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MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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![**Title: Calculating the Correlation Coefficient from Given Data**
**Objective:**
Learn how to compute the correlation coefficient using a given set of data.
**Instructions:**
To find the correlation coefficient, you will use the listed data points for variables \( x \) and \( y \).
**Data:**
| \( x \) | \( y \) |
|-------|-------|
| 1 | 3 |
| 5 | 5 |
| 6 | 1 |
| 3 | 6 |
| 4 | 4 |
| 2 | 2 |
**Steps:**
1. Plot the data on a scatter plot to visually assess any potential correlation.
2. Use the formula for the Pearson correlation coefficient \( r \) to compute the linear relationship between \( x \) and \( y \).
3. The formula for \( r \) is:
\[
r = \frac{n(\sum xy) - (\sum x)(\sum y)}{\sqrt{[n\sum x^2 - (\sum x)^2][n\sum y^2 - (\sum y)^2]}}
\]
- \( n \) is the number of data points.
- \( \sum xy \) is the sum of the products of paired scores.
- \( \sum x \) and \( \sum y \) are the sums of the \( x \) and \( y \) scores, respectively.
- \( \sum x^2 \) and \( \sum y^2 \) are the sums of the squared \( x \) and \( y \) scores, respectively.
4. Interpret the value of \( r \):
- \( r = 1 \): perfect positive correlation
- \( r = -1 \): perfect negative correlation
- \( r = 0 \): no correlation
This exercise helps develop a fundamental understanding of statistical relationships between two variables and their practical implications.](https://content.bartleby.com/qna-images/question/7bf351b9-92b6-46f8-a8e3-5061ac485878/03cb679c-ba02-4940-ae41-4a3de7c70dfb/4iq9bgh_thumbnail.jpeg)
Transcribed Image Text:**Title: Calculating the Correlation Coefficient from Given Data**
**Objective:**
Learn how to compute the correlation coefficient using a given set of data.
**Instructions:**
To find the correlation coefficient, you will use the listed data points for variables \( x \) and \( y \).
**Data:**
| \( x \) | \( y \) |
|-------|-------|
| 1 | 3 |
| 5 | 5 |
| 6 | 1 |
| 3 | 6 |
| 4 | 4 |
| 2 | 2 |
**Steps:**
1. Plot the data on a scatter plot to visually assess any potential correlation.
2. Use the formula for the Pearson correlation coefficient \( r \) to compute the linear relationship between \( x \) and \( y \).
3. The formula for \( r \) is:
\[
r = \frac{n(\sum xy) - (\sum x)(\sum y)}{\sqrt{[n\sum x^2 - (\sum x)^2][n\sum y^2 - (\sum y)^2]}}
\]
- \( n \) is the number of data points.
- \( \sum xy \) is the sum of the products of paired scores.
- \( \sum x \) and \( \sum y \) are the sums of the \( x \) and \( y \) scores, respectively.
- \( \sum x^2 \) and \( \sum y^2 \) are the sums of the squared \( x \) and \( y \) scores, respectively.
4. Interpret the value of \( r \):
- \( r = 1 \): perfect positive correlation
- \( r = -1 \): perfect negative correlation
- \( r = 0 \): no correlation
This exercise helps develop a fundamental understanding of statistical relationships between two variables and their practical implications.
Expert Solution
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Step 1
The correlation coefficient r is computed using the formula below:
x | y | xy | ||
1 | 1 | 1 | 1 | 1 |
5 | 5 | 25 | 25 | 25 |
6 | 6 | 36 | 36 | 36 |
3 | 5 | 9 | 25 | 15 |
4 | 4 | 16 | 16 | 16 |
2 | 2 | 4 | 4 | 4 |
sum=21 | sum=23 | sum=91 | sum=107 | sum=97 |
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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
- I need help please! Thank you pre calculusarrow_forwardA behavioral economics psychologist wanted to see what factors were important when a person selects speakers. The tested price of speakers (of low and high) and sound amplitude (soft and loud), as some research shows the louder speakers sound better to people. He asked participants to rate the sound quality of the speakers they listened to from 0-10, with a score of 10 being the highest quality. Write the hypothesis (in words), perform the ANOVA and include the partial eta squared calculations in your APA write up of the results of the following data.Test at an alpha level of α=.05. Factor B low high soft 0 4 1 6 4 5 3 4 2 3 Mean 2 4.4 N=20 SS 10 5.2 G=104 Factor A Total 10 22 ∑x2=682 loud 8 8 6 5 9 5 5 9 10 7 Mean 7.6 6.8 SS 17.2 12.8 Total 38 34arrow_forwardSe -30arrow_forward
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