public void RegressTest() { MultipleLinearRegression target = new MultipleLinearRegression(1, true); double[][] inputs = { new double[] { 80 }, new double[] { 60 }, new double[] { 10 }, new double[] { 20 }, new double[] { 30 }, }; double[] outputs = { 20, 40, 30, 50, 60 }; double error = target.Regress(inputs, outputs); double slope = target.Coefficients[0]; double intercept = target.Coefficients[1]; Assert.AreEqual(-0.264706, slope, 1e-5); Assert.AreEqual(50.588235, intercept, 1e-5); Assert.AreEqual(761.764705, error, 1e-5); double r = target.CoefficientOfDetermination(inputs, outputs); Assert.AreEqual(0.23823529, r, 1e-6); string str = target.ToString(null, System.Globalization.CultureInfo.GetCultureInfo("pt-BR")); Assert.AreEqual("y(x0) = -0,264705882352941*x0 + 50,5882352941176", str); }
/// <summary> /// Gets the coefficient of determination, as known as R² (r-squared). /// </summary> /// /// <remarks> /// <para> /// The coefficient of determination is used in the context of statistical models /// whose main purpose is the prediction of future outcomes on the basis of other /// related information. It is the proportion of variability in a data set that /// is accounted for by the statistical model. It provides a measure of how well /// future outcomes are likely to be predicted by the model.</para> /// <para> /// The R² coefficient of determination is a statistical measure of how well the /// regression line approximates the real data points. An R² of 1.0 indicates /// that the regression line perfectly fits the data.</para> /// </remarks> /// /// <returns>The R² (r-squared) coefficient for the given data.</returns> /// public double CoefficientOfDetermination(double[] inputs, double[] outputs, bool adjust) { double[][] X = new double[inputs.Length][]; for (int i = 0; i < inputs.Length; i++) { // b[0]*1 + b[1]*inputs[i] X[i] = new double[] { 1.0, inputs[i] }; } return(regression.CoefficientOfDetermination(X, outputs, adjust)); }
/// <summary> /// Gets the coefficient of determination, as known as R² (r-squared). /// </summary> /// /// <remarks> /// <para> /// The coefficient of determination is used in the context of statistical models /// whose main purpose is the prediction of future outcomes on the basis of other /// related information. It is the proportion of variability in a data set that /// is accounted for by the statistical model. It provides a measure of how well /// future outcomes are likely to be predicted by the model.</para> /// <para> /// The R² coefficient of determination is a statistical measure of how well the /// regression line approximates the real data points. An R² of 1.0 indicates /// that the regression line perfectly fits the data.</para> /// </remarks> /// /// <returns>The R² (r-squared) coefficient for the given data.</returns> /// public double CoefficientOfDetermination(double[] inputs, double[] outputs, bool adjust) { double[][] X = new double[inputs.Length][]; for (int i = 0; i < inputs.Length; i++) { X[i] = new double[NumberOfInputs]; for (int j = 0; j < X[i].Length; j++) { X[i][j] = Math.Pow(inputs[i], j); } } return(regression.CoefficientOfDetermination(X, outputs, adjust)); }
/// <summary> /// Gets the coefficient of determination, as known as R² (r-squared). /// </summary> /// /// <remarks> /// <para> /// The coefficient of determination is used in the context of statistical models /// whose main purpose is the prediction of future outcomes on the basis of other /// related information. It is the proportion of variability in a data set that /// is accounted for by the statistical model. It provides a measure of how well /// future outcomes are likely to be predicted by the model.</para> /// <para> /// The R² coefficient of determination is a statistical measure of how well the /// regression line approximates the real data points. An R² of 1.0 indicates /// that the regression line perfectly fits the data.</para> /// </remarks> /// /// <returns>The R² (r-squared) coefficient for the given data.</returns> /// public double CoefficientOfDetermination(double[] inputs, double[] outputs, bool adjust, double[] weights = null) { var polynomial = new double[inputs.Length][]; for (int i = 0; i < inputs.Length; i++) { polynomial[i] = new double[this.Degree]; for (int j = 0; j < polynomial[i].Length; j++) { polynomial[i][j] = Math.Pow(inputs[i], this.Degree - j); } } return(regression.CoefficientOfDetermination(polynomial, outputs, adjust, weights)); }
public void RegressTest3() { // We will try to model a plane as an equation in the form // "ax + by + c = z". We have two input variables (x and y) // and we will be trying to find two parameters a and b and // an intercept term c. // Create a multiple linear regression for two input and an intercept MultipleLinearRegression target = new MultipleLinearRegression(2, true); // Now suppose you have some points double[][] inputs = { new double[] { 1, 1 }, new double[] { 0, 1 }, new double[] { 1, 0 }, new double[] { 0, 0 }, }; // located in the same Z (z = 1) double[] outputs = { 1, 1, 1, 1 }; // Now we will try to fit a regression model double error = target.Regress(inputs, outputs); // As result, we will be given the following: double a = target.Coefficients[0]; // a = 0 double b = target.Coefficients[1]; // b = 0 double c = target.Coefficients[2]; // c = 1 // This is the plane described by the equation // ax + by + c = z => 0x + 0y + 1 = z => 1 = z. Assert.AreEqual(0.0, a, 1e-6); Assert.AreEqual(0.0, b, 1e-6); Assert.AreEqual(1.0, c, 1e-6); Assert.AreEqual(0.0, error, 1e-6); double r = target.CoefficientOfDetermination(inputs, outputs); Assert.AreEqual(1.0, r); }
public void RegressTest2() { MultipleLinearRegression target = new MultipleLinearRegression(1, false); double[][] inputs = { new double[] { 80, 1 }, new double[] { 60, 1 }, new double[] { 10, 1 }, new double[] { 20, 1 }, new double[] { 30, 1 }, }; double[] outputs = { 20, 40, 30, 50, 60 }; double error = target.Regress(inputs, outputs); double slope = target.Coefficients[0]; double intercept = target.Coefficients[1]; Assert.AreEqual(-0.264706, slope, 1e-5); Assert.AreEqual(50.588235, intercept, 1e-5); Assert.AreEqual(761.764705, error, 1e-5); double r = target.CoefficientOfDetermination(inputs, outputs); Assert.AreEqual(0.23823529, r, 1e-6); string str = target.ToString(); Assert.AreEqual("y(x0, x1) = -0,264705882352942*x0 + 50,5882352941177*x1", str); }
public void RegressTest6() { MultipleLinearRegression target = new MultipleLinearRegression(2, false); double[][] inputs = { new double[] { 0, 0 }, new double[] { 0, 0 }, new double[] { 0, 0 }, new double[] { 0, 0 }, new double[] { 0, 0 }, }; double[] outputs = { 20, 40, 30, 50, 60 }; double error = target.Regress(inputs, outputs); double slope = target.Coefficients[0]; double intercept = target.Coefficients[1]; Assert.AreEqual(0, slope, 1e-5); Assert.AreEqual(0, intercept, 1e-5); Assert.AreEqual(9000, error); double r = target.CoefficientOfDetermination(inputs, outputs); Assert.AreEqual(-8, r, 1e-6); string str = target.ToString(null, System.Globalization.CultureInfo.GetCultureInfo("pt-BR")); Assert.AreEqual("y(x0, x1) = 0*x0 + 0*x1", str); }
public void ComputeTest() { // Example 5.1 from // http://www.weibull.com/DOEWeb/estimating_regression_models_using_least_squares.htm double[][] inputs = { new double[] { 41.9, 29.1 }, // 1 new double[] { 43.4, 29.3 }, // 2 new double[] { 43.9, 29.5 }, // 3 new double[] { 44.5, 29.7 }, // 4 new double[] { 47.3, 29.9 }, // 5 new double[] { 47.5, 30.3 }, // 6 new double[] { 47.9, 30.5 }, // 7 new double[] { 50.2, 30.7 }, // 8 new double[] { 52.8, 30.8 }, // 9 new double[] { 53.2, 30.9 }, // 10 new double[] { 56.7, 31.5 }, // 11 new double[] { 57.0, 31.7 }, // 12 new double[] { 63.5, 31.9 }, // 13 new double[] { 65.3, 32.0 }, // 14 new double[] { 71.1, 32.1 }, // 15 new double[] { 77.0, 32.5 }, // 16 new double[] { 77.8, 32.9 }, // 17 }; double[] outputs = { 251.3, 251.3, 248.3, 267.5, 273.0, 276.5, 270.3, 274.9, 285.0, 290.0, 297.0, 302.5, 304.5, 309.3, 321.7, 330.7, 349.0, }; var target = new MultipleLinearRegressionAnalysis(inputs, outputs, intercept: true); target.Compute(); Assert.AreEqual(0.968022, target.RSquared, 1e-5); Assert.AreEqual(0.963454, target.RSquareAdjusted, 1e-5); Assert.AreEqual(2, target.Table[0].DegreesOfFreedom); Assert.AreEqual(14, target.Table[1].DegreesOfFreedom); Assert.AreEqual(16, target.Table[2].DegreesOfFreedom); Assert.AreEqual(12816.345909673832, target.Table[0].SumOfSquares, 1e-10); Assert.AreEqual(423.37409032616614, target.Table[1].SumOfSquares, 1e-10); Assert.AreEqual(13239.719999999998, target.Table[2].SumOfSquares, 1e-10); Assert.IsFalse(Double.IsNaN(target.Table[0].SumOfSquares)); Assert.IsFalse(Double.IsNaN(target.Table[1].SumOfSquares)); Assert.IsFalse(Double.IsNaN(target.Table[2].SumOfSquares)); Assert.AreEqual(6408.1729548369158, target.Table[0].MeanSquares, 1e-10); Assert.AreEqual(30.241006451869008, target.Table[1].MeanSquares, 1e-10); Assert.IsFalse(Double.IsNaN(target.Table[0].MeanSquares)); Assert.IsFalse(Double.IsNaN(target.Table[1].MeanSquares)); Assert.AreEqual(211.90342871147618, target.Table[0].Statistic.Value, 1e-10); Assert.AreEqual(0.000000000034191538489380946, target.Table[0].Significance.PValue, 1e-16); Assert.IsFalse(Double.IsNaN(target.Table[0].Significance.PValue)); Assert.AreEqual(1.2387232694931045, target.Coefficients[0].Value, 1e-10); Assert.AreEqual(12.082353323342893, target.Coefficients[1].Value, 1e-10); Assert.AreEqual(-153.51169396147372, target.Coefficients[2].Value, 1e-10); Assert.IsFalse(Double.IsNaN(target.Coefficients[0].Value)); Assert.IsFalse(Double.IsNaN(target.Coefficients[1].Value)); Assert.IsFalse(Double.IsNaN(target.Coefficients[2].Value)); Assert.IsFalse(target.Coefficients[0].IsIntercept); Assert.IsFalse(target.Coefficients[1].IsIntercept); Assert.IsTrue(target.Coefficients[2].IsIntercept); Assert.AreEqual(0.394590262021004, target.Coefficients[0].StandardError, 1e-10); Assert.AreEqual(3.9322914100115307, target.Coefficients[1].StandardError, 1e-10); Assert.IsFalse(Double.IsNaN(target.Coefficients[0].StandardError)); Assert.IsFalse(Double.IsNaN(target.Coefficients[1].StandardError)); Assert.AreEqual(3.1392646720388844, target.Coefficients[0].TTest.Statistic, 1e-10); Assert.AreEqual(3.0725986615797285, target.Coefficients[1].TTest.Statistic, 1e-10); Assert.IsFalse(Double.IsNaN(target.Coefficients[0].TTest.Statistic)); Assert.IsFalse(Double.IsNaN(target.Coefficients[1].TTest.Statistic)); DoubleRange range; range = target.Coefficients[0].TTest.GetConfidenceInterval(0.9); Assert.AreEqual(0.54372744151743968, range.Min, 1e-10); Assert.AreEqual(1.9337190974687695, range.Max, 1e-10); range = target.Coefficients[1].TTest.GetConfidenceInterval(0.9); Assert.AreEqual(5.1563686060690417, range.Min, 1e-10); Assert.AreEqual(19.008338040616746, range.Max, 1e-10); MultipleLinearRegression mlr = new MultipleLinearRegression(2, true); mlr.Regress(inputs, outputs); double r2 = mlr.CoefficientOfDetermination(inputs, outputs, false); double r2a = mlr.CoefficientOfDetermination(inputs, outputs, true); Assert.AreEqual(r2, target.RSquared); Assert.AreEqual(r2a, target.RSquareAdjusted); }
public void RegressTest7() { double[][] example2 = { new double[] { -0.47, 1.16, -1.25 }, new double[] { 0.55, 1.15, -0.78 }, new double[] { 1.38, 0.63, -0.84 }, new double[] { 0.99, 0.63, -0.81 }, new double[] { 1.72, 0.62, -1.59 }, new double[] { 1.05, 0.62, -1.05 }, new double[] { -0.51, 0.62, -0.98 }, new double[] { 1.83, 0.61, 0.86 }, new double[] { 1.16, 0.61, 0.15 }, new double[] { 0.59, 0.61, -0.28 }, new double[] { 0.40, 0.60, -0.30 }, new double[] { 0.48, 0.60, -0.41 }, new double[] { 1.28, 0.53, -0.31 }, new double[] { 0.36, 0.53, -0.41 }, new double[] { 0.93, 0.16, -0.19 }, new double[] { -0.61, 0.16, -0.32 }, new