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, two employees were assigned to assemble the subassemblies. They produced 15 during a one-hour period. Then four employees assembled them. They produced 25 during a one-hour period. The complete set of paired observations follows.

Number of Assemblers				One-Hour Production (units)
	2				15
	4				25
	1				10
	5				40
	3				30

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

3. Compute the coefficient correlation. (Negative values should be indicated by a minus sign. Round s_x, s_y and r to 3 decimal places.)

x	y	x−x⎯⎯x-x¯	y−y⎯⎯y-y¯	(x−x⎯⎯)2x-x¯2	(y−y⎯⎯)2y-y¯2	(x−x⎯⎯) (y−y⎯⎯)x-x¯ y-y¯
2	15		−9		81
4	25	1		1		1
1	10		−14		196
5	40	2		4		32
3	30		6	0		0

x⎯⎯x¯

=

y⎯⎯y¯

=

Sx

=

Sy

=

r

=

Answer 1

-1.000   
1.000
-2.000
2.000

X - Mx	Y - My	(X - Mx)2	(Y - My)2	(X - Mx)(Y - My)
-1.000    1.000 -2.000 2.000 0.000 Mx: 3.000	-9.000 1.000 -14.000 16.000 6.000 My: 24.000	1.000 1.000 4.000 4.000 0.000 Sum: 10.000	81.000 1.000 196.000 256.000 36.000 Sum: 570.000	9.000 1.000 28.000 32.000 0.000 Sum: 70.000

0.000

Mx: 3.000

Result Details & Calculation

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

Y Values
∑ = 120
Mean = 24
∑(Y - My)2 = SSy = 570

X and Y Combined
N = 5
∑(X - Mx)(Y - My) = 70

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

r = 70 / √((10)(570)) = 0.9272

Meta Numerics (cross-check)
r = 0.9272

Key

X: X Values
Y: Y Values
Mx: Mean of X Values
My: Mean of Y Values
X - Mx & Y - My: Deviation scores
(X - Mx)2 & (Y - My)2: Deviation Squared
(X - Mx)(Y - My): Product of Deviation Scores

The value of R is 0.9272.