Calculate Standard Error of the Regression for a linear model (#464)

* Addd code to calculated Standard Error of the Regression for a linear model
* Added distinction between Standard Error calculations for populations vs. samples.
* Added copyright blurb to StandardErrorTest.cs
* Fixed filename in copyright blurb in StandardErrorTest.cs

src/Numerics/GoodnessOfFit.cs

@@ -25,7 +25,9 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
+using System;
 using System.Collections.Generic;
+using MathNet.Numerics.Properties;
 using MathNet.Numerics.Statistics;
 
 namespace MathNet.Numerics
@@ -33,7 +35,7 @@ namespace MathNet.Numerics
     public static class GoodnessOfFit
     {
         /// <summary>
-        /// Calculated the R-Squared value, also known as coefficient of determination,
+        /// Calculates the R-Squared value, also known as coefficient of determination,
         /// given modelled and observed values
         /// </summary>
         /// <param name="modelledValues">The values expected from the modelled</param>
@@ -46,7 +48,7 @@ namespace MathNet.Numerics
         }
 
         /// <summary>
-        /// Calculated the R value, also known as linear correlation coefficient,
+        /// Calculates the R value, also known as linear correlation coefficient,
         /// given modelled and observed values
         /// </summary>
         /// <param name="modelledValues">The values expected from the modelled</param>
@@ -56,5 +58,54 @@ namespace MathNet.Numerics
         {
             return Correlation.Pearson(modelledValues, observedValues);
         }
+
+        /// <summary>
+        /// Calculates the Standard Error of the regression, given a sequence of
+        /// modeled/predicted values, and a sequence of actual/observed values 
+        /// </summary>
+        /// <param name="modelledValues">The modelled/predicted values</param>
+        /// <param name="observedValues">The observed/actual values</param>
+        /// <returns>The Standard Error of the regression</returns>
+        public static double PopulationStandardError(IEnumerable<double> modelledValues, IEnumerable<double> observedValues)
+        {
+            return SampleStandardError(modelledValues, observedValues, 0);
+        }
+
+        /// <summary>
+        /// Calculates the Standard Error of the regression, given a sequence of
+        /// modeled/predicted values, and a sequence of actual/observed values
+        /// </summary>
+        /// <param name="modelledValues">The modelled/predicted values</param>
+        /// <param name="observedValues">The observed/actual values</param>
+        /// <param name="degreesOfFreedom">The degrees of freedom by which the 
+        /// number of samples is reduced for performing the Standard Error calculation</param>
+        /// <returns>The Standard Error of the regression</returns>
+        public static double SampleStandardError(IEnumerable<double> modelledValues, IEnumerable<double> observedValues, int degreesOfFreedom)
+        {
+            using (IEnumerator<double> ieM = modelledValues.GetEnumerator())
+            using (IEnumerator<double> ieO = observedValues.GetEnumerator())
+            {
+                double n = 0;
+                double accumulator = 0;
+                while (ieM.MoveNext())
+                {
+                    if (!ieO.MoveNext())
+                    {
+                        throw new ArgumentOutOfRangeException("modelledValues", Resources.ArgumentArraysSameLength);
+                    }
+                    double currentM = ieM.Current;
+                    double currentO = ieO.Current;
+                    var diff = currentM - currentO;
+                    accumulator += diff * diff;
+                    n++;
+                }
+
+                if (degreesOfFreedom >= n)
+                {
+                    throw new ArgumentOutOfRangeException("degreesOfFreedom", Resources.DegreesOfFreedomMustBeLessThanSampleSize);
+                }
+                return Math.Sqrt(accumulator / (n - degreesOfFreedom));
+            }
+        }
     }
 }

src/Numerics/Properties/Resources.Designer.cs

@@ -602,6 +602,15 @@ namespace MathNet.Numerics.Properties {
             }
         }
         
