• С. М. Лапач National Technical University of Ukraine «Kyiv Polytechnic Institute», Kyiv, Ukraine



linear regression analysis, cutting process modeling, model specification, model adequacy, transformation of background factors, Chebyshev polynomial


The comparison of different approaches to cutting operations model specification and their feasibility from statistical and substantial viewpoints was made. It is shown that the linearization to be used for solving the problem for the multiplicative model leads to a change in the correlation coefficients between the covariates and the response. The result is a distortion of the model structure (composition and relative importance of the covariates). When using Chebyshev polynomials distortion does not occur. Demonstrated a conflict between the various statistical indicators, which also ceteris paribus leads to different structure models. The solutions of specific tasks show the disadvantages of traditional multiplicative model (from statistical and physical viewpoints), also discrepancy between statistical estimate of adequacy in regression analysis and requirements to the model in object region. It is suggested not to use multiplicative models due to absence of their feasibility and as leading to changes of original problem. The adequacy of model is suggested to be estimated coming from the requirements of object region


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