c. Compute the coefficient correlation. (Negative amounts should be indicated by a minus sign. Round sx, Sy and r to 3 decimal places.) y 15 (z ) (x – ¤) (y – g) 2 -9 81 4 25 1 196 10 40 -14 32 3 30 15 T= Sy =

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
icon
Concept explainers
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.

[Click here for the Excel Data File]

a. Draw a scatter diagram.

1. On the graph below, use the point tool to plot the point corresponding to the first Number of Assemblers and her Production (No of Assemblers1).
2. Repeat the process for the remainder of the sample (No of Assemblers2, No of Assemblers3, ... ).
3. To enter exact coordinates, double-click on the point and enter the exact coordinates of x and y.

**Graph Explanation**: 

The graph consists of a vertical axis labeled "Production" ranging from 0 to 50 and a grid with no marked data points. There are placeholder points labeled from "No of Assemblers1" to "No of Assemblers4" on the right, intended for plotting based on the table's data. Instructions indicate plotting each assembler's data point against production to form a scatter plot.
Transcribed Image Text: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. [Click here for the Excel Data File] a. Draw a scatter diagram. 1. On the graph below, use the point tool to plot the point corresponding to the first Number of Assemblers and her Production (No of Assemblers1). 2. Repeat the process for the remainder of the sample (No of Assemblers2, No of Assemblers3, ... ). 3. To enter exact coordinates, double-click on the point and enter the exact coordinates of x and y. **Graph Explanation**: The graph consists of a vertical axis labeled "Production" ranging from 0 to 50 and a grid with no marked data points. There are placeholder points labeled from "No of Assemblers1" to "No of Assemblers4" on the right, intended for plotting based on the table's data. Instructions indicate plotting each assembler's data point against production to form a scatter plot.
**b. Based on the scatter diagram, does there appear to be any relationship between the number of assemblers and production?**

Yes, as the number of assemblers increases, so does the production.

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

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

\[
\bar{x} = 
\]

\[
\bar{y} = 
\]

\[
s_x = 
\]

\[
s_y = 
\]

\[
r = 
\]
Transcribed Image Text:**b. Based on the scatter diagram, does there appear to be any relationship between the number of assemblers and production?** Yes, as the number of assemblers increases, so does the production. **c. Compute the coefficient correlation.** *(Negative amounts should be indicated by a minus sign. Round \(s_x\), \(s_y\), and \(r\) to 3 decimal places.)* | \( x \) | \( y \) | \( x - \bar{x} \) | \( y - \bar{y} \) | \( (x - \bar{x})^2 \) | \( (y - \bar{y})^2 \) | \( (x - \bar{x})(y - \bar{y}) \) | |---------|---------|----------------|----------------|--------------------|--------------------|-----------------------------| | 2 | 15 | | -9 | | 81 | | | 4 | 25 | | 1 | 1 | | | | 1 | 10 | | -14 | | 196 | | | 5 | 40 | | | 4 | | 32 | | 3 | 30 | | 6 | 0 | | | \[ \bar{x} = \] \[ \bar{y} = \] \[ s_x = \] \[ s_y = \] \[ r = \]
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 1 images

Blurred answer
Knowledge Booster
Correlation, Regression, and Association
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman