Compute r, the correlaton coeffcient, USma the follout data X. 434
MATLAB: An Introduction with Applications
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Author:Amos Gilat
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7bf351b9-92b6-46f8-a8e3-5061ac485878%2F03cb679c-ba02-4940-ae41-4a3de7c70dfb%2F4iq9bgh_processed.jpeg&w=3840&q=75)
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
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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