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	114		4		301		124		38
Sue Trythall	115		10		335		128		30

The equation is:

yˆ y⁢^⁢  = 11.0 + 0.6x₁ + 0.286x₂ + 0.512x₃ + 0.009x₄

1. What is this equation called?

• Multiple regression equation

• Multiple standard error of estimate

• Coefficient of determination

2. How many dependent and independent variables are there?

3. What is the number 0.286 called?

• Regression coefficient

• Coefficient of determination

• Homoscedasticity

• Multicollinearity

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

5. Carl Knox applied for a job at Photo Works. He has been in the business for 10 years and scored 210 on the mechanical aptitude test. Carl’s prior on-the-job performance rating is 100, and he is 75 years old. Estimate Carl’s performance on the new machine. (Round your answer to 3 decimal places.)

Answer 1

What is this equation called?

Ans : Multiple regression equation.

Multiple regression is a technique for predicting the value of a dependent variable, based on the values of two or more independent variables.

Dependent variable : y : performance on the new processing machines

Independent variables:

x₁ = Length of time an employee was in the industry

x₂ = Mechanical aptitude test score

x₃ = Prior on-the-job rating

x₄ = Age

b.How many dependent and independent variables are there?

Ans:

Dependent variables : 1

Independent variables : 4

c. What is the number 0.286 called

Ans : Regression coefficient

The regression equation that expresses the linear relationships between a single dependent variable and one or more independent variables is:

ŷ = b₀ + b₁x₁ + b₂x₂ + … + b_k-1x_k-1 + b_kx_k

the b's - b₀, b₁, b₂, … , b_k. The b's are constants, called regression coefficients.

For the given problem,The regression equation

 ⁢  = 11.0 + 0.6x₁ + 0.286x₂ + 0.512x₃ + 0.009x₄

b_o = 11.o; b₁ =0.6 b₂=0.286 b₃=0.512 b​​​​​₄=0.009 are called regression coefficients

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

i.e x₄ increases by one year then the : estimated performance on the new machine increases by the regression coefficient of x₄ i.e 0.009

Ans : 0.009

e. Carl Knox applied for a job at Photo Works. He has been in the business for 10 years and scored 210 on the mechanical aptitude test. Carl’s prior on-the-job performance rating is 100, and he is 75 years old. Estimate Carl’s performance on the new machine

x₁ = Length of time an employee was in the industry: He has been in the business for 10 years = 10

x₂ = Mechanical aptitude test score : scored 210 on the mechanical aptitude test =210

x₃ = Prior on-the-job rating : prior on-the-job performance rating is 100 = 100

x₄ = Age he is 75 years old = 75

Substituting these values in the

 ⁢  = 11.0 + 0.6x₁ + 0.286x₂ + 0.512x₃ + 0.009x₄

Estimate Carl’s performance on the new machine: = 128.935

Ans : 128.935