/// <summary>
/// Compute the regressors coefficients from MCO
/// beta = inv(X'*X)*X'*Y
/// </summary>
/// <returns>
/// beta
/// </returns>
/// <acknowledgment>
/// https://github.com/SarahFrem/AutoRegressive_model_cs/blob/master/RegressionLineaire.cs
/// </acknowledgment>
public double[,] RegressorsMCO()
{
var R = RegressionMatrix();
var beta = Operations.Multiply(Operations.Multiply(Operations.Inverse(Operations.Multiply(Operations.Transpose(R), R)), Operations.Transpose(R)), responseVariable);
return(beta);
}
/// <summary>
/// Residuals the variance.
/// </summary>
/// <returns></returns>
/// <acknowledgment>
/// https://github.com/SarahFrem/AutoRegressive_model_cs/blob/master/RegressionLineaire.cs
/// </acknowledgment>
public double ResidualVariance()
{
var E = Errors();
var var = Operations.Multiply(Operations.Transpose(E), E);
var size = (double)E.GetLength(0);
return(var[0, 0] / size);
}
/// <summary>
/// Variances the covariance beta.
/// </summary>
/// <returns></returns>
/// <acknowledgment>
/// https://github.com/SarahFrem/AutoRegressive_model_cs/blob/master/RegressionLineaire.cs
/// </acknowledgment>
public double[,] VarianceCovarianceBeta()
{
var R = RegressionMatrix();
var var = ResidualVariance();
var res = Operations.Inverse(Operations.Multiply(Operations.Transpose(R), R));
var resRow = res.GetLength(0);
var resCol = res.GetLength(1);
for (var i = 0; i < resRow; i++)
{
for (var j = 0; j < resCol; j++)
{
res[i, j] *= var;
}
}
return(res);
}
/// <summary> /// Predictionses this instance. /// </summary> /// <returns></returns> /// <acknowledgment> /// https://github.com/SarahFrem/AutoRegressive_model_cs/blob/master/RegressionLineaire.cs /// </acknowledgment> public double[,] Predictions() => Operations.Multiply(RegressionMatrix(), RegressorsMCO());