diff --git a/src/Numerics/GoodnessOfFit.cs b/src/Numerics/GoodnessOfFit.cs
index 5972384f..29ad6cca 100644
--- a/src/Numerics/GoodnessOfFit.cs
+++ b/src/Numerics/GoodnessOfFit.cs
@@ -3,6 +3,8 @@
// http://numerics.mathdotnet.com
// http://github.com/mathnet/mathnet-numerics
//
+// Copyright (c) 2009-2018 Math.NET
+//
// Permission is hereby granted, free of charge, to any person
// obtaining a copy of this software and associated documentation
// files (the "Software"), to deal in the Software without
@@ -61,7 +63,7 @@ namespace MathNet.Numerics
///
/// Calculates the Standard Error of the regression, given a sequence of
- /// modeled/predicted values, and a sequence of actual/observed values
+ /// modeled/predicted values, and a sequence of actual/observed values
///
/// The modelled/predicted values
/// The observed/actual values
@@ -77,7 +79,7 @@ namespace MathNet.Numerics
///
/// The modelled/predicted values
/// The observed/actual values
- /// The degrees of freedom by which the
+ /// The degrees of freedom by which the
/// number of samples is reduced for performing the Standard Error calculation
/// The Standard Error of the regression
public static double StandardError(IEnumerable modelledValues, IEnumerable observedValues, int degreesOfFreedom)
@@ -107,5 +109,65 @@ namespace MathNet.Numerics
return Math.Sqrt(accumulator / (n - degreesOfFreedom));
}
}
+
+ ///
+ /// Calculates the R-Squared value, also known as coefficient of determination,
+ /// given some modelled and observed values.
+ ///
+ /// The values expected from the model.
+ /// The actual values obtained.
+ /// Coefficient of determination.
+ public static double CoefficientOfDetermination(IEnumerable modelledValues, IEnumerable observedValues)
+ {
+ var y = observedValues;
+ var f = modelledValues;
+ int n = 0;
+
+ double meanY = 0;
+ double ssTot = 0;
+ double ssRes = 0;
+
+ using (IEnumerator ieY = y.GetEnumerator())
+ using (IEnumerator ieF = f.GetEnumerator())
+ {
+ while (ieY.MoveNext())
+ {
+ if (!ieF.MoveNext())
+ {
+ throw new ArgumentOutOfRangeException("modelledValues", Resources.ArgumentArraysSameLength);
+ }
+
+ double currentY = ieY.Current;
+ double currentF = ieF.Current;
+
+ // If a large constant C is added to every y value,
+ // then each new y have an error of about C*eps,
+ // thus each new deltaY will change by about C*eps (compared to the old deltaY),
+ // and thus ssTot will change by only C*eps*deltaY on each step
+ // thus C*eps*deltaY*n in total.
+ // (This error cannot be eliminated by a Kahan algorithm,
+ // because it is introduced when C is added to the old Y value).
+ //
+ // This is better than summing the square of y values
+ // and then substracting the correct multiple of the square of the sum of y values,
+ // in this latter case ssTot will change by eps*n*(C^2+2*C*meanY) in total.
+ double deltaY = currentY - meanY;
+ double scaleDeltaY = deltaY / ++n;
+
+ meanY += scaleDeltaY;
+ ssTot += scaleDeltaY* deltaY* (n - 1);
+
+ // This calculation is as safe as ssTot
+ // in the case when a constant is added to both y and f.
+ ssRes += (currentY - currentF)* (currentY-currentF);
+ }
+
+ if (ieF.MoveNext())
+ {
+ throw new ArgumentOutOfRangeException("observedValues", Resources.ArgumentArraysSameLength);
+ }
+ }
+ return 1 - ssRes/ssTot;
+ }
}
}