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 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 (4 variables), Diagnostic (7 variables). Treatment (4 variables), and Community (6 variables).
a. Write the equation of F(y) for the complete model.
b. Give the null hypothesis for testing whether the 7 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 < .0001. Interpret this result in the words of the problem.