A large research and development firm rates the performance of each member of its technical staff on a scale of 0 to 100, and this merit rating is used to determine the size of the person's pay raise for the coming year. The firm's personnel department is interested in developing a regression model to help them forecast the merit rating that an applicant for a technical position will receive after being employed 3 years. The firm proposes to use the following second-order model to forecast the merit ratings of applicants who have just completed their graduate studies and have no prior related job experience:
E(y) = β0 + β1x1 + β2x2 + β3x1x2 +β4x22 +β5x22
where
y = Applicant's merit rating after 3 years
x1=Applicant's GPA in graduate school
x2 = Applicant's total score (verbal plus quantitative) on the Graduate Record Examination (GRE)
The model, fit to data collected for a random sample of n = 40 employees, resulted in SSE = 1,830.44 and SS(model) = 4,911.5. The reduced model E(y) = β0 + β1x1 + β2x2 is also fit to the same data, resulting in SSE = 3, 197.16.
a. Identify the appropriate null and alternative hypotheses to test whether the complete (second-order) model contributes information for the prediction of y.
b. Conduct the test of hypothesis given in part a. Test using α = 05. Interpret the results in the context of this problem.
c. Identify the appropriate null and alternative hypotheses to test whether the complete model contributes more information than the reduced (first-order) model for the prediction of y.
d. Conduct the test of hypothesis given in part c. Test using α = .05. Interpret the results in the context of this problem.
e. Which model, if either, would you use to predict y? Explain.