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Regress.MulLinRegress Method ([In] TVec, [In] TMtx, [In] TVec, [In] TVec, bool, [In] TVec, [In] TMtx, TRegSolveMethod)
Regress Class  Regress Members  Dew.Stats.Units Namespace  MulLinRegress Method  Example  See Also
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Multivariante linear regression.

Syntax
C#
Visual Basic
public static void MulLinRegress([In] TVec Y, [In] TMtx A, [In] TVec b, [In] TVec Weights, bool Constant, [In] TVec YCalc, [In] TMtx ATA, TRegSolveMethod Method);
Parameters
Parameters 
Description 
[In] TVec Y 
Defines vector of dependant variable. 
[In] TMtx A 
Defines matrix of independant (also X) variables. 
[In] TVec b 
Returns calculated regression coefficiens. 
[In] TVec Weights 
Defines weights (optional). 
bool Constant 
If true then intercept term b(0) will be included in calculations. If false, set intercept term b(0) to 0.0. 
[In] TVec YCalc 
Returns vector of calculated dependant variable, where YCalc = A*b. 
[In] TMtx ATA 
Returns inverse matrix of normal equations i.e [A(T)*A]^-1. 
TRegSolveMethod Method 
Use QR, SVD, or LU solver. Typically QR will yield best compromise between stability and performance. 
Remarks

Routine 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. 

To calculate additional regression statistical values, use RegressTest routine.

See Also
Example

The following example performs multiple linear regression.

using Dew.Math; using Dew.Stats.Units; using Dew.Stats; namespace Dew.Examples { private void Example() { Matrix A = new Matrix(0, 0); Matrix ATA = new Matrix(0, 0); Vector y = new Vector(0); Vector b = new Vector(0); Vector w = new Vector(0); Vector yhat = new Vector(0); Vector residuals = new Vector(0); Vector BStdDev = new Vector(0); TRegStats rs; // independent variables A.SetIt(4, 2, false, new double[] {1.0, 2.0, -3.2, 2.5, 8.0, -0.5, -2.2, 1.8}); w.SetIt(false, new double[] { 1, 2, 2, 1 }); // weights y.SetIt(false, new double[] { -3.0, 0.25, 8.0, 5.5 }); // dependent variables Regress.MulLinRegress(y, A, b, w, true, yhat, ATA, TRegSolveMethod.regSolveLQR); //do regression // b=(19.093757944, -2.0141843616, -10.082487055) Regress.RegressTest(y, yhat, ATA, out rs, residuals, BStdDev, true, w); // do basic regression stats // RegStat = (ResidualVar:0.037230395108; R2:0.99965713428; // AdjustedR2:0.99897140285; F:1457.7968725; SignifProb: 0.01851663347) } }
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