ISmNonLinearLeastSquare.CoefficientsOrder

Syntax

CoefficientsOrder: String;

Description

The CoefficientsOrder property determines the coefficients order.

Comments

If there are several coefficients, specify them divided by the semicolon. For example: A1;A2;A3;A4.

Example

To execute the example, add a link to the Stat system assembly.

Sub UserProc;
Var
    NLS: SmNonLinearLeastSquare;
    can, fra: Array[43] Of Double;
    expl: INonLinearRegressionExplanatory;
    InitEst: Array[2] Of Double;
    res, i: Integer;
    MC: ISlConstCoefficients;
    coef: String;
    SumStat: ISummaryStatistics;
Begin
    // Create a method
    NLS := New SmNonLinearLeastSquare.Create;
    // Specify value of the can variable
    can[00] := 6209; can[11] := Double.Nan; can[22] := 10863; can[33] := 14197;
    can[01] := 6385; can[12] := Double.Nan; can[23] := 11693; can[34] := 15010;
    can[02] := 6752; can[13] := 7722; can[24] := 12242; can[35] := Double.Nan;
    can[03] := 6837; can[14] := 8088; can[25] := 12227; can[36] := Double.Nan;
    can[04] := 6495; can[15] := 8516; can[26] := 12910; can[37] := Double.Nan;
    can[05] := 6907; can[16] := 8941; can[27] := 13049; can[38] := 17394;
    can[06] := 7349; can[17] := 9064; can[28] := 13384; can[39] := 17758;
    can[07] := 7213; can[18] := 9380; can[29] := 14036; can[40] := 17308;
    can[08] := 7061; can[19] := 9746; can[30] := 14242; can[41] := 16444;
    can[09] := 7180; can[20] := 9907; can[31] := 14704; can[42] := 16413;
    can[10] := Double.Nan; can[21] := 10333; can[32] := 13802;
    // Set value of the "fra" variable
    fra[00] := 4110; fra[11] := 6218; fra[22] := 10217; fra[33] := 11900;
    fra[01] := 4280; fra[12] := 6521; fra[23] := 10763; fra[34] := 11986;
    fra[02] := 4459; fra[13] := 6788; fra[24] := 10683; fra[35] := 12206;
    fra[03] := 4545; fra[14] := 7222; fra[25] := 10494; fra[36] := 12734;
    fra[04] := 4664; fra[15] := 7486; fra[26] := 10938; fra[37] := Double.Nan;
    fra[05] := 4861; fra[16] := 7832; fra[27] := 11198; fra[38] := Double.Nan;
    fra[06] := 5195; fra[17] := 8153; fra[28] := 11546; fra[39] := Double.Nan;
    fra[07] := 5389; fra[18] := 8468; fra[29] := 11865; fra[40] := 14141;
    fra[08] := 5463; fra[19] := 9054; fra[30] := 11781; fra[41] := 14141;
    fra[09] := 5610; fra[20] := 9499; fra[31] := 11681; fra[42] := 14237;
    fra[10] := 5948; fra[21] := 9866; fra[32] := 11903;
    // Set calculation periods
    NLS.ModelPeriod.FirstPoint := 1;
    NLS.ModelPeriod.LastPoint := 30;
    NLS.Forecast.LastPoint := 43;
    // Set explained variable
    NLS.Explained.Value := can;
    // Set explanatory variable
    expl := NLS.Explanatories.Add;
    expl.Serie.Value := fra;
    expl.VariableName := "fra";
    // Set function
    NLS.FunctionString := "A1 + A2 * fra";
    // Set coefficients order
    NLS.CoefficientsOrder := "A1;A2";
    // Set values of primary approximations
    InitEst[0] := 0.02; InitEst[1] := 0.02;
    NLS.InitApproximation := InitEst;
    // Primary values are not used by default
    NLS.UseDefaultInitValues := False;
    // Set tolerance and maximum number of iterations
    NLS.Tolerance := 0.001;
    NLS.MaxIteration := 600;

    // Set optimization method
    NLS.OptimizationMethod := NLSOptimizationMethod.LevenbergMarquardt;
    // Specify missing data treatment method
    NLS.MissingData.Method := MissingDataMethod.SampleAverage;
    // Do not use derivatives on calculation
    NLS.UseDerivatives := False;
    // Take into account that coefficients are found approximately
    NLS.Forecast.CoefUncertaintyInSECalc := True;
    // Run calculation and output the results to console window
    res := NLS.Execute;
    Debug.WriteLine(NLS.Errors);
    If (res = 0) Then
        Debug.WriteLine("Coefficient estimations:");
        Debug.Indent; coef := "A1";
        For i := 0 To 1 Do
            MC := NLS.ModelCoefficients(coef);
            Debug.WriteLine(coef + ":");
            Debug.WriteLine(" - value: " + MC.Estimate.ToString);
            Debug.WriteLine(" - standard error: " + MC.StandardError.ToString);
            Debug.WriteLine(" - t-statistic: " + MC.TStatistic.ToString);
            Debug.WriteLine(" - probability: " + MC.Probability.ToString);
            coef := "A2";
        End For;
        Debug.Unindent; Debug.WriteLine("");
        Debug.Write("Optimal value of sum of squared residuals: ");
        Debug.WriteLine(NLS.OptimalSumOfSquare);
        Debug.WriteLine(""); Debug.WriteLine("Summary statistics:");
        SumStat := NLS.SummaryStatistics;
        Debug.WriteLine(" - determination coefficient: " + SumStat.R2.ToString);
        Debug.WriteLine(" - Fisher statistic: " + SumStat.Fstat.ToString);
        Debug.WriteLine(" - sum of squared residuals:" + SumStat.SSR.ToString);
        Debug.WriteLine(" - number of iterations:" + SumStat.NumOfIter.ToString);
        Debug.WriteLine(""); Debug.WriteLine("Explanatory series:");
        Print(NLS.Explained.Value);
        Debug.WriteLine(""); Debug.WriteLine("Modeling series:");
        Print(NLS.Fitted);
        Debug.WriteLine(""); Debug.WriteLine("Residual series:");
        Print(NLS.Residuals);
        Debug.WriteLine(""); Debug.WriteLine("Forecasting series:");
        Print(NLS.Forecast.Value);
        Debug.WriteLine(""); Debug.WriteLine("Lower confidence limit");
        Print(NLS.Forecast.LowerConfidenceLevel);
        Debug.WriteLine(""); Debug.WriteLine("Upper confidence limit");
        Print(NLS.Forecast.UpperConfidenceLevel);
        Debug.WriteLine(""); Debug.WriteLine("Actually used initial approximations");
        Print(NLS.InitApproximationActual);
    End If;
End Sub UserProc;

// Data output procedure
Sub Print(Data: Array Of Double);
Var
    i: Integer;
Begin
    Debug.Indent;
    For i := 0 To Data.Length - 1 Do
        Debug.WriteLine(i.ToString + " " + Data[i].ToString);
    End For;
    Debug.Unindent;
End Sub Print;

After executing the example the non-linear regression is calculated using the least squares method, the calculation results are displayed to the console window.