Question

3.    Thompson Machine Works purchased several new, highly sophisticated machines. The production department needed some guidance with respect to the qualifications needed by the operator. Is age a factor? Is the length of service as a machine operator important? In order to explore further the factors needed to predict performance on the new machines, four variables were listed:

                        X₁  =                length of time the employee was a machinist

                        

                        X₂  =                mechanical aptitude test score

                        X₃  =               prior on-the-job rating

                        X₄  =                age

Performance on the new machine is designated Y.

Twelve machinists were selected at random. Data were collected for each, and their performances on the new machines were recorded. The regression equation is:

                                Y hat = 11.6 + 0.4X₁ + 0.286X₂  + 0.112X₃  + 0.002X₄

a.    How many independent variables are there in the model? (2 pts.)

b.    What is the expected performance difference between two workers identical in all respects except that one worker is 30 years old and the other is 40 years old? (4 pts)

c.    Carl Knox applied for a job on a new machine. He has been a machinist for six years, and he scored a 280 on the mechanical aptitude test. Carl's prior on-the-job performance rating is 97, and he is 35 years old. The best available evidence says that an operator should perform at a 110 performance level rating on the new machine to pose no safety risks. What decision is appropriate in the application of Carl Knox? (5 pts)

Answer 1

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Answer:

a)

Y=11.6+0.4X1+0.286X2+0.112X3+0.002X4

The variable Y is dependent on the variables X1, X2, X3 and X4. So there is only one dependent variable, Y which represents the performance on the new machine and 4 independent variables X1, X2, X3 and X4 which represents length of time an employee was in the industry, mechanical aptitude test score, prior on the job rating and age respectively.

b)

Expected performance difference between the two workers identical in allrespects except that one is 30 years old and other is 40 years old = 0.286 (40-30) = 2.86

c)

In this situation 110 performance level is better than the new machine. Therefore the evidence that says that an operator should perform at a 110 performance level rating on the new machine to pose no safety risks. is correct. The application of Carl Knox should be rejected