double[] { -0.58, 0.16, -0.01 }, new double[] { 0.53, 0.16, -0.13 }, new double[] { 1.48, 0.16, 1.12 }, new double[] { -0.34, 0.15, -0.10 }, new double[] { 0.81, 0.15, 0.14 }, new double[] { 0.85, 0.15, -0.02 }, new double[] { 0.69, 0.15, -0.16 }, new double[] { 0.39, 0.15, -0.33 }, new double[] { 0.70, 0.00, 2.00 }, new double[] { 0.25, 0.00, -0.01 }, new double[] { -0.96, 0.85, -0.19 }, new double[] { 1.04, 0.84, 0.35 }, new double[] { 0.30, 0.83, 0.05 }, new double[] { 0.28, 0.83, 0.84 }, new double[] { 0.18, 0.82, 0.06 }, new double[] { 0.49, 0.81, 0.41 }, new double[] { 0.40, 0.81, 0.50 }, new double[] { 0.41, 0.80, 0.00 }, new double[] { 0.06, 0.79, 0.39 }, new double[] { 0.55, 0.79, 0,55 }, }; double[][] inputs = example2.GetColumns(1, 2); double[] outputs = example2.GetColumn(0); bool thrown = false; MultipleLinearRegressionAnalysis target; try { target = new MultipleLinearRegressionAnalysis(inputs, outputs, new string[0], "Test", false); } catch (ArgumentException) { thrown = true; } Assert.IsTrue(thrown); target = new MultipleLinearRegressionAnalysis(inputs, outputs, new string[2], "Test", false); target.Compute(); Assert.AreEqual(target.Array, inputs); Assert.AreEqual(target.Outputs, outputs); Assert.AreEqual(-0.19371930561139417, target.RSquared, 1e-5); Assert.AreEqual(-0.26606593019390279, target.RSquareAdjusted, 1e-5); Assert.AreEqual(2, target.Table[0].DegreesOfFreedom); Assert.AreEqual(33, target.Table[1].DegreesOfFreedom); Assert.AreEqual(35, target.Table[2].DegreesOfFreedom); Assert.AreEqual(-2.9165797494934651, target.Table[0].SumOfSquares, 1e-10); Assert.AreEqual(17.972279749493463, target.Table[1].SumOfSquares, 1e-10); Assert.AreEqual(15.055699999999998, target.Table[2].SumOfSquares, 1e-10); Assert.IsFalse(Double.IsNaN(target.Table[0].SumOfSquares)); Assert.IsFalse(Double.IsNaN(target.Table[1].SumOfSquares)); Assert.IsFalse(Double.IsNaN(target.Table[2].SumOfSquares)); Assert.AreEqual(-1.4582898747467326, target.Table[0].MeanSquares, 1e-10); Assert.AreEqual(0.54461453786343827, target.Table[1].MeanSquares, 1e-10); Assert.IsFalse(Double.IsNaN(target.Table[0].MeanSquares)); Assert.IsFalse(Double.IsNaN(target.Table[1].MeanSquares)); Assert.AreEqual(-2.6776550630978524, target.Table[0].Statistic.Value, 1e-10); Assert.AreEqual(1, target.Table[0].Significance.PValue, 1e-16); Assert.IsFalse(Double.IsNaN(target.Table[0].Significance.PValue)); Assert.AreEqual(0.72195200211671728, target.Coefficients[0].Value, 1e-10); Assert.AreEqual(0.15872233321508125, target.Coefficients[1].Value, 1e-10); Assert.IsFalse(Double.IsNaN(target.Coefficients[0].Value)); Assert.IsFalse(Double.IsNaN(target.Coefficients[1].Value)); Assert.IsFalse(target.Coefficients[0].IsIntercept); Assert.IsFalse(target.Coefficients[1].IsIntercept); Assert.AreEqual(0.20506051379737225, target.Coefficients[0].StandardError, 1e-10); Assert.AreEqual(0.18842330299464302, target.Coefficients[1].StandardError, 1e-10); Assert.IsFalse(Double.IsNaN(target.Coefficients[0].StandardError)); Assert.IsFalse(Double.IsNaN(target.Coefficients[1].StandardError)); Assert.AreEqual(3.5206778172325479, target.Coefficients[0].TTest.Statistic, 1e-10); Assert.AreEqual(0.84237103740609942, target.Coefficients[1].TTest.Statistic, 1e-10); Assert.IsFalse(Double.IsNaN(target.Coefficients[0].TTest.Statistic)); Assert.IsFalse(Double.IsNaN(target.Coefficients[1].TTest.Statistic)); DoubleRange range; range = target.Coefficients[0].TTest.GetConfidenceInterval(0.9); Assert.AreEqual(0.37491572761667513, range.Min, 1e-10); Assert.AreEqual(1.0689882766167593, range.Max, 1e-10); range = target.Coefficients[1].TTest.GetConfidenceInterval(0.9); Assert.AreEqual(-0.16015778606945111, range.Min, 1e-10); Assert.AreEqual(0.47760245249961364, range.Max, 1e-10); MultipleLinearRegression mlr = new MultipleLinearRegression(2, false); mlr.Regress(inputs, outputs); double r2 = mlr.CoefficientOfDetermination(inputs, outputs, false); double r2a = mlr.CoefficientOfDetermination(inputs, outputs, true); Assert.AreEqual(r2, target.RSquared); Assert.AreEqual(r2a, target.RSquareAdjusted); }
