  Regression is one of the most commonly used statistical techniques. However,
testing regression systems is a great challenge because of the absence of test
oracle in general. In this paper, we show that Metamorphic Testing is an
effective approach to test multiple linear regression systems. In doing so, we
identify intrinsic mathematical properties of linear regression, and then
propose 11 Metamorphic Relations to be used for testing. Their effectiveness is
examined using mutation analysis with a range of different regression programs.
We further look at how the testing could be adopted in a more effective way.
Our work is applicable to examine the reliability of predictive systems based
on regression that has been widely used in economics, engineering and science,
as well as of the regression calculation manipulated by statistical users.
