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:

	Performance on New Machine,		Length of Time in Industry,		Mechanical Aptitude Score,		Prior On-the-Job Performance,		Age,
Name	y		x1		x2		x3		x4
Mike Miraglia	110		3		385		128		44
Sue Trythall	120		10		347		117		30

The equation is:

yˆ y⁢^⁢  = 10.4 + 0.3x₁ + 0.686x₂ + 0.412x₃ + 0.003x₄

As age increases by one year, how much does estimated performance on the new machine increase?

Carl Knox applied for a job at Photo Works. He has been in the business for 5 years and scored 290 on the mechanical aptitude test. Carl’s prior on-the-job performance rating is 90, and he is 39 years old. Estimate Carl’s performance on the new machine. (Round your answer to 3 decimal places.)

Answer 1

Result:

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:

	Performance on New Machine,	Length of Time in Industry,	Mechanical Aptitude Score,	Prior On-the-Job Performance,	Age,
Name	y	x1	x2	x3	x4
Mike Miraglia	110		3		385		128		44
Sue Trythall	120		10		347		117		30

The equation is:

yˆ ⁢  = 10.4 + 0.3x₁ + 0.686x₂ + 0.412x₃ + 0.003x₄

As age increases by one year, how much does estimated performance on the new machine increase?

Regression coefficient for age = 0.003

As age increases by one year, estimated performance on the new machine increase by 0.003

Carl Knox applied for a job at Photo Works. He has been in the business for 5 years and scored 290 on the mechanical aptitude test. Carl’s prior on-the-job performance rating is 90, and he is 39 years old. Estimate Carl’s performance on the new machine. (Round your answer to 3 decimal places.)

When

Length of Time in Industry =5

Mechanical Aptitude Score =290

Prior On-the-Job Performance=90

Age=39

Predicted Performance on New Machine

yˆ ⁢ = 10.4 + 0.3*5 + 0.686*290 + 0.412*90 + 0.003*39

=248.037