The general form of the watercut Y_W regression is:

(1)	$\begin{array}{l}\displaystyle Y_W^{-1} = Y_{W0}^{-1} + \mbox{Regression}(\{q_k\}), \quad k=[1..N]\end{array}$

where

$\begin{array}{l}(\{q_k\} = \{ q_1, \, q_2, \, ... q_N \}\end{array}$

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One can build various types of regression including the Artificial Neural Network or the closed-form regressions.

The simplest form of the linear closed-form regression is:

(2)	$\begin{array}{l}\displaystyle Y_W^{-1} = Y_{W0}^{-1} + \sum_{k=1}^N w_k \cdot q_k, \quad k=[1..N]\end{array}$

The simplest form of the non-linear closed-form regression is polynomial:

(3)	$\begin{array}{l}\displaystyle Y_W^{-1} = Y_{W0}^{-1} + \sum_{k=1}^N w_k \cdot q_k ^ {n_k}\end{array}$

The more general of the non-linear closed-form regression is rational:

(4)	$\begin{array}{l}\displaystyle Y_W^{-1} = Y_{W0}^{-1} + \frac{\sum_{k=1}^N w_k \cdot q_k ^ {n_k} }{\sum_{k=1}^N z_k \cdot q_k ^ {m_k} }, \quad \|z\| = \sqrt{\sum_k z_k} >0\end{array}$

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