ISmQuantileRegression.Explained

Syntax

Explained: ISlSerie;

Description

The Explained property determines an explained series.

Comments

The number of observations in the explained series cannot be smaller than the number of estimated parameters.

Example

Add a link to the Stat system assembly.

//Array output procedure
Sub Print(Data: Array Of Double; start: integer = 1);
Var
i: Integer;
Begin
    debug.Indent;
    For i := start - 1 To Data.Length - 1 Do
        Debug.WriteLine(i.ToString + " " + Data[i].ToString);
    End For;
    debug.Unindent;
End Sub Print;

Sub UserProc;
Var
    can, fra: Array[43] Of double;
    i, j, res: integer;
    str: string;
    qreg: ISmQuantileRegression;
    qMCI: IIntercept;
    qMCC: ICoefficients;
Begin
    qreg := New SmQuantileRegression.Create;

    // Variable values
    Can[0] := 6209; fra[0] := 4110;
    Can[1] := 6385; fra[1] := 4280;
    Can[2] := 6752; fra[2] := 4459;
    Can[3] := 6837; fra[3] := 4545;
    Can[4] := 6495; fra[4] := 4664;
    Can[5] := 6907; fra[5] := 4861;
    Can[6] := 7349; fra[6] := 5195;
    Can[7] := 7213; fra[7] := 5389;
    Can[8] := 7061; fra[8] := 5463;
    Can[9] := 7180; fra[9] := 5610;
    Can[10] := 7132; fra[10] := 5948;
    Can[11] := 7137; fra[11] := 6218;
    Can[12] := 7473; fra[12] := 6521;
    Can[13] := 7722; fra[13] := 6788;
    Can[14] := 8088; fra[14] := 7222;
    Can[15] := 8516; fra[15] := 7486;
    Can[16] := 8941; fra[16] := 7832;
    Can[17] := 9064; fra[17] := 8153;
    Can[18] := 9380; fra[18] := 8468;
    Can[19] := 9746; fra[19] := 9054;
    Can[20] := 9907; fra[20] := 9499;
    Can[21] := 10333; fra[21] := 9866;
    Can[22] := 10863; fra[22] := 10217;
    Can[23] := 11693; fra[23] := 10763;
    Can[24] := 12242; fra[24] := 10683;
    Can[25] := 12227; fra[25] := 10494;
    Can[26] := 12910; fra[26] := 10938;
    Can[27] := 13049; fra[27] := 11198;
    Can[28] := 13384; fra[28] := 11546;
    Can[29] := 14036; fra[29] := 11865;
    Can[30] := 14242;
    Can[31] := 14704;
    Can[32] := 13802;
    Can[33] := 14197;
    Can[34] := 15010;
    Can[35] := 15589;
    Can[36] := 15932;
    Can[37] := 16631;
    Can[38] := 17394;
    Can[39] := 17758;
    Can[40] := 17308;
    Can[41] := 16444;
    Can[42] := 16413;

// Sample period
qreg.ModelPeriod.FirstPoint := 1;
qreg.ModelPeriod.LastPoint := 30;
// Forecast variable
qreg.Forecast.LastPoint := 43;
// Select explained variable
qreg.Explained.Value := fra;
// Select regressors
qreg.Explanatories.Clear;
qreg.Explanatories.Add.Value := can;
// Constant in regressors
qreg.ModelCoefficients.Intercept.Mode := InterceptMode.AutoEstimate;
// Quantile level
qreg.Quantile := 0.3;
// Number of iterations
qreg.MaxIteration := 100;
// Missing data treatment method
qreg.MissingData.Method := MissingDataMethod.Casewise;
// Calculate and display results
res := qreg.Execute;
Debug.WriteLine(qreg.Errors);
    For i := 0 To qreg.WarningsCount - 1 Do
        Debug.WriteLine(qreg.Warnings[i]);
    End For;
Debug.WriteLine("Constant: ");
    qMCI := qreg.ModelCoefficients.Intercept;
    Debug.WriteLine(qMCI.Estimate.ToString + " " + qMCI.StandardError.ToString + " " + qMCI.TStatistic.ToString + " " + qMCI.Probability.ToString);
Debug.WriteLine("Coefficient estimates:");
    qMCC := qreg.ModelCoefficients.Coefficients;
    For i := 0 To qreg.ModelCoefficients.Coefficients.Estimate.Length - 1 Do
        Debug.WriteLine(qMCC.Estimate[i].ToString + " " + qMCC.StandardError[i].ToString + " " + qMCC.TStatistic[i].ToString + " " + qMCC.Probability[i].ToString);
    End For;
Debug.WriteLine("Covariance matrix");
    For i := 0 To qreg.CovarianceMatrix.GetUpperBound(1) Do
        str := "";
        For j := 0 To qreg.CovarianceMatrix.GetUpperBound(2) Do
            str := str + "  " + (qreg.CovarianceMatrix[i, j] As Double).ToString;
        End For;
        Debug.WriteLine(str);
    End For;

Debug.WriteLine("Quantile regression characteristics");
Debug.Indent;
Debug.WriteLine("Determination pseudocoefficient: " + qreg.QRegStatistics.PseudoR2.ToString);
Debug.WriteLine("Adjusted determination coefficient: " + qreg.QRegStatistics.AdjR2.ToString);
Debug.WriteLine("Criterion function value: " + qreg.QRegStatistics.Objective.ToString);
Debug.WriteLine("Restricted criterion function value: " + qreg.QRegStatistics.RestrObjective.ToString);
Debug.WriteLine("Explained variable quantile: " + qreg.QRegStatistics.QDependentVar.ToString);
Debug.WriteLine("Observation sparcity: " + qreg.QRegStatistics.Sparsity.ToString);
Debug.UnIndent;
Debug.WriteLine("Summary statistics");
Debug.Indent;
Debug.WriteLine("Number of iterations, after which the method has converged: " + qreg.SummaryStatistics.NumOfIter.ToString);
Debug.WriteLine("Standard error: " + qreg.SummaryStatistics.SE.ToString);
Debug.WriteLine("Sum of squared residuals: " + qreg.SummaryStatistics.SSR.ToString);
Debug.UnIndent;
Debug.WriteLine("Modeling series");
Print(qreg.Fitted);
Debug.WriteLine("Residual series");
Print(qreg.Residuals);
Debug.WriteLine("Forecast");
Print(qreg.Forecast.Value, qreg.ModelPeriod.LastPoint + 1);
Debug.WriteLine("Lower forecast confidence limit");
Print(qreg.Forecast.LowerConfidenceLevel, qreg.ModelPeriod.LastPoint + 1);
Debug.WriteLine("Upper forecast confidence limit");
Print(qreg.Forecast.UpperConfidenceLevel, qreg.ModelPeriod.LastPoint + 1);
End Sub UserProc;

Result of example execution: the console window displays the results of quantile regression calculation.