A psychologist wants to evaluate three therapies for treating people with a gambling ­addiction. A study is designed to randomly select 25 patients at clinics using each of the three therapies. After the patients had undergone 3 months of inpatient/ outpatient treatment, an ­assessment of each patient’s inclination to continue gambling is made, resulting in a gambling ­inclination score, y, for each patient. The psychologist would like to determine if there is a relation-ship between the degree to which each patient gambled, as measured by the amount of money the patient had lost gambling the year prior to being admitted to treatment, x, and the gambling score, y. One manner of comparing the difference in the three therapies is to compare the slopes and intercepts of the lines relating y to x.
a. Write a general linear model relating the response, gambling inclination, y, to the explanatory variable, amount of money loss gambling, x, and type of therapy. Make sure to define all variables and parameters in your model.
b. Modify the model of part (a) to reflect that the three therapies have the same slope.