IsNearlyEqual(PA[1], PB[0]));
Assert.IsTrue(TestUtilities.IsNearlyEqual(CA[0, 0], CB[1, 1])); Assert.IsTrue(TestUtilities.IsNearlyEqual(CA[0, 1], CB[1, 0])); Assert.IsTrue(TestUtilities.IsNearlyEqual(CA[1, 1], CB[0, 0]));
BivariateSample SC = SA.TwoColumns(1, 0);
GeneralLinearRegressionResult RC = SC.LinearRegression();
ColumnVector PC = RC.Parameters.ValuesVector;
SymmetricMatrix CC = RC.Parameters.CovarianceMatrix;
Assert.IsTrue(TestUtilities.IsNearlyEqual(PA, PC));
Assert.IsTrue(TestUtilities.IsNearlyEqual(CA, CC));
}
public void MultivariateLinearRegressionNullDistribution()
{
int d = 4;
Random rng = new Random(1);
NormalDistribution n = new NormalDistribution();
Sample fs = new Sample();
for (int i = 0; i < 64; i++)
{
MultivariateSample ms = new MultivariateSample(d);
for (int j = 0; j < 8; j++)
{
double[] x = new double[d];
for (int k = 0; k < d; k++)
{
x[k] = n.GetRandomValue(rng);
}
ms.Add(x);
}
GeneralLinearRegressionResult r = ms.LinearRegression(0);
fs.Add(r.F.Statistic.Value);
}
// conduct a KS test to check that F follows the expected distribution
TestResult ks = fs.KolmogorovSmirnovTest(new FisherDistribution(3, 4));
Assert.IsTrue(ks.Probability > 0.05);
}
public void BivariateLinearPolynomialRegressionAgreement()
{
// A degree-1 polynomial fit should give the same answer as a linear fit
BivariateSample B = new BivariateSample();
B.Add(0.0, 5.0);
B.Add(3.0, 6.0);
B.Add(1.0, 7.0);
B.Add(4.0, 8.0);
B.Add(2.0, 9.0);
GeneralLinearRegressionResult PR = B.PolynomialRegression(1);
GeneralLinearRegressionResult LR = B.LinearRegression();
Assert.IsTrue(TestUtilities.IsNearlyEqual(PR.Parameters.ValuesVector, LR.Parameters.ValuesVector));
Assert.IsTrue(TestUtilities.IsNearlyEqual(PR.Parameters.CovarianceMatrix, LR.Parameters.CovarianceMatrix));
}
