The joint modelling of mean and dispersion in quasi-likelihood models which greatly extend the scope of generalized linear models, is required in case that the dispersion parameter, the variance component of response variables, is not constant but changes by depending on any covariates. In this paper, by using statistical package GENSTAT(release 5.3.2, 1996) which makes a easily analyze real data through this joint modelling, we mention necessities that must consider this joint modelling rather than existing mean models through model checking based on graphic methods for esterase assay data introduced by Carrol and Ruppert(1987, pp.46-47), and then study methods finding reasonable joint model of mean and dispersion for this data.