Dr Kevin Burke is a Lecturer in Statistics at the University of Limerick.

Classical linear regression involves introducing predictor variables through the mean of the response variable, whereas the variance is a constant common to all individuals. However, there is no reason believe that this should be true in practice – just as the mean varies with predictor variables, so too can the variance (albeit the constant variance assumption leads to elegant classical theory). A more flexible “multi-parameter regression” (MPR) approach is to allow both mean and variance parameters to depend on predictor variables; this is known as “heteroskedastic regression” in econometrics.