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);
}
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();
double[,] sourceMatrix = sourceTable.ToMatrix(independentNames);
// Creates the Simple Descriptive Analysis of the given source
DescriptiveAnalysis sda = new DescriptiveAnalysis(sourceMatrix, independentNames);
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");
// Create the Multiple Linear Regression Analysis of the given source
mlr = new MultipleLinearRegressionAnalysis(input, output, independentNames, dependentName, true);
// Compute the Linear Regression Analysis
mlr.Compute();
dgvLinearCoefficients.DataSource = mlr.Coefficients;
dgvRegressionAnova.DataSource = mlr.Table;
tbRSquared.Text = mlr.RSquared.ToString("N5");
tbRSquaredAdj.Text = mlr.RSquareAdjusted.ToString("N5");
tbChiPValue.Text = mlr.ChiSquareTest.PValue.ToString("N5");
tbFPValue.Text = mlr.FTest.PValue.ToString("N5");
tbZPValue.Text = mlr.ZTest.PValue.ToString("N5");
tbChiStatistic.Text = mlr.ChiSquareTest.Statistic.ToString("N5");
tbFStatistic.Text = mlr.FTest.Statistic.ToString("N5");
tbZStatistic.Text = mlr.ZTest.Statistic.ToString("N5");
cbChiSignificant.Checked = mlr.ChiSquareTest.Significant;
cbFSignificant.Checked = mlr.FTest.Significant;
cbZSignificant.Checked = mlr.ZTest.Significant;
// 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;
}
public void ComputeTest2()
{
// 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(0, 1);
double[] output = example.GetColumn(2);
// Next, we can create a new multiple linear regression for the variables
var regression = new MultipleLinearRegressionAnalysis(inputs, output, intercept: true);
regression.Compute(); // compute the analysis
// Now we can show a summary of analysis
// Accord.Controls.DataGridBox.Show(regression.Coefficients);
// We can also show a summary ANOVA
// Accord.Controls.DataGridBox.Show(regression.Table);
// And also extract other useful information, such
// as the linear coefficients' values and std errors:
double[] coef = regression.CoefficientValues;
double[] stde = regression.StandardErrors;
// Coefficients of performance, such as r²
double rsquared = regression.RSquared;
// Hypothesis tests for the whole model
ZTest ztest = regression.ZTest;
FTest ftest = regression.FTest;
// and for individual coefficients
TTest ttest0 = regression.Coefficients[0].TTest;
TTest ttest1 = regression.Coefficients[1].TTest;
// and also extract confidence intervals
DoubleRange ci = regression.Coefficients[0].Confidence;
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);
Assert.AreEqual(0.99999999999999822, ztest.PValue);
Assert.AreEqual(0.018986050133298293, ftest.PValue, 1e-10);
Assert.AreEqual(0.0062299844256985537, ttest0.PValue);
Assert.AreEqual(0.53484850318449118, ttest1.PValue, 1e-14);
Assert.IsFalse(Double.IsNaN(ttest1.PValue));
Assert.AreEqual(3.2616314640800566, ci.Min);
Assert.AreEqual(14.219378746271506, ci.Max);
}
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);
}
private void buildModel()
{
if (independentVls == null) getMatrix();
if (intOrigin)
{
rA = new MultipleLinearRegressionAnalysis(independentVls, dependentVls, false);
}
else
{
rA = new MultipleLinearRegressionAnalysis(independentVls, dependentVls, true);
}
rA.Compute();
rmse = rA.StandardError;
ftest = rA.FTest.Statistic;
pv = rA.FTest.PValue;
r2 = rA.RSquared;
ar2 = rA.RSquareAdjusted;
double[]c = rA.CoefficientValues;
double[] c2;
int adj = 1;
if (intOrigin)
{
c2 = new double[c.Length + 1];
adj = 0;
}
else
{
c2 = new double[c.Length];
}
for (int i = 0; i < c2.Length - adj; i++)
{
c2[i + 1] = c[i];
}
if (intOrigin) c2[0] = 0;
else c2[0] = c.Last();
coefficients = c2;
double[] s = rA.StandardErrors;
double[] s2 = new double[c2.Length];
for (int i = 0; i < s2.Length - adj; i++)
{
s2[i + 1] = s[i];
}
if (intOrigin) s2[0] = 0;
else s2[0] = s.Last();
