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Showing content from http://accord-framework.net/docs/html/T_Accord_Math_Optimization_Losses_RSquaredLoss.htm below:

R² (r-squared) loss.

Accord.Math (in Accord.Math.dll) Version: 3.8.0

[SerializableAttribute]
public class RSquaredLoss : LossBase<double[][], double[][], double[]>, 
	ILoss<double[]>, ILoss<double[], double>

<SerializableAttribute>
Public Class RSquaredLoss
	Inherits LossBase(Of Double()(), Double()(), Double())
	Implements ILoss(Of Double()), ILoss(Of Double(), Double)

The RSquaredLoss type exposes the following members.

Gets whether the adjusted version of the R² measure should be computed instead.

Gets the expected outputs (the ground truth).

Gets or sets the number of variables being fit in the problem.

Gets or sets the weights associated with each input-output pair.

Determines whether the specified object is equal to the current object.

Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection.

Serves as the default hash function.

Gets the Type of the current instance.

Computes the loss between the expected values (ground truth) and the given actual values that have been predicted.

Computes the loss between the expected values (ground truth) and the given actual values that have been predicted.

Creates a shallow copy of the current Object.

Returns a string that represents the current object.

Checks whether an object implements a method with the given name.

Compares two objects for equality, performing an elementwise comparison if the elements are vectors or matrices.

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.

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.

This example shows how to fit a multiple linear regression model and compute adjusted and non-adjusted versions of the R² coefficient of determination at the end:

Servo servo = new Servo();
object[][] instances = servo.Instances; 
double[] outputs = servo.Output;        








var codebook = new Codification<object>()
{
    { "motor", CodificationVariable.Categorical },
    { "screw", CodificationVariable.Categorical },
    { "pgain", CodificationVariable.Continuous },
    { "vgain", CodificationVariable.Continuous },
};


codebook.Learn(instances);


int numberOfInputs = codebook.NumberOfInputs;   
int numberOfOutputs = codebook.NumberOfOutputs; 


double[][] inputs = codebook.ToDouble().Transform(instances);



var ols = new OrdinaryLeastSquares()
{
    UseIntercept = true
};


MultipleLinearRegression regression = ols.Learn(inputs, outputs);


double[] predicted = regression.Transform(inputs);


double error = new SquareLoss(outputs).Loss(predicted);


double r2 = new RSquaredLoss(numberOfOutputs, outputs).Loss(predicted); 


var r2loss = new RSquaredLoss(numberOfOutputs, outputs)
{
    Adjust = true,        
    
};

double ar2 = r2loss.Loss(predicted); 


double ur2 = regression.CoefficientOfDetermination(inputs, outputs, adjust: true); 

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