mathnet-numerics/src/Numerics.Tests/GoodnessOfFit/RSquaredTest.cs

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// Math.NET Numerics, part of the Math.NET Project
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// http://github.com/mathnet/mathnet-numerics
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using System;
using System.Collections.Generic;
using NUnit.Framework;

namespace MathNet.Numerics.UnitTests.GoodnessOfFit
{
    [TestFixture, Category("Regression")]
    public class RSquaredTest
    {
        /// <summary>
        /// Test the R-squared value of a values with itself
        /// </summary>
        [Test]
        public void WhenCalculatingRSquaredOfLinearDistributionWithItselfThenRSquaredIsOne()
        {
            var data = new List<double>();
            for (int i = 1; i <= 10; i++)
            {
                data.Add(i);
            }

            Assert.That(Numerics.GoodnessOfFit.RSquared(data, data), Is.EqualTo(1));
        }

        /// <summary>
        /// Test the R-squared value of values with itself
        /// </summary>
        [Test]
        public void CoefficentOfDetermination_OfDataWithItself_EqualsOne()
        {
            var data = Generate.LinearRange(1, 100);
            AssertHelpers.AlmostEqual(Numerics.GoodnessOfFit.CoefficientOfDetermination(data, data), 1.0, 14);
        }

        /// <summary>
        /// Test the R-squared value of values with correlated values
        /// </summary>
        [Test]
        public void CoefficentOfDetermination_OfCorrelatedData_DoesNotEqualOne()
        {
            // parameters
            int n = 100;
            int offset = 1;

            // actual values and comparison
            var data = Generate.LinearRange(1, n);
            var model = Generate.LinearRange(1+offset, n+offset);
            double R2Calc = Numerics.GoodnessOfFit.CoefficientOfDetermination(model, data);
            Assert.That(R2Calc, Is.Not.EqualTo(1));
        }

        /// <summary>
        /// Test the R-squared value of values with correlated values
        /// </summary>
        [Test]
        public void CoefficentOfDetermination_OfCorrelatedData_KnownOutput()
        {
            // parameters
            int n = 100;
            int offset = 1;

            // theoretical values
            double ssTot = (n*(n-1)*(n+1))/12.0;
            double ssRes = n*offset*offset;
            double R2 = 1-ssRes/ssTot;

            // actual values and comparison
            var data = Generate.LinearRange(1, n);
            var model = Generate.LinearRange(1+offset, n+offset);
            double R2Calc = Numerics.GoodnessOfFit.CoefficientOfDetermination(model, data);
            AssertHelpers.AlmostEqual(R2Calc, R2, 14);
        }

        [Test]
        public void WhenGivenTwoDatasetsOfDifferentSizeThenThrowsArgumentException()
        {
            var observedData = new List<double> { 23, 9, 5, 7, 10, 5, 4, 1, 2, 1 };
            var modelledData = new List<double> { 8, 9, 10 };

            Assert.Throws<ArgumentOutOfRangeException>(() => Numerics.GoodnessOfFit.RSquared(modelledData, observedData));
        }

        [Test]
        public void WhenCalculatingRSquaredOfUnevenDistributionWithLInearDistributionThenRSquaredIsCalculated()
        {
            var observedData = new List<double> { 1, 2.3, 3.1, 4.8, 5.6, 6.3 };
            var modelledData = new List<double> { 2.6, 2.8, 3.1, 4.7, 5.1, 5.3 };

            Assert.That(Math.Round(Numerics.GoodnessOfFit.RSquared(modelledData, observedData), 11), Is.EqualTo(Math.Round(0.94878520708673d, 11)));
        }
    }
}