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. Draw a scatter diagram. Please state exact coordinates Based on the scatter diagram, does there appear to be any relationship between the number of assemblers and production? Compute the coefficient correlation. (Negative values should be indicated by a minus sign. Round sx, sy 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 =

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Exercise 13-4 (LO13-2)

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.

Draw a scatter diagram.
Please state exact coordinates

Based on the scatter diagram, does there appear to be any relationship between the number of assemblers and production?

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¯

S_x

S_y

The task is to compute the coefficient of correlation. It's important to note that negative values should be indicated with a minus sign and that the calculations for $s_x$, $s_y$, and $r$ should be rounded to 3 decimal places.

Here is the table provided:

| $x$ | $y$ | $x - \bar{x}$ | $y - \bar{y}$ | $(x - \bar{x})^2$ | $(y - \bar{y})^2$ | $(x - \bar{x})(y - \bar{y})$ |
|-------|-------|------------------|------------------|---------------------|---------------------|------------------------------|
| 2 | 15 | | -9 | | 81 | |
| 4 | 25 | | | 1 | | |
| 1 | 10 | | -14 | | 196 | |
| 5 | 40 | | | 4 | 32 | |
| 3 | 30 | | 6 | 0 | | |

The calculations to be filled in include:

- $\bar{x}$ =
- $\bar{y}$ =
- $s_x$ =
- $s_y$ =
- $r$ =

Make sure to use the provided equations and fill in all missing values.

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