In applications, sometimes data are classified into groups, and within each group a separate regression model of Y on X may be postulated. For example, the regression of “forced expiratory volume” (Y) on age (X) may be considered separately for men in different occupational groups because different occupations may havedifferent effects on the lung health of workers.Differencesbetween the regression lines, especially the slopes, are our primary interest.
AN EXAMPLESuppose we study “vital capacity” among men working in the cadmium industry; the main purpose of the study was to see whether exposure to fumes was associated with a change in respiratory function. However, we must take into account the effect of “age” because respiratory performance declines with age. The men in the sample were divided into three groups: (1) those who were exposed for at least 10 years, (2) those who were exposed for less than 10 years, and (3) Control group consisted of men notexposed to fumes.We then consider three regression lines: Y = Vital Capacities (liters) versus X = Age
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