Visual expression of factor decomposition in regression analysis: An example of Japanese housing rents

This paper presents the importance of the visual expression of factor decomposition in regression analysis, which is particularly worthwhile for undergraduate students whose majors are not mathematics but social science. The conventional purpose of regression analysis is to examine specific hypotheses empirically. In particular, the statistical significance of the explanatory variable was tested, which may have been difficult for many students to understand mathematically. To remedy this, factor decomposition is introduced in the same way that human body composition is broken down into water, fat, and muscle. As an illustrative example, multiple regression was applied to the determinants of housing rents in Japan. The explanatory variables were the living area, building age, and walking time from the nearest station. The findings suggest that, with the help of visual expression, a student can easily appreciate which variable significantly affects housing rents.