Compute the Pearson correlation for the following data. r = X 7 3 6 Y 3 1 5 4 4 5 2
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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![**Compute the Pearson Correlation for the Following Data**
Below is a table of paired data representing two variables, X and Y. To determine the strength and direction of the linear relationship between these variables, calculate the Pearson correlation coefficient (r).
| X | Y |
|---|---|
| 7 | 3 |
| 3 | 1 |
| 6 | 5 |
| 4 | 4 |
| 5 | 2 |
**Formula for Pearson Correlation Coefficient:**
\[
r = \frac{n(\sum{XY}) - (\sum{X})(\sum{Y})}{\sqrt{[n\sum{X^2} - (\sum{X})^2][n\sum{Y^2} - (\sum{Y})^2]}}
\]
Where:
- \( n \) is the number of data points.
- \( \sum{XY} \) is the sum of the products of corresponding X and Y values.
- \( \sum{X} \) is the sum of X values.
- \( \sum{Y} \) is the sum of Y values.
- \( \sum{X^2} \) is the sum of the squares of X values.
- \( \sum{Y^2} \) is the sum of the squares of Y values.
**Result:**
\[
r = \underline{\quad}
\]
Use the formula and the data provided to compute the value of \( r \). Input your result in the space provided.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F70550eb8-aa65-4083-8eb4-f6c8d8ee1b0c%2F541a20a3-98fa-4946-9cb2-8a071b6dd489%2F6f3zrkt_processed.png&w=3840&q=75)
Transcribed Image Text:**Compute the Pearson Correlation for the Following Data**
Below is a table of paired data representing two variables, X and Y. To determine the strength and direction of the linear relationship between these variables, calculate the Pearson correlation coefficient (r).
| X | Y |
|---|---|
| 7 | 3 |
| 3 | 1 |
| 6 | 5 |
| 4 | 4 |
| 5 | 2 |
**Formula for Pearson Correlation Coefficient:**
\[
r = \frac{n(\sum{XY}) - (\sum{X})(\sum{Y})}{\sqrt{[n\sum{X^2} - (\sum{X})^2][n\sum{Y^2} - (\sum{Y})^2]}}
\]
Where:
- \( n \) is the number of data points.
- \( \sum{XY} \) is the sum of the products of corresponding X and Y values.
- \( \sum{X} \) is the sum of X values.
- \( \sum{Y} \) is the sum of Y values.
- \( \sum{X^2} \) is the sum of the squares of X values.
- \( \sum{Y^2} \) is the sum of the squares of Y values.
**Result:**
\[
r = \underline{\quad}
\]
Use the formula and the data provided to compute the value of \( r \). Input your result in the space provided.
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