public void RegressTest2() { var target = new MultipleLinearRegression(2, false); Assert.IsFalse(target.HasIntercept); double[][] inputs = { new double[] { 80, 1 }, new double[] { 60, 1 }, new double[] { 10, 1 }, new double[] { 20, 1 }, new double[] { 30, 1 }, }; double[] outputs = { 20, 40, 30, 50, 60 }; double error = target.Regress(inputs, outputs); Assert.AreEqual(2, target.NumberOfInputs); Assert.AreEqual(1, target.NumberOfOutputs); double slope = target.Coefficients[0]; double intercept = target.Coefficients[1]; Assert.AreEqual(-0.264706, slope, 1e-5); Assert.AreEqual(50.588235, intercept, 1e-5); Assert.AreEqual(761.764705, error, 1e-5); double r = target.CoefficientOfDetermination(inputs, outputs); Assert.AreEqual(0.23823529, r, 1e-6); string str = target.ToString(null, System.Globalization.CultureInfo.GetCultureInfo("en-US")); Assert.AreEqual("y(x0, x1) = -0.264705882352941*x0 + 50.5882352941176*x1", str); }
private void btnSampleRunAnalysis_Click(object sender, EventArgs e) { // Check requirements if (sourceTable == null) { MessageBox.Show("A sample spreadsheet can be found in the " + "Resources folder in the same directory as this application.", "Please load some data before attempting an analysis"); return; } if (checkedListBox1.CheckedItems.Count == 0) { MessageBox.Show("Please select the dependent input variables to be used in the regression model.", "Please choose at least one input variable"); } // Finishes and save any pending changes to the given data dgvAnalysisSource.EndEdit(); sourceTable.AcceptChanges(); // Gets the column of the dependent variable String dependentName = (string)comboBox1.SelectedItem; DataTable dependent = sourceTable.DefaultView.ToTable(false, dependentName); // Gets the columns of the independent variables List<string> names = new List<string>(); foreach (string name in checkedListBox1.CheckedItems) { names.Add(name); } String[] independentNames = names.ToArray(); DataTable independent = sourceTable.DefaultView.ToTable(false, independentNames); // Creates the input and output matrices from the source data table double[][] input = independent.ToArray(); double[] output = dependent.Columns[dependentName].ToArray(); String[] sourceColumns; double[,] sourceMatrix = sourceTable.ToMatrix(out sourceColumns); // Creates the Simple Descriptive Analysis of the given source DescriptiveAnalysis sda = new DescriptiveAnalysis(sourceMatrix, sourceColumns); sda.Compute(); // Populates statistics overview tab with analysis data dgvDistributionMeasures.DataSource = sda.Measures; // Creates the Logistic Regression Analysis of the given source lra = new LogisticRegressionAnalysis(input, output, independentNames, dependentName); // Compute the Logistic Regression Analysis lra.Compute(); // Populates coefficient overview with analysis data dgvLogisticCoefficients.DataSource = lra.Coefficients; // Populate details about the fitted model tbChiSquare.Text = lra.ChiSquare.Statistic.ToString("N5"); tbPValue.Text = lra.ChiSquare.PValue.ToString("N5"); checkBox1.Checked = lra.ChiSquare.Significant; tbDeviance.Text = lra.Deviance.ToString("N5"); tbLogLikelihood.Text = lra.LogLikelihood.ToString("N5"); // Perform linear regression mlr = new MultipleLinearRegression(independentNames.Length, true); mlr.Regress(input, output); tbLinearExpression.Text = mlr.ToString(); tbLinearR.Text = mlr.CoefficientOfDetermination(input, output, false).ToString("N5"); tbLinearAdjustedR.Text = mlr.CoefficientOfDetermination(input, output, true).ToString("N5"); // Populate projection source table string[] cols = independentNames; if (!independentNames.Contains(dependentName)) cols = independentNames.Concatenate(dependentName); DataTable projSource = sourceTable.DefaultView.ToTable(false, cols); dgvProjectionSource.DataSource = projSource; }