Community adjustment of mental health clients. An article in the Community Mental Health Journal (August 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 based on 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 for the prediction of y.
(c) Give the equation of the reduced model appropriate for the test, part b.
(d) The test, part b, resulted in a test statistic of F = 59.3 and p-value.