An investigator studied the effects of three different antidepressants (A, B, and C) on patient ratings of depression. To do this, patients were stratified into six age€“ gender combinations. From a random sample of three patients from each stratum, the experimenter randomly allocated the three antidepressants. On the day the study was to be initiated, a baseline (pretreatment) depression scale rating was obtained from each patient. The assigned therapy was then administered and maintained for 1 week. At that time, a second rating (posttreatment) was obtained from each patient. The pre- and posttreatment ratings appear next (a higher score indicates more depression).

a. Identify the experimental design.
b. Write a first- order model relating the posttreatment response y to the pretreat-ment rating x1 for each treatment.

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Pretreatment Posttreatment Age Block Gender (vears) A F 20 48 F 2040 43 F 40 44 M 20 42 M 20-40 37 M 40 41 31 28 21 17 19 18 17 15 19 31 35 21 24 18 26 21 18 29 34 24 24 26