procedure LinRegress(const X: TVec; const Y: TVec; const B: TVec; Constant: Boolean; const Weights: TVec; const YCalc: TVec; const ATA: TMtx);
Simple linear regression.
| # | Name | Type | Description |
|---|---|---|---|
| 1 | X | TVec | |
| 2 | Y | TVec | |
| 3 | B | TVec | |
| 4 | Constant | Boolean | |
| 5 | Weights | TVec | |
| 6 | YCalc | TVec | |
| 7 | ATA | TMtx |
Result: stored in self (calling object)
Remarks:
The 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) and b(1). In case constant term is used, the observed values obey the following equation:
y(k) = b(0) + b(1) * x
i.e
Y = b(0) + b(1)*X.
or if constant term is NOT used:
y(k) = b(0) * x
To calculate additional regression statistical parameters, use Regress.RegressTest routine.
Examples
Uses MtxExpr, MtxVecTee, Regress;
procedure Example;
var x,y,b,yhat: Vector;
begin
x.SetIt(false,[1.0, 1.5, 2.3, 3.8, 4.2, 5.0, 5.3, 5.9]);
y.SetIt(false,[11, 12, 12.5, 14, 14.3, 15.2, 15.3, 17]);
LinRegress(x,y,b,true,nil,yhat,nil);
DrawValues(x,y,Series1,false); // draw original data
DrawValues(x,yhat,Series2,false); // draw fitted data
end;See Also: Regress.MulLinRegress, Regress.RegressTest