Question

The production department of Celltronics International wants to explore the relationship between the number of employees...

The production department of Celltronics International wants to explore the relationship between the number of employees who assemble a subassembly and the number produced. As an experiment, 2 employees were assigned to assemble the subassemblies. They produced 11 during a one-hour period. Then 4 employees assembled them. They produced 18 during a one-hour period. The complete set of paired observations follows.

Number of
Assemblers
One-Hour
Production (units)
2 11
4 18
1 7
5 29
3 20

The dependent variable is production; that is, it is assumed that different levels of production result from a different number of employees.

Compute the coefficient of correlation.

X Y (x- x̄ ) (y- ȳ ) (x- x̄)2 (y-ȳ )2 (x-x̄ )(y- ȳ)
2 11    -6    36   
4 18 1   1      1  
1 7    -10    100   
5 29 2      4      24
3 20    3 0      0  
        

x̄=_______                       ȳ=________              Sx=_________

Sy=_______                   r=__________

Homework Answers

Answer #1

X Values
∑ = 15
Mean = 3
∑(X - Mx)2 = SSx = 10

Y Values
∑ = 85
Mean = 17
∑(Y - My)2 = SSy = 290

X and Y Combined
N = 5
∑(X - Mx)(Y - My) = 51

R Calculation
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

r = 51 / √((10)(290)) = 0.947

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