Adding a constant to the variables in the regression through the origin: the effect on the uncentered $$R^2$$

Abstract

AbstractIt is well known the effect on uncentered $$R^2$$ R 2 stemming from adding a constant to dependent variable in a linear regression model with intercept. In this paper, we investigate the effect of adding a constant to variables on the uncentered $$R^2$$ R 2 when a linear regression through the origin is used. In particular, we consider two cases. First, a constant $$c \in \mathbb {R}$$ c ∈ R is added to all observations of the dependent variable. Second, a constant $$c \in \mathbb {R}$$ c ∈ R is added to all the observations of both the dependent variable and at least an independent variable. We show that in both cases there is an artificial variation of the uncentered $$R^2$$ R 2 . This quantity is not invariant under location change.