  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.
