diff --git a/src/Numerics/Fit.cs b/src/Numerics/Fit.cs
index 2a829c5e..9960e87a 100644
--- a/src/Numerics/Fit.cs
+++ b/src/Numerics/Fit.cs
@@ -3,9 +3,9 @@
 // http://numerics.mathdotnet.com
 // http://github.com/mathnet/mathnet-numerics
 // http://mathnetnumerics.codeplex.com
-// 
-// Copyright (c) 2009-2013 Math.NET
-// 
+//
+// Copyright (c) 2009-2015 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
@@ -14,10 +14,10 @@
 // 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
@@ -94,6 +94,7 @@ namespace MathNet.Numerics
         /// <summary>
         /// Least-Squares fitting the points (x,y) to a k-order polynomial y : x -> p0 + p1*x + p2*x^2 + ... + pk*x^k,
         /// returning its best fitting parameters as [p0, p1, p2, ..., pk] array, compatible with Evaluate.Polynomial.
+        /// A polynomial with order/degree k has (k+1) coefficients and thus requires at least (k+1) samples.
         /// </summary>
         public static double[] Polynomial(double[] x, double[] y, int order, DirectRegressionMethod method = DirectRegressionMethod.QR)
         {
@@ -104,6 +105,7 @@ namespace MathNet.Numerics
         /// <summary>
         /// Least-Squares fitting the points (x,y) to a k-order polynomial y : x -> p0 + p1*x + p2*x^2 + ... + pk*x^k,
         /// returning a function y' for the best fitting polynomial.
+        /// A polynomial with order/degree k has (k+1) coefficients and thus requires at least (k+1) samples.
         /// </summary>
         public static Func<double, double> PolynomialFunc(double[] x, double[] y, int order, DirectRegressionMethod method = DirectRegressionMethod.QR)
         {
@@ -114,6 +116,7 @@ namespace MathNet.Numerics
         /// <summary>
         /// Weighted Least-Squares fitting the points (x,y) and weights w to a k-order polynomial y : x -> p0 + p1*x + p2*x^2 + ... + pk*x^k,
         /// returning its best fitting parameters as [p0, p1, p2, ..., pk] array, compatible with Evaluate.Polynomial.
+        /// A polynomial with order/degree k has (k+1) coefficients and thus requires at least (k+1) samples.
         /// </summary>
         public static double[] PolynomialWeighted(double[] x, double[] y, double[] w, int order)
         {
diff --git a/src/Numerics/LinearRegression/MultipleRegression.cs b/src/Numerics/LinearRegression/MultipleRegression.cs
index 42e1a705..d925c65e 100644
--- a/src/Numerics/LinearRegression/MultipleRegression.cs
+++ b/src/Numerics/LinearRegression/MultipleRegression.cs
@@ -3,9 +3,9 @@
 // http://numerics.mathdotnet.com
 // http://github.com/mathnet/mathnet-numerics
 // http://mathnetnumerics.codeplex.com
-// 
-// Copyright (c) 2009-2014 Math.NET
-// 
+//
+// Copyright (c) 2009-2015 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
@@ -14,10 +14,10 @@
 // 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
@@ -31,6 +31,7 @@
 using System;
 using System.Collections.Generic;
 using MathNet.Numerics.LinearAlgebra;
+using MathNet.Numerics.Properties;
 
 namespace MathNet.Numerics.LinearRegression
 {
@@ -135,6 +136,16 @@ namespace MathNet.Numerics.LinearRegression
         /// <returns>Best fitting vector for model parameters β</returns>
         public static Vector<T> NormalEquations<T>(Matrix<T> x, Vector<T> y) where T : struct, IEquatable<T>, IFormattable
         {
+            if (x.RowCount != y.Count)
+            {
+                throw new ArgumentException(string.Format(Resources.SampleVectorsSameLength, x.RowCount, y.Count));
+            }
+
+            if (x.ColumnCount > y.Count)
+            {
+                throw new ArgumentException(string.Format(Resources.RegressionNotEnoughSamples, x.ColumnCount, y.Count));
+            }
+
             return x.TransposeThisAndMultiply(x).Cholesky().Solve(x.TransposeThisAndMultiply(y));
         }
 
