Forecasting a job applicant’s merit rating. A large

QUESTION:

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:

\(E(y)=\beta_{0}+\beta_{1} x_{1}+\beta_{2} x_{2}+\beta_{3} x_{1} x_{2}+\beta_{4} x_{1}^{2}+\beta_{5} x_{2}^{2}\)

where

y = Applicant’s merit rating after 3 years

\(x_1\) = Applicant’s GPA in graduate school

\(x_2\) = 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 andSS(model) = 4,911.5. The reduced model \(E(y)=\beta_{0}+\beta_{1} x_{1}+\beta_{2} x_{2}\) 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 \(\alpha\ =\ .05\). 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 \(\alpha\ =\ .05\). Interpret the results in the context of this problem.

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