Thompson Photo Works purchased several new, highly sophisticated processing mach

Question

Thompson Photo Works purchased several new, highly sophisticated processing 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 an operator (in years) important? In order to explore further the factors needed to estimate performance on the new processing machines, four variables were listed:

X1 = Length of time an employee was in the industry

X2 = Mechanical aptitude test score

X3 = Prior on-the-job rating

X4 = Age

Performance on the new machine is designated Y.

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

  Name

Performance
on New
Machine,
Y

Length of
Time in
Industry,
X1

Mechanical
Aptitude
Score,
X2

Prior
on-the-Job
Performance,
X3

Age,
X4

  Mike Miraglia

120

11

385

117

36

  Sue Trythall

118

6

372

119

25

The equation is:

= 11.2 + 0.3X1 + 0.286X2 + 0.712X3 + 0.007X4

d.

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

e.

Carl Knox applied for a job at Photo Works. He has been in the business for 11 years and scored 270 on the mechanical aptitude test. Carl’s prior on-the-job performance rating is 80, and he is 25 years old. Estimate Carl’s performance on the new machine. (Round your answer to 3 decimal places.)

Thompson Photo Works purchased several new, highly sophisticated processing 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 an operator (in years) important? In order to explore further the factors needed to estimate performance on the new processing machines, four variables were listed:

Explanation / Answer

d.

Age increasing by one year means adding 1 to X4. So if you call Ya the performance on the machine by a employee A with age X4a and the other variables just X1, X2 and X3 then:
Ya = 11.2 + 0.3X1 + 0.286X2 + 0.712X3 + 0.007X4a
Now if we take another employee, B, with all the same qualities as employee A except that employee B is one year older. Then all the qualities X1, X2 and X3 are both the same for A and B. However: X4b = X4a +1 since B is one year older.
Now: Yb= 11.2 + 0.3X1 + 0.286X2 + 0.712X3 + 0.007X4b

             = 11.2 + 0.3X1 + 0.286X2 + 0.712X3 + 0.007(X4a +1)

             = 11.2 + 0.3X1 + 0.286X2 + 0.712X3 + 0.007X4a+0.007

              = Ya +.007 (remember that Ya = 11.2 + 0.3X1 + 0.286X2 + 0.712X3 + 0.007X4a) So by increasing age by one year, Y increases by 0.007.

e.

Ya = 11.2 + 0.3X1 + 0.286X2 + 0.712X3 + 0.007X4

     =11.2+0.3(11)+0.286(270)+0.712(80)+0.007(25)

     =148.855

Thus the Estimate Carl’s performance on the new machine is 148.855

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