@@ -147,6 +158,16 @@ namespace MathNet.Numerics.LinearRegression
         /// <returns>Best fitting vector for model parameters β</returns>
         public static Matrix<T> NormalEquations<T>(Matrix<T> x, Matrix<T> y) where T : struct, IEquatable<T>, IFormattable
         {
+            if (x.RowCount != y.RowCount)
+            {
+                throw new ArgumentException(string.Format(Resources.SampleVectorsSameLength, x.RowCount, y.RowCount));
+            }
+
+            if (x.ColumnCount > y.RowCount)
+            {
+                throw new ArgumentException(string.Format(Resources.RegressionNotEnoughSamples, x.ColumnCount, y.RowCount));
+            }
+
             return x.TransposeThisAndMultiply(x).Cholesky().Solve(x.TransposeThisAndMultiply(y));
         }
 
@@ -166,6 +187,16 @@ namespace MathNet.Numerics.LinearRegression
                 predictor = predictor.InsertColumn(0, Vector<T>.Build.Dense(predictor.RowCount, Vector<T>.One));
             }
 
+            if (predictor.RowCount != y.Length)
+            {
+                throw new ArgumentException(string.Format(Resources.SampleVectorsSameLength, predictor.RowCount, y.Length));
+            }
+
+            if (predictor.ColumnCount > y.Length)
+            {
+                throw new ArgumentException(string.Format(Resources.RegressionNotEnoughSamples, predictor.ColumnCount, y.Length));
+            }
+
             var response = Vector<T>.Build.Dense(y);
             return predictor.TransposeThisAndMultiply(predictor).Cholesky().Solve(predictor.TransposeThisAndMultiply(response)).ToArray();
         }
@@ -192,6 +223,16 @@ namespace MathNet.Numerics.LinearRegression
         /// <returns>Best fitting vector for model parameters β</returns>
         public static Vector<T> QR<T>(Matrix<T> x, Vector<T> y) where T : struct, IEquatable<T>, IFormattable
         {
+            if (x.RowCount != y.Count)
+            {
+                throw new ArgumentException(string.Format(Resources.SampleVectorsSameLength, x.RowCount, y.Count));
+            }
+
+            if (x.ColumnCount > y.Count)
+            {
+                throw new ArgumentException(string.Format(Resources.RegressionNotEnoughSamples, x.ColumnCount, y.Count));
+            }
+
             return x.QR().Solve(y);
         }
 
@@ -204,6 +245,16 @@ namespace MathNet.Numerics.LinearRegression
         /// <returns>Best fitting vector for model parameters β</returns>
         public static Matrix<T> QR<T>(Matrix<T> x, Matrix<T> y) where T : struct, IEquatable<T>, IFormattable
         {
+            if (x.RowCount != y.RowCount)
+            {
+                throw new ArgumentException(string.Format(Resources.SampleVectorsSameLength, x.RowCount, y.RowCount));
+            }
+
+            if (x.ColumnCount > y.RowCount)
+            {
+                throw new ArgumentException(string.Format(Resources.RegressionNotEnoughSamples, x.ColumnCount, y.RowCount));
+            }
+
             return x.QR().Solve(y);
         }
 
@@ -223,6 +274,16 @@ namespace MathNet.Numerics.LinearRegression
                 predictor = predictor.InsertColumn(0, Vector<T>.Build.Dense(predictor.RowCount, Vector<T>.One));
             }
 
+            if (predictor.RowCount != y.Length)
+            {
+                throw new ArgumentException(string.Format(Resources.SampleVectorsSameLength, predictor.RowCount, y.Length));
+            }
+
+            if (predictor.ColumnCount > y.Length)
+            {
+                throw new ArgumentException(string.Format(Resources.RegressionNotEnoughSamples, predictor.ColumnCount, y.Length));
+            }
+
             return predictor.QR().Solve(Vector<T>.Build.Dense(y)).ToArray();
         }
 
