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	112	6	305	125	44
Sue Trythall	120	10	354	124	24

The equation is:

YˆY^ = 11 + 0.6X1 + 0.986X2 + 0.512X3 + 0.008X4

(a)	What is this equation called?
	(Click to select)Coefficient of determinationMultiple regression equationMultiple standard error of estimate

(b)	How many dependent and independent variables are there?
	(Click to select)FourThreeFiveTwoOne dependent, (Click to select)OneThreeFiveFourTwo independent

(c)	What is the number 0.512 called?
	(Click to select)HomoscedasticityMulticollinearityCoefficient of determinationA regression coefficient

(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 10 years, and scored 240 on the mechanical aptitude test. Carl’s prior on-the-job performance rating is 90, and he is 40 years old. Estimate Carl’s performance on the new machine. (Round your answer to 3 decimal places.)

Answer 1

Answer a. Multiple Regression Equation

Explanation:

The equation, , explaining the relationship between Y and several (Multiple) independent variables is the Multiple Regression Equation. This, in particular, is Estimated Multiple Regression Equation.

Answer b. One dependent variable and Four Independent Variable

Explanation:

There are 4 Independent variables, namely

X1 = Length of time an employee was in the industry

X2 = Mechanical aptitude test score

X3 = Prior on-the-job rating

X4 = Age

which are trying to explain or predict one dependent variable, namely,

Y = Performance of New Machine

Answer c. Regression Coefficient

Explanation:

Here, which is the regression coefficient corresponding to explanatory variable X3 = Prior on-the job Rating.

Answer d. 0.008

Explanation:

The Regression Coefficient tells the marginal effect of that explanatory variable on the dependent variable holding all other independent variables constant.

Therefore, As age increases by one year,estimated performance on the new machine increases by 0.008 units.

Answer e. 300.040

Explanation:

We will use the above predicted Multiple Regression Equation to find the estimated performance on new machine given X1 = 10 , X2 = 240 , X3 = 90 and X4 = 40