Question

Thomson 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 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:

Perfomance Length Mechanical Prior
on new of time in aptitude on-the-job
MAchine Industry Score Performance Age
Name Y X1 X2 X3 X4
Mike Miraglia 112 12 312 121 52
Sue Trythall 113 2 380 123 27

The equation is:
Y= 11.6 + 0.4X1 + 0.286X2 + 0.112X3 + 0.002X4

a. What is this equation called?
b. How many dependent variables are there? Independent variables?
c. What is the number 0.286 called?
d. As age increases by one year, how much does estimated performance on the new machine increase?
e. Carl Knox applied for a job at Photo Works. He has been in the business 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.
f. Explain what the constant term tells us.

Answer 1

a

The equation is called Least-squares multiple variable linear regression equation.

b

There is one dependent variable and 4 independent variables.

c

The number 0.286 is called the slope coefficient for the variable X2 and represents that with a unit change in the mechanical aptitude test score the performance of the machine increases by 0.286 units.

d

With an increase in age by one year the performance on the new machine increases by 0.002 units.

e

The performance on the new machine with an experience of 6 years, a mechanical aptitude test score of 280, a prior on the job performance rating of 97 and the age of 35 years is 105.014.

f

The constant terms tell that the performance on the new machine will be 11.6 if rest of the independent variables are zero.

Explanation:

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