TMtxMulLinReg Class

Summary

Performs multiple linear regression.

Hierarchy
TMtxMulLinReg

Description

Use TMtxMulLinReg component to perform multiple linear regression on dataset. The TMulLinRegress component fits equations to data by minimizing the sum of squared residuals:

SS = Sum [y(k) - ycalc(k)]^2 ,

where y(k) and ycalc(k) are respectively the observed and calculated value of the dependent variable for observation k. ycalc(k) is a function of the regression parameters b(0), b(1) ... Here the observed values obey the following equation:

y(k) = b(0) + b(1) * x(1,k) + b(2) * x(2,k) + ...

i.e

y = A * b

How to use TMtxMulLinReg component?

1) Drop a TMtxMulLinReg component on the form
2) Define A, the matrix of independent variables.
3) Define Y, vector of dependent variables.
4) Define Weights (optional) vector.
5) If you don't want to use intercept term b(0) in your calculations, set Constant property to false
6) Call the Recalc method to trigger calculation.

Results:
1) RegressResult : regression coefficients (b), regression coefficients confidence intervals (BConfInt) and standard deviation (BStdDev), residuals (Residuals) and calculated dependent variables (YCalc).
2) RegressStatistics : basic regression statistics (R2, Adjusted R2, residuals variance, F statistics, significance probability)

See Also
StatToolsDialogs

Example 1

How to setup and run multiple linear regression? In this example we've also used the weights. This is done by specifying weights for each variable and setting UseWeights property to true.

    Uses Statistics, StatTools, MtxVec;
    procedure Example(MtxMLReg: TMtxMulLinReg);
    begin
      // y = A*b
      MtxMLReg.A.SetIt(3,2,false,[-5,2,
                                    1,4,
                                    8,0.5]);
      MtxMLReg.Y.SetIt(false,[-2,
                                1,
                                11]);
      MtxMLReg.Weights.SetIt(false,[2,6,1]);
      MtxMLReg.UseWeights := true;
      MtxMLReg.Recalc;
      // Result ==> b = ( 4.586, 0.871, -1.114 )
    end;

    #include "MtxVec.hpp"
    #include "Math387.hpp"
    #include "Statistics.hpp"
    #include "StatTools.hpp"
    void __fastcall Example(TMtxMulLinReg* mlr)
    {
      // y = A*b
      mlr->A->SetIt(3,2,false,OPENARRAY(TSample,(-5,2,
                                    1,4,
                                    8,0.5)));
      mlr->Y->SetIt(false,OPENARRAY(TSample,(-2,1,11)));
      mlr->Weights->SetIt(false,OPENARRAY(TSample,(2,6,1)));
      mlr->UseWeights = true;
      mlr->Recalc();
      // Result ==> b = ( 4.586, 0.871, -1.114 )
    }

    using Dew.Stats;
    using Dew.Stats.Units;
    namespace Dew.Examples
    {
      private void Example(StatTools.TMtxMulLinReg mlr)
      {
        // y = A*b
        mlr.A.SetIt(3,2,false,new double[] {-5,2,
                                    1,4,
                                    8,0.5});
        mlr.Y.SetIt(false,new double[] {-2,1,11});
        mlr.Weights.SetIt(false, new double[] {2,6,1});
        mlr.UseWeights = true;
        mlr.Recalc();
        // Result ==> b = ( 4.586, 0.871, -1.114 )
      }
    }

Properties

Name	Summary
A	Matrix of independent variables.
Alpha	Desired significant value for the statistical tests.
AutoUpdate
Constant	Intercept term.
Dirty
RegressResult	Regression results.
RegressStatistics	Regression results statistics.
SolveMethod	Defines A*x=b solving method.
UseWeights	Weighted multiple linear regression.
Weights	Weights for MLR.
Y	Vector of dependent variables.

Methods

Name	Summary
Loaded
Recalc	Triggers multiple linear regression recalculation.
ValidSystem	Checks if system is valid.