public void learn_Test()
{
#region doc_learn_part1
// Consider the following data. An experimenter would
// like to infer a relationship between two variables
// A and B and a corresponding outcome variable R.
double[][] example =
{
// A B R
new double[] { 6.41, 10.11, 26.1 },
new double[] { 6.61, 22.61, 33.8 },
new double[] { 8.45, 11.11, 52.7 },
new double[] { 1.22, 18.11, 16.2 },
new double[] { 7.42, 12.81, 87.3 },
new double[] { 4.42, 10.21, 12.5 },
new double[] { 8.61, 11.94, 77.5 },
new double[] { 1.73, 13.13, 12.1 },
new double[] { 7.47, 17.11, 86.5 },
new double[] { 6.11, 15.13, 62.8 },
new double[] { 1.42, 16.11, 17.5 },
};
// For this, we first extract the input and output
// pairs. The first two columns have values for the
// input variables, and the last for the output:
double[][] inputs = example.GetColumns(new[] { 0, 1 });
double[] output = example.GetColumn(2);
// We can create a new multiple linear analysis for the variables
var mlra = new MultipleLinearRegressionAnalysis(intercept: true);
// Compute the analysis and obtain the estimated regression
MultipleLinearRegression regression = mlra.Learn(inputs, output);
#endregion
// We can also show a summary ANOVA
// Accord.Controls.DataGridBox.Show(regression.Table);
#region doc_learn_part2
// And also extract other useful information, such
// as the linear coefficients' values and std errors:
double[] coef = mlra.CoefficientValues;
double[] stde = mlra.StandardErrors;
// Coefficients of performance, such as r²
double rsquared = mlra.RSquared; // 0.62879
// Hypothesis tests for the whole model
ZTest ztest = mlra.ZTest; // 0.99999
FTest ftest = mlra.FTest; // 0.01898
// and for individual coefficients
TTest ttest0 = mlra.Coefficients[0].TTest; // 0.00622
TTest ttest1 = mlra.Coefficients[1].TTest; // 0.53484
// and also extract confidence intervals
DoubleRange ci = mlra.Coefficients[0].Confidence; // [3.2616, 14.2193]
// We can use the analysis to predict an output for a sample
double y = mlra.Regression.Transform(new double[] { 10, 15 });
// We can also obtain confidence intervals for the prediction:
DoubleRange pci = mlra.GetConfidenceInterval(new double[] { 10, 15 });
// and also prediction intervals for the same prediction:
DoubleRange ppi = mlra.GetPredictionInterval(new double[] { 10, 15 });
#endregion
Assert.AreEqual(3, coef.Length);
Assert.AreEqual(8.7405051051757816, coef[0]);
Assert.AreEqual(1.1198079243314365, coef[1], 1e-10);
Assert.AreEqual(-19.604474518407862, coef[2], 1e-10);
Assert.IsFalse(coef.HasNaN());
Assert.AreEqual(2.375916659234715, stde[0], 1e-10);
Assert.AreEqual(1.7268508921418664, stde[1], 1e-10);
Assert.AreEqual(30.989640986710953, stde[2], 1e-10);
Assert.IsFalse(coef.HasNaN());
Assert.AreEqual(0.62879941171298936, rsquared, 1e-10);
Assert.AreEqual(0.99999999999999822, ztest.PValue, 1e-10);
Assert.AreEqual(0.018986050133298293, ftest.PValue, 1e-10);
Assert.AreEqual(0.0062299844256985537, ttest0.PValue, 1e-10);
Assert.AreEqual(0.53484850318449118, ttest1.PValue, 1e-14);
Assert.IsFalse(Double.IsNaN(ttest1.PValue));
Assert.AreEqual(3.2616314640800566, ci.Min, 1e-10);
Assert.AreEqual(14.219378746271506, ci.Max, 1e-10);
double[][] im = mlra.InformationMatrix;
double mse = regression.GetStandardError(inputs, output);
DoubleRange epci = regression.GetConfidenceInterval(new double[] { 10, 15 }, mse, inputs.Length, im);
Assert.AreEqual(epci.Min, pci.Min, 1e-10);
Assert.AreEqual(epci.Max, pci.Max, 1e-10);
Assert.AreEqual(55.27840511658215, pci.Min, 1e-10);
Assert.AreEqual(113.91698568006086, pci.Max, 1e-10);
Assert.AreEqual(28.783074454641557, ppi.Min, 1e-10);
Assert.AreEqual(140.41231634200145, ppi.Max, 1e-10);
}
