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This paper describes the application of sliced inverse regression to model the electrochemical process of aluminum smelter plants. Real data measurements obtained during several years in a Spanish industrial environment are used to illustrate the main dependencies between parameters. Nonlinear relations between the output variables and relevant linear combinations of input variables are deduced. An exploratory statistical analysis is also presented, checking for correlations and possible linear dependencies. The developed model is used to analyze the range of electrical power demand variations as a consequence of modifications in chemical and electrical parameters. An example is described maintaining constant the aluminum production. The results can be considered for future load flexibility programs, which might include aluminum smelter plants as a flexible industrial customer.