  It is generally difficult to make any statements about the expected
prediction error in an univariate setting without further knowledge about how
the data were generated. Recent work showed that knowledge about the real
underlying causal structure of a data generation process has implications for
various machine learning settings. Assuming an additive noise and an
independence between data generating mechanism and its input, we draw a novel
connection between the intrinsic causal relationship of two variables and the
expected prediction error. We formulate the theorem that the expected error of
the true data generating function as prediction model is generally smaller when
the effect is predicted from its cause and, on the contrary, greater when the
cause is predicted from its effect. The theorem implies an asymmetry in the
error depending on the prediction direction. This is further corroborated with
empirical evaluations in artificial and real-world data sets.
