/// <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[regression.Coefficients.Length];
for (int j = 0; j < X[i].Length; j++)
{
// Create polynomial members
X[i][j] = Math.Pow(inputs[i], j);
}
}
return(regression.CoefficientOfDetermination(X, outputs, adjust));
}