+        /// <summary>
+        ///   Looks up a localized string similar to The sample size must be larger than the given degrees of freedom..
+        /// </summary>
+        public static string DegreesOfFreedomMustBeLessThanSampleSize {
+            get {
+                return ResourceManager.GetString("DegreesOfFreedomMustBeLessThanSampleSize", resourceCulture);
+            }
+        }
+        
         /// <summary>
         ///   Looks up a localized string similar to This feature is not implemented yet (but is planned)..
         /// </summary>

src/Numerics/Properties/Resources.resx

@@ -445,4 +445,7 @@
   <data name="SampleVectorsSameLength" xml:space="preserve">
     <value>All sample vectors must have the same length. However, vectors with disagreeing length {0} and {1} have been provided. A sample with index i is given by the value at index i of each provided vector.</value>
   </data>
+  <data name="DegreesOfFreedomMustBeLessThanSampleSize" xml:space="preserve">
+    <value>The sample size must be larger than the given degrees of freedom.</value>
+  </data>
 </root>

src/UnitTests/GoodnessOfFit/StandardErrorTest.cs

@@ -0,0 +1,86 @@
+// <copyright file="StandardErrorTest.cs" company="Math.NET">
+// Math.NET Numerics, part of the Math.NET Project
+// http://numerics.mathdotnet.com
+// http://github.com/mathnet/mathnet-numerics
+//
+// Copyright (c) 2009-2013 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
+// restriction, including without limitation the rights to use,
+// copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the
+// Software is furnished to do so, subject to the following
+// conditions:
+//
+// The above copyright notice and this permission notice shall be
+// included in all copies or substantial portions of the Software.
+//
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
+// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
+// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+// OTHER DEALINGS IN THE SOFTWARE.
+// </copyright>
+
+using System;
+using System.Linq;
+using NUnit.Framework;
+
+namespace MathNet.Numerics.UnitTests.GoodnessOfFit
+{
+    [TestFixture, Category("Regression")]
+    public class StandardErrorTest
+    {
+        [Test]
+        public void ComputesPopulationStandardErrorOfTheRegression()
+        {
+            // Definition as described at: http://onlinestatbook.com/lms/regression/accuracy.html
+            var xes = new[] { 1.0, 2, 3, 4, 5 };
+            var ys = new[] { 1, 2, 1.3, 3.75, 2.25 };
+            var fit = Fit.Line(xes, ys);
+            var a = fit.Item1;
+            var b = fit.Item2;
+            var predictedYs = xes.Select(x => a + b * x);
+            var standardError = Numerics.GoodnessOfFit.PopulationStandardError(predictedYs, ys);
+
+            Assert.AreEqual(0.747, standardError, 1e-3);
+        }
+
+        [Test]
+        public void ComputesSampleStandardErrorOfTheRegression()
+        {
+            // Definition as described at: http://onlinestatbook.com/lms/regression/accuracy.html
+            var xes = new[] { 1.0, 2, 3, 4, 5 };
+            var ys = new[] { 1, 2, 1.3, 3.75, 2.25 };
+            var fit = Fit.Line(xes, ys);
+            var a = fit.Item1;
+            var b = fit.Item2;
+            var predictedYs = xes.Select(x => a + b * x);
+            var standardError = Numerics.GoodnessOfFit.SampleStandardError(predictedYs, ys, degreesOfFreedom: 2);
+
+            Assert.AreEqual(0.964, standardError, 1e-3);
+        }
+
+        [Test]
+        public void PopulationStandardErrorShouldThrowIfInputsSequencesDifferInLength()
+        {
+            var y1 = new[] { 0.0, 1 };
+            var y2 = new[] { 1.0 };
+
+            Assert.Throws<ArgumentOutOfRangeException>(() => Numerics.GoodnessOfFit.PopulationStandardError(y1, y2));
+        }
+
+        [Test]
+        public void SampleStandardErrorShouldThrowIfSampleSizeIsSmallerThanGivenDegreesOfFreedom()
+        {
+            var modelled = new[] { 1.0 };
+            var observed = new[] { 1.0 };
+            Assert.Throws<ArgumentOutOfRangeException>(() => Numerics.GoodnessOfFit.SampleStandardError(modelled, observed, 2));
+        }
+    }
+}

src/UnitTests/UnitTests.csproj

@@ -142,6 +142,7 @@
     <Compile Include="FinancialTests\SemiDeviationTests.cs" />
     <Compile Include="GenerateTests.cs" />
     <Compile Include="GoodnessOfFit\RSquaredTest.cs" />
+    <Compile Include="GoodnessOfFit\StandardErrorTest.cs" />
     <Compile Include="Providers\FourierTransform\FourierTransformProviderTests.cs" />
     <Compile Include="IntegralTransformsTests\FourierTest.cs" />
     <Compile Include="IntegralTransformsTests\HartleyTest.cs" />