EFFICIENT GROUPING, REGRESSION AND CORRELATION IN ENGEL CURVE ANALYSIS*

Abstract Prais and Aitchison have shown that the common practice of grouping the individual observations in Engel curve analysis does not introduce a bias in the estimate of the regression coefficient, and that the classification of the individual households by income minimizes the increase in the variance of the estimate. The present paper provides an approximate numerical evaluation of the effects of such efficient grouping under the usual conditions of budget survey analysis. It is shown that in this case (i) the regression estimates based on individual observations and on weighted income class means are highly correlated; (ii) the variance of the estimates increases by a few per cent at most; and (iii) the correlation coefficient is vastly overstated by the grouped data.