SAP HANA Predictive Analysis Library (PAL)

Assume we have m observation pairs (x i ,y i ). Then we obtain an overdetermined linear system
=Y,
with is m×(n+1) matrix, is (n+1)×1 matrix, and Y is m×1 matrix, where m>n+1. Since equality is
usually not exactly satisfiable, when m > n+1, the least squares solution
minimizes the squared Euclidean
norm of the residual vector r(
) so that
Elastic net regularization for multiple linear regression seeks to find
that minimizes:
Where .
Here
and λ≥0. If α=0, we have the ridge regularization; if α=1, we have the LASSO regularization.
The implementation also supports calculating F and R^2 to determine statistical significance.
Prerequisites
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No missing or null data in the inputs.
The data is numeric, not categorical.
Given n independent variables, there must be at least n+1 records available for analysis.
LRREGRESSION
This is a multiple linear regression function.
Procedure Generation
CALL SYS.AFLLANG_WRAPPER_PROCEDURE_CREATE (‘AFLPAL’, ‘LRREGRESSION’,
‘’, '', );
SAP HANA Predictive Analysis Library (PAL)
PAL Functions P U B L I C 265