PolynomialRegression Class 
Namespace: Accord.Statistics.Models.Regression.Linear
[SerializableAttribute] public class PolynomialRegression : TransformBase<double, double>, ILinearRegression, IFormattable
The PolynomialRegression type exposes the following members.
Name  Description  

PolynomialRegression 
Creates a new Polynomial Linear Regression.
 
PolynomialRegression(Int32) 
Creates a new Polynomial Linear Regression.
 
PolynomialRegression(MultipleLinearRegression) 
Creates a new Polynomial Linear Regression.

Name  Description  

Coefficients  Obsolete.
Gets the coefficients of the polynomial regression,
with the first being the higherorder term and the last
the intercept term.
 
Degree 
Gets the degree of the polynomial used by the regression.
 
Intercept 
Gets or sets the intercept value for the regression.
 
NumberOfInputs 
Gets the number of inputs accepted by the model.
(Inherited from TransformBaseTInput, TOutput.)  
NumberOfOutputs 
Gets the number of outputs generated by the model.
(Inherited from TransformBaseTInput, TOutput.)  
Weights 
Gets or sets the linear weights of the regression model. The
intercept term is not stored in this vector, but is instead
available through the Intercept property.

Name  Description  

CoefficientOfDetermination(Double, Double, Double) 
Gets the coefficient of determination, as known as R² (rsquared).
 
CoefficientOfDetermination(Double, Double, Boolean, Double) 
Gets the coefficient of determination, as known as R² (rsquared).
 
Compute(Double)  Obsolete.
Computes the regressed model output for the given input.
 
Compute(Double)  Obsolete.
Computes the regressed model output for the given inputs.
 
Equals  Determines whether the specified object is equal to the current object. (Inherited from Object.)  
Finalize  Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.)  
FromData 
Creates a new polynomial regression directly from data points.
 
GetHashCode  Serves as the default hash function. (Inherited from Object.)  
GetType  Gets the Type of the current instance. (Inherited from Object.)  
MemberwiseClone  Creates a shallow copy of the current Object. (Inherited from Object.)  
Regress  Obsolete.
Performs the regression using the input and output
data, returning the sum of squared errors of the fit.
 
ToString 
Returns a System.String representing the regression.
(Overrides ObjectToString.)  
ToString(IFormatProvider) 
Returns a System.String representing the regression.
 
ToString(String) 
Returns a System.String representing the regression.
 
ToString(String, IFormatProvider) 
Returns a System.String representing the regression.
 
Transform(TInput) 
Applies the transformation to a set of input vectors,
producing an associated set of output vectors.
(Inherited from TransformBaseTInput, TOutput.)  
Transform(Double) 
Applies the transformation to an input, producing an associated output.
(Overrides TransformBaseTInput, TOutputTransform(TInput).)  
Transform(Double, Double) 
Applies the transformation to an input, producing an associated output.
(Overrides TransformBaseTInput, TOutputTransform(TInput, TOutput).) 
Name  Description  

HasMethod 
Checks whether an object implements a method with the given name.
(Defined by ExtensionMethods.)  
IsEqual 
Compares two objects for equality, performing an elementwise
comparison if the elements are vectors or matrices.
(Defined by Matrix.)  
To(Type)  Overloaded.
Converts an object into another type, irrespective of whether
the conversion can be done at compile time or not. This can be
used to convert generic types to numeric types during runtime.
(Defined by ExtensionMethods.)  
ToT  Overloaded.
Converts an object into another type, irrespective of whether
the conversion can be done at compile time or not. This can be
used to convert generic types to numeric types during runtime.
(Defined by ExtensionMethods.) 
// Let's say we would like to learn 2nd degree polynomial that // can map the first column X into its second column Y. We have // 5 examples of those (x,y) pairs that we can use to learn this // function: double[,] data = { // X Y { 12, 144 }, // example #1 { 15, 225 }, // example #2 { 20, 400 }, // example #3 { 25, 625 }, // example #4 { 35, 1225 }, // example #5 }; // Let's retrieve the input and output data: double[] inputs = data.GetColumn(0); // X double[] outputs = data.GetColumn(1); // Y // We can create a learning algorithm var ls = new PolynomialLeastSquares() { Degree = 2 }; // Now, we can use the algorithm to learn a polynomial PolynomialRegression poly = ls.Learn(inputs, outputs); // The learned polynomial will be given by string str = poly.ToString("N1"); // "y(x) = 1.0x^2 + 0.0x^1 + 0.0" // Where its weights can be accessed using double[] weights = poly.Weights; // { 1.0000000000000024, 1.2407665029287351E13 } double intercept = poly.Intercept; // 1.5652369518855253E12 // Finally, we can use this polynomial // to predict values for the input data double[] pred = poly.Transform(inputs); // Where the meansquarederror (MSE) should be double error = new SquareLoss(outputs).Loss(pred); // 0.0