General Forms of a Class of Multivariable Regression Models

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There are two possible general forms of multiple input multiple output (MIMO) regression models, which are either linear with respect to their parameters or non-linear, but in order to estimate their parameters, at a certain stage it could be assumed that they are linear. This is in fact the basic assumption behind the linear approach for parameters estimation. There are two possible representations of a MIMO model, which at a certain level could be fictitiously presented as linear functions of its parameters. One representation is when the parameters are collected in a matrix and hence, the regressors are in a vector. The other possible case is the parameters to be in a vector, but the regressors at a given instant to be placed in a matrix. Both types of representations are considered in the paper. Their advantages and disadvantages are summarized and their applicability within the whole experimental modelling process is also discussed.


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