This paper is concerned with the application of the general linear model to the situation in which the observations are divided into several groups. It is assumed that some of the regression coefficients may be common to all groups whilst other regression coefficients and also the error variance may vary from group to group. The problems of estimation and hypothesis testing are discussed. The least squares method is applicable if the model involves the assumption of a common error variance, but if the error variance differs from group to group the maximum likelihood approach is called for. An example is given of the testing of the hypothesis of equal error variances in a study of ventilatory function in coal miners.