The paper considers an application of martingales for testing the hypothesis that the data are generated by the Gauss linear model. In addition, the martingales are also used for suggesting some possible clustering of the data. A Russian household dataset is taken to show results of this approach. In particular, with the help of martingales the households were split into groups with a similar structure of expenditure. It was assumed that within each group dependence of the household total consumption on its income can be described by the Gauss linear model. The structure of expenditure was tested for the households within the groups.