Forecasting a job applicant’s merit rating. 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: E1y2 = b0 + b1x1 + b2x2 + b3x1x2 + b4x1 2 + b5x2 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 SS1model2 = 4,911.5. The reduced model E1y2 = b0 + b1x1 + b2x2 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 a = .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 a = .05. Interpret the results in the context of this problem.

e. Which model, if either, would you use to predict y? Explain.