Question

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=__________

Answer 1

X Values
∑ = 15
Mean = 3
∑(X - M_x)² = SS_x = 10

Y Values
∑ = 85
Mean = 17
∑(Y - M_y)² = SS_y = 290

X and Y Combined
N = 5
∑(X - M_x)(Y - M_y) = 51

R Calculation
r = ∑((X - M_y)(Y - M_x)) / √((SS_x)(SS_y))

r = 51 / √((10)(290)) = 0.947