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;
}