Question

hompson 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	113		13		340		116		50
Sue Trythall	119		10		386		117		26

The equation is:

yˆy⁢^⁢  = 10.6 + 0.8x₁ + 0.786x₂ + 0.612x₃ + 0.001x₄

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 0.786 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 6 years and scored 370 on the mechanical aptitude test. Carl’s prior on-the-job performance rating is 90, and he is 24 years old. Estimate Carl’s performance on the new machine. (Round your answer to 3 decimal places.)

Answer 1

solution Given data, Name X1 X 3 X4 Y Mike 113 13 340 116 50 Miraglia 26 119 10 Sue Trythall 386 117 ç equation is s Y^= 10.6 +0.8 x, +0.786 x 2 +0.612 X3 + 0.00l 14 @ + Here, since ore Variables and there your independent the given equation & linear multiple regression equation. a so, this ia @T 3 here, there and four is one dependent variable, y independent variables , x's. → Here, The number 0.786 indicate the change in performance on the new machine when the mechanical aptitude test score increases by This is Regression coefficient : one.

(d) increased by One year, new machine the when the age the performance increases 0.00) explanation : 10.6 + 0.8 x 0 + 0-786 XO + 0.612 O +0.001 x 1 10.601 Here, The estimated I performance y^= 10.6+ 0. g(6) + 0.786 (370) + 0.612090) +0.001 (24) = 10-6 + 4.8 + 290.82 + 55-08 + 0.024 y = 361.324 * Thank you &