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

Umberto Triacca ()
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Umberto Triacca: University of L’Aquila

Quality & Quantity: International Journal of Methodology, 2023, vol. 57, issue 3, No 39, 2789 pages

Abstract: Abstract It 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.

Keywords: Coefficient of determination; Least squares; Linear regression model; Measure of goodness of fit; 62J05; 62J99 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s11135-022-01495-6

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