  Artificial intelligence is applied in a range of sectors, and is relied upon
for decisions requiring a high level of trust. For regression methods, trust is
increased if they approximate the true input-output relationships and perform
accurately outside the bounds of the training data. But often performance
off-test-set is poor, especially when data is sparse. This is because the
conditional average, which in many scenarios is a good approximation of the
`ground truth', is only modelled with conventional Minkowski-r error measures
when the data set adheres to restrictive assumptions, with many real data sets
violating these. To combat this there are several methods that use prior
knowledge to approximate the `ground truth'. However, prior knowledge is not
always available, and this paper investigates how error measures affect the
ability for a regression method to model the `ground truth' in these scenarios.
Current error measures are shown to create an unhelpful bias and a new error
measure is derived which does not exhibit this behaviour. This is tested on 36
representative data sets with different characteristics, showing that it is
more consistent in determining the `ground truth' and in giving improved
predictions in regions beyond the range of the training data.