standarderrors = s2;
}
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);
}
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(new[] { 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(2, target.NumberOfInputs);
Assert.AreEqual(1, target.NumberOfOutputs);
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);
Assert.AreEqual(2, target.NumberOfInputs);
Assert.AreEqual(1, target.NumberOfOutputs);
double[] actual = target.Transform(inputs);
double[] expected = mlr.Transform(inputs);
Assert.IsTrue(Matrix.IsEqual(actual, expected, 1e-8));
double r2 = mlr.CoefficientOfDetermination(inputs, outputs, false);
double r2a = mlr.CoefficientOfDetermination(inputs, outputs, true);
Assert.AreEqual(r2, target.RSquared, 1e-6);
Assert.AreEqual(r2a, target.RSquareAdjusted, 1e-6);
}
public void ComputeTest2()
{
// 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);
// Next, we can create a new multiple linear regression for the variables
var regression = new MultipleLinearRegressionAnalysis(inputs, output, intercept: true);
regression.Compute(); // compute the analysis
// Now we can show a summary of analysis
// Accord.Controls.DataGridBox.Show(regression.Coefficients);
// We can also show a summary ANOVA
// Accord.Controls.DataGridBox.Show(regression.Table);
// And also extract other useful information, such
// as the linear coefficients' values and std errors:
double[] coef = regression.CoefficientValues;
double[] stde = regression.StandardErrors;
// Coefficients of performance, such as r²
double rsquared = regression.RSquared;
// Hypothesis tests for the whole model
ZTest ztest = regression.ZTest;
FTest ftest = regression.FTest;
// and for individual coefficients
TTest ttest0 = regression.Coefficients[0].TTest;
TTest ttest1 = regression.Coefficients[1].TTest;
// and also extract confidence intervals
DoubleRange ci = regression.Coefficients[0].Confidence;
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);
}
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);
}
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
this.inputs = independent.ToArray();
this.outputs = dependent.Columns[dependentName].ToArray();
// Creates the Simple Descriptive Analysis of the given source
var sda = new DescriptiveAnalysis()
{
ColumnNames = independentNames
}.Learn(inputs);
// TODO: Standardize the InputNames/OutputNames properties
// Populates statistics overview tab with analysis data
dgvDistributionMeasures.DataSource = sda.Measures;
// Creates the Logistic Regression Analysis of the given source
this.lra = new LogisticRegressionAnalysis()
{
Inputs = independentNames,
Output = dependentName
};
// Compute the Logistic Regression Analysis
LogisticRegression lr = lra.Learn(inputs, outputs);
// 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");
// Create the Multiple Linear Regression Analysis of the given source
this.mlr = new MultipleLinearRegressionAnalysis(intercept: true)
{
Inputs = independentNames,
Output = dependentName
};
// Compute the Linear Regression Analysis
MultipleLinearRegression reg = mlr.Learn(inputs, outputs);
dgvLinearCoefficients.DataSource = mlr.Coefficients;
dgvRegressionAnova.DataSource = mlr.Table;
tbRSquared.Text = mlr.RSquared.ToString("N5");
tbRSquaredAdj.Text = mlr.RSquareAdjusted.ToString("N5");
tbChiPValue.Text = mlr.ChiSquareTest.PValue.ToString("N5");
tbFPValue.Text = mlr.FTest.PValue.ToString("N5");
tbZPValue.Text = mlr.ZTest.PValue.ToString("N5");
tbChiStatistic.Text = mlr.ChiSquareTest.Statistic.ToString("N5");
tbFStatistic.Text = mlr.FTest.Statistic.ToString("N5");
tbZStatistic.Text = mlr.ZTest.Statistic.ToString("N5");
cbChiSignificant.Checked = mlr.ChiSquareTest.Significant;
cbFSignificant.Checked = mlr.FTest.Significant;
cbZSignificant.Checked = mlr.ZTest.Significant;
// 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;
}
