Thường xuyên dữ liệu được phân loại thành các nhóm, và trong mỗi nhóm một hồi quy tuyến tính của y trên x có thể được mặc nhiên công nhận. Ví dụ, hồi quy của các khối lượng thở ra buộc vào tuổi tác có thể được xem xét một cách riêng rẽ đối với nam giới trong các nhóm nghề nghiệp khác nhau | 322 Modelling continuous data Regression in groups Frequently data are classified into groups and within each group a linear regression of y on X may be postulated. For example the regression of forced expiratory volume on age may be considered separately for men in different occupational groups. Possible differences between the regression lines are then often of interest. In this section we consider comparisons of the slopes of the regression lines. If the slopes clearly differ from one group to another then so of course must the mean values of y at least for some values of X. In Fig. a the slopes of the regression lines differ from group to group. The lines for groups i and ii cross. Those for i and iii and for ii and iii would also cross if extended sufficiently far but here there is some doubt as to whether the linear regressions would remain valid outside the range of observed values of X. If the slopes do not differ the lines are parallel as in Fig. b and c and here it becomes interesting to ask whether as in b the lines differ in their height above the X axis which depends on the coefficient a in the equation y a b c Fig. Differences between regression lines fitted to three groups of observations. The lines differ in slope and position in a differ only in position in b and coincide in c . -------- i ii iii . Regression in groups 323 E y a px or whether as in c the lines coincide. In practice the fitted regression lines would rarely have precisely the same slope or position and the question is to what extent differences between the lines can be attributed to random variation. Differences in position between parallel lines are discussed in . In this section we concentrate on the question of differences between slopes. Suppose that there are k groups with ĩiị pairs of observations in the zth group. Denote the mean values of X and y in the zth group by Xi and ỹi and the regression line calculated as in by Yị y bi x - Xi . 11-12 .
