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Regression analysis in quantum language

Although regression analysis has a great history, we consider that it has always continued being confused. For example, the fundamental terms in regression analysis (e.g., "regression", "least-squares method", "explanatory variable", "response variable", etc.) seem to be historically conventional, that is, these words do not express the essence of regression analysis. Recently, we proposed quantum language (or, classical and quantum measurement theory), which is characterized as the linguistic turn of the Copenhagen interpretation of quantum mechanics. We believe that this language has a great power of description, and therefore, even statistics can be described by quantum language. Therefore, in this paper, we discuss the regression analysis and the generalized linear model (i.e., multiple regression analysis) in quantum language, and clarify that the terms "explanatory variable" and "response variable" is respectively characterized as a kind of causality and the measured value.