Question

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

X₁ = Length of time employee was a machinist

X₂ = Mechanical aptitude test score

X₃ = Prior on-the-job rating

X₄ = Age

Performance on the new machine is designated as Y.

Thirty machinists were selected at random. Data were collected for each, and their performances on the new machines were recorded. A few results are as follows:

Name	Performance on New Machine, Y		Length of Time as a Machinist, X1		Mechanical Aptitude Score, X2		Prior On-the-Job Performance, X3		Age,= X4
Andy Kosin	107		9		350		123		35
Sue Annis	109		3		317		123		45

The equation is:

Y' = 11.2 + 0.3X₁ + 0.286X₂ + 0.112X₃ + 0.006X₄

a. As age increases by one year, how much does estimated performance on the new machine increase? (Round the final answer to 3 decimal places.)

Estimated performance =

b. Carl Knox applied for a job at Photo Works. He has been a machinist for six years, and scored 280 on the mechanical aptitude test. Carl’s prior on-the-job performance rating is 97, and he is 35 years old. Estimate Carl’s performance on the new machine. (Round the final answer to 3 decimal places.)

Carl’s performance =

Answer 1

(a)

As age increases by one year, the estimated performance on the new machine increases by

0.006

Explanation:

The given Regression equation is:

Y' = 11.2 + 0.3X1 + 0.286X2 + 0.112X3 + 0.006X4

Here X4 is age and its coefficient is 0.006

(b)

The given Regression equation is:

Y' = 11.2 + 0.3X1 + 0.286X2 + 0.112X3 + 0.006X4

Given:

X1 = Length of time employee was a machinist = 6

X2 = Mechanical aptitude test score = 280

X3 = Prior on-the-job rating = 97

X4 = Age = 35

Substituting, we get:

Y' = 11.2 + (0.3 X 6) + (0.286 X 280) + (0.112 X 97) + (0.006 X 35)

= 11.2 + 1.8 + 80.08 + 10.864 + 0.21

= 104.154

So,

Answer is:

104.154