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

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  • Umberto Triacca

    (University of L’Aquila)

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.

Suggested Citation

  • Umberto Triacca, 2023. "Adding a constant to the variables in the regression through the origin: the effect on the uncentered $$R^2$$ R 2," Quality & Quantity: International Journal of Methodology, Springer, vol. 57(3), pages 2781-2789, June.
    • Handle: RePEc:spr:qualqt:v:57:y:2023:i:3:d:10.1007_s11135-022-01495-6
    DOI: 10.1007/s11135-022-01495-6
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