An article in the Community Mental Health Journal (Aug. 2000) used multiple-regression analysis to model the level of community adjustment of clients of the Department of Mental Health and Addiction Services in Connecticut. The dependent variable, community adjustment (y), was measured quantitatively on the basis of staff ratings of the clients. (Lower scores indicate better adjustment.) The complete model was a first-order model with 21 independent variables. The independent variables were categorized as demographic (four variables), diagnostic (seven variables), treatment (four variables), and community (six variables).
a. Write the equation of E (y) for the complete model.
b. Give the null hypothesis for testing whether the seven diagnostic variables contribute information relevant to the prediction of y.
c. Give the equation of the reduced model appropriate for the test suggested in part b.
d. The test in part b was carried out and resulted in a test statistic of F = 59.3 and p-value <.0001. Interpret this result in the words of the problem.