@@ -248,6 +309,16 @@ namespace MathNet.Numerics.LinearRegression
         /// <returns>Best fitting vector for model parameters β</returns>
         public static Vector<T> Svd<T>(Matrix<T> x, Vector<T> y) where T : struct, IEquatable<T>, IFormattable
         {
+            if (x.RowCount != y.Count)
+            {
+                throw new ArgumentException(string.Format(Resources.SampleVectorsSameLength, x.RowCount, y.Count));
+            }
+
+            if (x.ColumnCount > y.Count)
+            {
+                throw new ArgumentException(string.Format(Resources.RegressionNotEnoughSamples, x.ColumnCount, y.Count));
+            }
+
             return x.Svd().Solve(y);
         }
 
@@ -260,6 +331,16 @@ namespace MathNet.Numerics.LinearRegression
         /// <returns>Best fitting vector for model parameters β</returns>
         public static Matrix<T> Svd<T>(Matrix<T> x, Matrix<T> y) where T : struct, IEquatable<T>, IFormattable
         {
+            if (x.RowCount != y.RowCount)
+            {
+                throw new ArgumentException(string.Format(Resources.SampleVectorsSameLength, x.RowCount, y.RowCount));
+            }
+
+            if (x.ColumnCount > y.RowCount)
+            {
+                throw new ArgumentException(string.Format(Resources.RegressionNotEnoughSamples, x.ColumnCount, y.RowCount));
+            }
+
             return x.Svd().Solve(y);
         }
 
@@ -279,6 +360,16 @@ namespace MathNet.Numerics.LinearRegression
                 predictor = predictor.InsertColumn(0, Vector<T>.Build.Dense(predictor.RowCount, Vector<T>.One));
             }
 
+            if (predictor.RowCount != y.Length)
+            {
+                throw new ArgumentException(string.Format(Resources.SampleVectorsSameLength, predictor.RowCount, y.Length));
+            }
+
+            if (predictor.ColumnCount > y.Length)
+            {
+                throw new ArgumentException(string.Format(Resources.RegressionNotEnoughSamples, predictor.ColumnCount, y.Length));
+            }
+
             return predictor.Svd().Solve(Vector<T>.Build.Dense(y)).ToArray();
         }
 
diff --git a/src/Numerics/LinearRegression/SimpleRegression.cs b/src/Numerics/LinearRegression/SimpleRegression.cs
index 1b2cbc1a..41332cdd 100644
--- a/src/Numerics/LinearRegression/SimpleRegression.cs
+++ b/src/Numerics/LinearRegression/SimpleRegression.cs
@@ -3,9 +3,9 @@
 // http://numerics.mathdotnet.com
 // http://github.com/mathnet/mathnet-numerics
 // http://mathnetnumerics.codeplex.com
-// 
+//
 // 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
@@ -14,10 +14,10 @@
 // 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
@@ -47,12 +47,12 @@ namespace MathNet.Numerics.LinearRegression
         {
             if (x.Length != y.Length)
             {
-                throw new ArgumentException(Resources.ArgumentVectorsSameLength);
+                throw new ArgumentException(string.Format(Resources.SampleVectorsSameLength, x.Length, y.Length));
             }
 
             if (x.Length <= 1)
             {
-                throw new ArgumentException(string.Format(Resources.ArrayTooSmall, 2));
+                throw new ArgumentException(string.Format(Resources.RegressionNotEnoughSamples, 2, x.Length));
             }
 
