Regress.MulLinRegress Method

Overload List

#	Signature	Description
1	procedure MulLinRegress(const Y: TVec; const A: TMtx; const b: TVec; const Weights: TVec; Constant: Boolean; const YCalc: TVec; const ATA: TMtx; Method: TRegSolveMethod);	Multivariante linear regression.
2	procedure MulLinRegress(const Y: TVec; const A: TMtx; const b: TVec; Constant: Boolean; const YCalc: TVec; const ATA: TMtx; Method: TRegSolveMethod);	Multivariante linear regression.

Overload 1: procedure MulLinRegress(const Y: TVec; const A: TMtx; const b: TVec; const Weights: TVec; Constant: Boolean; const YCalc: TVec; const ATA: TMtx; Method: TRegSolveMethod);

Multivariante linear regression.

#	Name	Description
1	Y	Defines vector of dependant variable.
2	A	Defines matrix of independant (also X) variables.
3	b	Returns calculated regression coefficiens.
4	Method	Use QR, SVD, or LU solver. Typically QR will yield best compromise between stability and performance.
5	Weights	Defines weights (optional).
6	Constant	If true then intercept term b(0) will be included in calculations. If false, set intercept term b(0) to 0.0.
7	YCalc	Returns vector of calculated dependant variable, where YCalc = A*b.
8	ATA	Returns inverse matrix of normal equations i.e [A(T)*A]^-1.

Result: stored in self (calling object)

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 Regress.RegressTest routine.

See Also: Regress.RegressTest, Regress.LinRegress, Regress.NLinRegress

Overload 2: procedure MulLinRegress(const Y: TVec; const A: TMtx; const b: TVec; Constant: Boolean; const YCalc: TVec; const ATA: TMtx; Method: TRegSolveMethod);

Multivariante linear regression.

#	Name	Type
1	Y	TVec
2	A	TMtx
3	b	TVec
4	Constant	Boolean
5	YCalc	TVec
6	ATA	TMtx
7	Method	TRegSolveMethod

Result: stored in self (calling object)

Examples

Uses Regress, MtxExpr;
procedure Example;
var y,b,w,yhat, resid, bstd: Vector;
A, ATA : Matrix;
RegStat : TRegStats;
begin
    A.SetIt(4,2,false,[1.0, 2.0,
    -3.2, 2.5,
    8.0,    -0.5,
    -2.2, 1.8]); // independent variables

    w.SetIt(false,[1,2,2,1]); // weights
    y.SetIt(false,[-3.0, 0.25, 8.0, 5.5]); // dependent variables
    MulLinRegress(y,A,b,w,true,yhat,ATA); //do regression
    // b=(19.093757944, -2.0141843616, -10.082487055)
    RegressTest(y,yhat,ATA,RegStat,resid, bstd, true,w); // do basic regression stats
    // RegStat = (ResidualVar:0.037230395108; R2:0.99965713428;
    // AdjustedR2:0.99897140285; F:1457.7968725; SignifProb: 0.01851663347)
end;