11.51 A large research and development company rates the performance of each of the members of its technical staff once a year. Each person is rated on a scale of zero to 100 by his or her immediate supervisor, and this merit rating is used to help determine the size of the person’s pay raise for the coming year. The company’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 he or she has been with the company three years. The company proposes to use the following model to forecast the merit ratings of applicants who have just completed their graduate studies and have no prior related job experience:

where Y applicant’s merit rating after three years x1 applicant’s grade-point average (GPA) in graduate school x2 applicant’s verbal score on the Graduate Record Examination (percentile)

A random sample of n 40 employees who have been with the company more than there years was selected. Each employee’s merit rating after three years, his or her graduate-school GPA, and the percentile in which the verbal Graduate Record Exam score fell were recorded. The above model was fit to these data and a portion of the resulting computer shown below.

E(Y) = b0 + b1x1 + b2x2 + b3x1x2 + b4x21

+ b5x22

The reduced model was fit to the same data, and the resulting computer printout is partially reproduced below.

a Identify the null and alternative hypothesesfor a test to determine whether the completemodel contributed information for the prediction of Y.
b Identify the null and alternative hypotheses for a test to determine whether a second-order model contributes more information than a first-order model for the prediction of Y.
c Conduct the hypothesis test you described in part (a).Test using = 0.05. Draw the appropriate conclusions in the context of the problem.
d Conduct the hypothesis test you described in part (b).Test using = 0.05. Draw the appropriate conclusions in the context of the problem.

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SOURCE DF SUM OF SQUARES MEAN SQUARE MODEL 5 4911.56 982.31 ERROR 34 1830.44 53.84 TOTAL 39 6742.00 R-SQUARE 0.729