             // First Pass: Mean (Less robust but faster than ArrayStatistics.Mean)
diff --git a/src/Numerics/Properties/Resources.Designer.cs b/src/Numerics/Properties/Resources.Designer.cs
index a8569c78..b4650370 100644
--- a/src/Numerics/Properties/Resources.Designer.cs
+++ b/src/Numerics/Properties/Resources.Designer.cs
@@ -1,7 +1,7 @@
 //------------------------------------------------------------------------------
 // <auto-generated>
 //     This code was generated by a tool.
-//     Runtime Version:4.0.30319.34209
+//     Runtime Version:4.0.30319.42000
 //
 //     Changes to this file may cause incorrect behavior and will be lost if
 //     the code is regenerated.
@@ -12,8 +12,8 @@ using System.Reflection;
 
 namespace MathNet.Numerics.Properties {
     using System;
-
-
+    
+    
     /// <summary>
     ///   A strongly-typed resource class, for looking up localized strings, etc.
     /// </summary>
@@ -25,15 +25,15 @@ namespace MathNet.Numerics.Properties {
     [global::System.Diagnostics.DebuggerNonUserCodeAttribute()]
     [global::System.Runtime.CompilerServices.CompilerGeneratedAttribute()]
     public class Resources {
-
+        
         private static global::System.Resources.ResourceManager resourceMan;
-
+        
         private static global::System.Globalization.CultureInfo resourceCulture;
-
+        
         [global::System.Diagnostics.CodeAnalysis.SuppressMessageAttribute("Microsoft.Performance", "CA1811:AvoidUncalledPrivateCode")]
         internal Resources() {
         }
-
+        
         /// <summary>
         ///   Returns the cached ResourceManager instance used by this class.
         /// </summary>
@@ -56,7 +56,7 @@ namespace MathNet.Numerics.Properties {
                 return resourceMan;
             }
         }
-
+        
         /// <summary>
         ///   Overrides the current thread's CurrentUICulture property for all
         ///   resource lookups using this strongly typed resource class.
@@ -394,7 +394,7 @@ namespace MathNet.Numerics.Properties {
                 return ResourceManager.GetString("ArgumentOutOfRangeSmaller", resourceCulture);
             }
         }
-
+        
         /// <summary>
         ///   Looks up a localized string similar to {0} must be smaller than or equal to {1}..
         /// </summary>
@@ -403,7 +403,7 @@ namespace MathNet.Numerics.Properties {
                 return ResourceManager.GetString("ArgumentOutOfRangeSmallerEqual", resourceCulture);
             }
         }
-
+        
         /// <summary>
         ///   Looks up a localized string similar to The chosen parameter set is invalid (probably some value is out of range)..
         /// </summary>
@@ -864,6 +864,15 @@ namespace MathNet.Numerics.Properties {
             }
         }
         
+        /// <summary>
+        ///   Looks up a localized string similar to A regression of the requested order requires at least {0} samples. Only {1} samples have been provided. .
+        /// </summary>
+        public static string RegressionNotEnoughSamples {
+            get {
+                return ResourceManager.GetString("RegressionNotEnoughSamples", resourceCulture);
+            }
+        }
+        
         /// <summary>
         ///   Looks up a localized string similar to The algorithm has failed, exceeded the number of iterations allowed or there is no root within the provided bounds..
         /// </summary>
@@ -909,6 +918,15 @@ namespace MathNet.Numerics.Properties {
             }
         }
         
+        /// <summary>
+        ///   Looks up a localized string similar to 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..
+        /// </summary>
+        public static string SampleVectorsSameLength {
+            get {
+                return ResourceManager.GetString("SampleVectorsSameLength", resourceCulture);
+            }
+        }
+        
         /// <summary>
         ///   Looks up a localized string similar to U is singular, and the inversion could not be completed..
         /// </summary>
diff --git a/src/Numerics/Properties/Resources.resx b/src/Numerics/Properties/Resources.resx
index d87f9a72..e3c53791 100644
--- a/src/Numerics/Properties/Resources.resx
+++ b/src/Numerics/Properties/Resources.resx
@@ -436,4 +436,10 @@
   <data name="SingularUMatrixWithElement" xml:space="preserve">
     <value>U is singular, and the inversion could not be completed. The {0}-th diagonal element of the factor U is zero.</value>
   </data>
+  <data name="RegressionNotEnoughSamples" xml:space="preserve">
+    <value>A regression of the requested order requires at least {0} samples. Only {1} samples have been provided. </value>
+  </data>
+  <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>
 </root>
\ No newline at end of file