Learning and Teaching of the Regression Line from the Viewpoint of Negation Theory

Abstract

　　 A purpose of this paper is to elucidate the process for developing the regression line from the viewpoint of negation theory in order to clarify the proper learning and teaching of the regression line. For achieving this purpose, some base concepts related to the regression line is identified, and the relations between the regression line and them are characterized by negation theory.

　　 As a result, two kinds of negation are necessary as follows. First, through recognizing that a linear function cannot be applied to the real context that two variables do not change regularly, “the straight line not to ignore the variability of data” is considered as the regression line. Then, through recognizing that the regression model cannot be applied for problem situation to quantify the degree of the symmetric relations between two variables, the regression model is seen as “the model that the relations between two variables are not asymmetry”.