Children with growth hormone H deficiency do not grow at normal rates. If they are given extra growth hormone, their growth rate can be improved. Hindmarsh and coworkers* made observations in growth...

Children with growth hormone H deficiency do not grow at normal rates. If they are given extra growth hormone, their growth rate can be improved. Hindmarsh and coworkers* made observations in growth hormone–deficient children that led them to hypothesize that children who have lower H at the outset of treatment respond more favorably and that this relationship should be nonlinear; that is, the treatment is more effective if treatment starts from a lower pretreatment H level. They measured a normalized growth rate G based on the change in height over time and the H level at the onset of treatment with additional growth hormone. (These data are in Table D-15, Appendix D.) Is there any evidence to support the investigator’s hypothesis that the relationship between G and H is nonlinear? Are there other problems with these data? Can the nonlinearity be handled with a transformation so that linear regression can be used?

Table D-15