public void MultivariateLinearRegressionVariances() { // define model y = a + b0 * x0 + b1 * x1 + noise double a = -3.0; double b0 = 2.0; double b1 = -1.0; ContinuousDistribution x0distribution = new LaplaceDistribution(); ContinuousDistribution x1distribution = new CauchyDistribution(); ContinuousDistribution eDistribution = new NormalDistribution(0.0, 4.0); FrameTable data = new FrameTable(); data.AddColumns <double>("a", "da", "b0", "db0", "b1", "db1", "ab1Cov", "p", "dp"); // draw a sample from the model Random rng = new Random(4); for (int j = 0; j < 64; j++) { List <double> x0s = new List <double>(); List <double> x1s = new List <double>(); List <double> ys = new List <double>(); for (int i = 0; i < 16; i++) { double x0 = x0distribution.GetRandomValue(rng); double x1 = x1distribution.GetRandomValue(rng); double e = eDistribution.GetRandomValue(rng); double y = a + b0 * x0 + b1 * x1 + e; x0s.Add(x0); x1s.Add(x1); ys.Add(y); } // do a linear regression fit on the model MultiLinearRegressionResult result = ys.MultiLinearRegression( new Dictionary <string, IReadOnlyList <double> > { { "x0", x0s }, { "x1", x1s } } ); UncertainValue pp = result.Predict(-5.0, 6.0); data.AddRow( result.Intercept.Value, result.Intercept.Uncertainty, result.CoefficientOf("x0").Value, result.CoefficientOf("x0").Uncertainty, result.CoefficientOf("x1").Value, result.CoefficientOf("x1").Uncertainty, result.Parameters.CovarianceOf("Intercept", "x1"), pp.Value, pp.Uncertainty ); } // The estimated parameters should agree with the model that generated the data. // The variances of the estimates should agree with the claimed variances Assert.IsTrue(data["a"].As <double>().PopulationStandardDeviation().ConfidenceInterval(0.99).ClosedContains(data["da"].As <double>().Mean())); Assert.IsTrue(data["b0"].As <double>().PopulationStandardDeviation().ConfidenceInterval(0.99).ClosedContains(data["db0"].As <double>().Mean())); Assert.IsTrue(data["b1"].As <double>().PopulationStandardDeviation().ConfidenceInterval(0.99).ClosedContains(data["db1"].As <double>().Mean())); Assert.IsTrue(data["a"].As <double>().PopulationCovariance(data["b1"].As <double>()).ConfidenceInterval(0.99).ClosedContains(data["ab1Cov"].As <double>().Mean())); Assert.IsTrue(data["p"].As <double>().PopulationStandardDeviation().ConfidenceInterval(0.99).ClosedContains(data["dp"].As <double>().Median())); }
public void MultivariateLinearRegressionSimple() { // define model y = a + b0 * x0 + b1 * x1 + noise double a = 1.0; double b0 = -2.0; double b1 = 3.0; ContinuousDistribution x0distribution = new CauchyDistribution(10.0, 5.0); ContinuousDistribution x1distribution = new UniformDistribution(Interval.FromEndpoints(-10.0, 20.0)); ContinuousDistribution noise = new NormalDistribution(0.0, 10.0); // draw a sample from the model Random rng = new Random(1); MultivariateSample sample = new MultivariateSample("x0", "x1", "y"); FrameTable table = new FrameTable(); table.AddColumns <double>("x0", "x1", "y"); for (int i = 0; i < 100; i++) { double x0 = x0distribution.GetRandomValue(rng); double x1 = x1distribution.GetRandomValue(rng); double eps = noise.GetRandomValue(rng); double y = a + b0 * x0 + b1 * x1 + eps; sample.Add(x0, x1, y); table.AddRow(x0, x1, y); } // do a linear regression fit on the model ParameterCollection oldResult = sample.LinearRegression(2).Parameters; MultiLinearRegressionResult newResult = table["y"].As <double>().MultiLinearRegression( table["x0"].As <double>(), table["x1"].As <double>() ); // the result should have the appropriate dimension Assert.IsTrue(oldResult.Count == 3); Assert.IsTrue(newResult.Parameters.Count == 3); // The parameters should match the model Assert.IsTrue(oldResult[0].Estimate.ConfidenceInterval(0.90).ClosedContains(b0)); Assert.IsTrue(oldResult[1].Estimate.ConfidenceInterval(0.90).ClosedContains(b1)); Assert.IsTrue(oldResult[2].Estimate.ConfidenceInterval(0.90).ClosedContains(a)); Assert.IsTrue(newResult.CoefficientOf(0).ConfidenceInterval(0.99).ClosedContains(b0)); Assert.IsTrue(newResult.CoefficientOf("x1").ConfidenceInterval(0.99).ClosedContains(b1)); Assert.IsTrue(newResult.Intercept.ConfidenceInterval(0.99).ClosedContains(a)); // The residuals should be compatible with the model predictions for (int i = 0; i < table.Rows.Count; i++) { FrameRow row = table.Rows[i]; double x0 = (double)row["x0"]; double x1 = (double)row["x1"]; double yp = newResult.Predict(x0, x1).Value; double y = (double)row["y"]; Assert.IsTrue(TestUtilities.IsNearlyEqual(newResult.Residuals[i], y - yp)); } }