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	111	7	315	127	50
Sue Trythall	112	2	306	127	29

  

The equation is:

  

Yˆ Y⁢^⁢  = 11.5 + 0.9X1 + 0.886X2 + 0.212X3 + 0.003X4

  

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

  

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

  

c.	What is the number 0.212 called?
	(Click to select)Regression coefficient, Coefficient of determination, Homoscedasticity, Multicollinearity

  

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 3 years and scored 305 on the mechanical aptitude test. Carl’s prior on-the-job performance rating is 95, and he is 30 years old. Estimate Carl’s performance on the new machine. (Round your answer to 3 decimal places.)

Answer 1

A multiple regression equation

Where Y: dependent variable ; X₁, X₂,.....Independent variables;

b₀, b₁, b₂ , ....are regression coefficients.

a. What is this equation called?

Multiple regression equation

b.
How many dependent and independent variables are there?

one Dependent variable :

Four Independent variables

c.

What is the number 0.212 called?

Regression coefficient.

d.

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

Age is represented as X₄ ; ie. As X₄ is increased by 1 ; then the Y: estimated performance on the new machine increases by the coefficient of X₄ i.e 0.003

Ans : 0.003

e.

Carl Knox applied for a job at Photo Works. He has been in the business for 3 years and scored 305 on the mechanical aptitude test. Carl’s prior on-the-job performance rating is 95, and he is 30 years old

i.e

X1 = Length of time an employee was in the industry=3 years

X2 = Mechanical aptitude test score=305

X3 = Prior on-the-job rating=95

X4 = Age=30

Substitute the values of  X₁ = 3 ; X₂ =305 ; X₃ =95 ; X₄ = 30 in the multiple regression equation: