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	119	12	395	125	47
Sue Trythall	116	4	366	122	26

The equation is:

YˆY^ = 11.6 + 0.3X₁ + 0.586X₂ + 0.312X₃ + 0.006X₄

(a)	What is this equation called?
	(Click to select) Multiple standard error of estimate, Coefficient of determination, or Multiple regression equation

(b)	How many dependent and independent variables are there?
	(Click to select)One, Five, Two, Three, or Four dependent, (Click to select)Three, Five, Four, One, or Two independent

(c)	What is the number 0.312 called?
	(Click to select) A regression coefficient, Multicollinearity, Coefficient of determination, or Homoscedasticity

(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 5 years, and scored 360 on the mechanical aptitude test. Carl’s prior on-the-job performance rating is 70, and he is 57 years old. Estimate Carl’s performance on the new machine. (Round your answer to 3 decimal places.)

Answer 1

a) This equation is called multiple regression equation. Because it has more than 1 number of independent variables.

Here independent variables are, Length of Time in Industry, Mechanical aptitude test score, Prior on-the-job rating, Age

b) There are one dependent and four independent variables.

Dependent variable : Performance on the new machine

Independent variables : Length of Time in Industry, Mechanical aptitude test score, Prior on-the-job rating, Age

c) 0.312 is a regression coefficient

d) As age increases by one year, the estimated performance on the new machine increases by 0.006

e) y = 11.6 + 0.3X₁ + 0.586X₂ + 0.312X₃ + 0.006X₄

X₁ = 5

X₂ = 360

X₃ = 70

X₄ = 57

y = 11.6 + 0.3 * 5 + 0.586 * 360 + 0.312 * 70 + 0.006 * 57 = 246.242