  Multivariate regression models and ANOVA are probably the most frequently
applied methods of all statistical analyses. We study the case where the
predictors are qualitative variables, and the response variable is
quantitative. In this case, we propose an alternative to the classic approaches
that does not assume homoscedasticity but assumes that a Markov chain can
describe the covariates' correlations. This approach transforms the dependent
covariates using a change of measure to independent covariates. The transformed
estimates allow a pairwise comparison of the mean and variance of the
contribution of different values of the covariates. We show that under standard
moment conditions, the estimators are asymptotically normally distributed. We
test our method with data from simulations and apply it to several classic data
sets.
