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);
FitResult PR = B.PolynomialRegression(1);
FitResult LR = B.LinearRegression();
Assert.IsTrue(TestUtilities.IsNearlyEqual(PR.Parameters, LR.Parameters));
Assert.IsTrue(TestUtilities.IsNearlyEqual(PR.CovarianceMatrix, LR.CovarianceMatrix));
Assert.IsTrue(TestUtilities.IsNearlyEqual(PR.GoodnessOfFit.Statistic, LR.GoodnessOfFit.Statistic));
}
public void BivariateLinearRegression()
{
// do a set of logistic regression fits
// make sure not only that the fit parameters are what they should be, but that their variances/covariances are as returned
Random rng = new Random(314159);
// define logistic parameters
double a0 = 2.0; double b0 = -1.0;
// keep track of sample of returned a and b fit parameters
BivariateSample ps = new BivariateSample();
// also keep track of returned covariance estimates
// since these vary slightly from fit to fit, we will average them
double caa = 0.0;
double cbb = 0.0;
double cab = 0.0;
// also keep track of test statistics
Sample fs = new Sample();
// do 100 fits
for (int k = 0; k < 100; k++) {
// we should be able to draw x's from any distribution; noise should be drawn from a normal distribution
Distribution xd = new LogisticDistribution();
Distribution nd = new NormalDistribution(0.0, 2.0);
// generate a synthetic data set
BivariateSample s = new BivariateSample();
for (int i = 0; i < 25; i++) {
double x = xd.GetRandomValue(rng);
double y = a0 + b0 * x + nd.GetRandomValue(rng);
s.Add(x, y);
}
// do the regression
FitResult r = s.LinearRegression();
// record best fit parameters
double a = r.Parameter(0).Value;
double b = r.Parameter(1).Value;
ps.Add(a, b);
// record estimated covariances
caa += r.Covariance(0, 0);
cbb += r.Covariance(1, 1);
cab += r.Covariance(0, 1);
// record the fit statistic
fs.Add(r.GoodnessOfFit.Statistic);
Console.WriteLine("F={0}", r.GoodnessOfFit.Statistic);
}
caa /= ps.Count;
cbb /= ps.Count;
cab /= ps.Count;
// check that mean parameter estimates are what they should be: the underlying population parameters
Assert.IsTrue(ps.X.PopulationMean.ConfidenceInterval(0.95).ClosedContains(a0));
Assert.IsTrue(ps.Y.PopulationMean.ConfidenceInterval(0.95).ClosedContains(b0));
Console.WriteLine("{0} {1}", caa, ps.X.PopulationVariance);
Console.WriteLine("{0} {1}", cbb, ps.Y.PopulationVariance);
// check that parameter covarainces are what they should be: the reported covariance estimates
Assert.IsTrue(ps.X.PopulationVariance.ConfidenceInterval(0.95).ClosedContains(caa));
Assert.IsTrue(ps.Y.PopulationVariance.ConfidenceInterval(0.95).ClosedContains(cbb));
Assert.IsTrue(ps.PopulationCovariance.ConfidenceInterval(0.95).ClosedContains(cab));
// check that F is distributed as it should be
Console.WriteLine(fs.KolmogorovSmirnovTest(new FisherDistribution(2, 48)).LeftProbability);
}
public void BivariateLinearRegressionGoodnessOfFitDistribution()
{
// create uncorrelated x and y values
// the distribution of F-test statistics returned by linear fits should follow the expected F-distribution
Random rng = new Random(987654321);
NormalDistribution xd = new NormalDistribution(1.0, 2.0);
NormalDistribution yd = new NormalDistribution(-3.0, 4.0);
Sample fs = new Sample();
for (int i = 0; i < 127; i++) {
BivariateSample xys = new BivariateSample();
for (int j = 0; j < 7; j++) {
xys.Add(xd.GetRandomValue(rng), yd.GetRandomValue(rng));
}
double f = xys.LinearRegression().GoodnessOfFit.Statistic;
fs.Add(f);
}
Distribution fd = new FisherDistribution(1, 5);
Console.WriteLine("{0} v. {1}", fs.PopulationMean, fd.Mean);
TestResult t = fs.KolmogorovSmirnovTest(fd);
Console.WriteLine(t.LeftProbability);
Assert.IsTrue(t.LeftProbability < 0.95);
}
// Not fixing this bug; use Polynomial interpolation for this scenario instead
//[TestMethod]
public void Bug6392()
{
// bug requests that we support regression with number of points equal to number
// of fit parameters, i.e. polynomial fit
var biSample = new BivariateSample();
biSample.Add(0, 1);
biSample.Add(1, -1);
var fitResult = biSample.LinearRegression();
}
