Chapter 14, Problem 2E

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:

$\begin{array}{l}{x}_1=\text{Length}\text{of}\text{time}\text{an}\text{employee}\text{was}\text{in}\text{the}\text{industry}\hfill \\ x_2=\text{Mechanical}\text{aptitude}\text{test}\text{score}\hfill \\ x_3=\text{Prior}\text{on-the-job}\text{rating}\hfill \\ x_4=\text{Age}\hfill \end{array}$

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:

The equation is:

$\hat{y}=11.6+0.4x_1+0.286x_2+0.112x_3+0.002x_4$

1. a. What is this equation called?
2. b. How many dependent variables are there? Independent variables?
3. c. What is the number 0.286 called?
4. d. As age increases by one year, how much does estimated performance on the new machine increase?
5. e. Carl Knox applied for a job at Photo Works. He has been in the business for 6 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.