SimpleLinearRegression Class

[SerializableAttribute]
public class SimpleLinearRegression : TransformBase<double, double>, 
	ILinearRegression

<SerializableAttribute>
Public Class SimpleLinearRegression
	Inherits TransformBase(Of Double, Double)
	Implements ILinearRegression

// Let's say we have some univariate, continuous sets of input data,
// and a corresponding univariate, continuous set of output data, such
// as a set of points in R². A simple linear regression is able to fit
// a line relating the input variables to the output variables in which
// the minimum-squared-error of the line and the actual output points
// is minimum.

// Declare some sample test data.
double[] inputs = { 80, 60, 10, 20, 30 };
double[] outputs = { 20, 40, 30, 50, 60 };

// Use Ordinary Least Squares to learn the regression
OrdinaryLeastSquares ols = new OrdinaryLeastSquares();

// Use OLS to learn the simple linear regression
SimpleLinearRegression regression = ols.Learn(inputs, outputs);

// Compute the output for a given input:
double y = regression.Transform(85); // The answer will be 28.088

// We can also extract the slope and the intercept term
// for the line. Those will be -0.26 and 50.5, respectively.
double s = regression.Slope;     // -0.264706
double c = regression.Intercept; // 50.588235

// This is the same data from the example available at
// http://mathbits.com/MathBits/TISection/Statistics2/logarithmic.htm

// Declare your inputs and output data
double[] inputs = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 };
double[] outputs = { 6, 9.5, 13, 15, 16.5, 17.5, 18.5, 19, 19.5, 19.7, 19.8 };

// Transform inputs to logarithms
double[] logx = Matrix.Log(inputs);

// Use Ordinary Least Squares to learn the regression
OrdinaryLeastSquares ols = new OrdinaryLeastSquares();

// Use OLS to learn the simple linear regression
SimpleLinearRegression lr = ols.Learn(logx, outputs);

// Compute predicted values for inputs
double[] predicted = lr.Transform(logx);

// Get an expression representing the learned regression model
// We just have to remember that 'x' will actually mean 'log(x)'
string result = lr.ToString("N4", CultureInfo.InvariantCulture);

// Result will be "y(x) = 6.1082x + 6.0993"

// The mean squared error between the expected and the predicted is
double error = new SquareLoss(outputs).Loss(predicted); // 0.261454