TMtxMulLinReg Class

Performs multiple linear regression.

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

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

CopyUses 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;
    // MtxMLReg.RegressResult.B = ( 4.586, 0.871, -1.114 )
end;