For the data below, calculate the correlation coefficient between X and Y. You may use the calculator to find the answer, or you can use the totals provided to aid in the calculation by hand, in which case partial credit can be awarded if an error is made. Please round your answer to 3 decimal places. X Y X² Y² XY 20 16 400 80 15 36 225 90 2 100 4 20 8 225 64 120 6 256 36 96 4 324 16 72 Total 55 957 745 478 -0.779 0.779 -0.798 0.824 -0.824 0.798 OO 4 6 10 15 16 18 69
For the data below, calculate the correlation coefficient between X and Y. You may use the calculator to find the answer, or you can use the totals provided to aid in the calculation by hand, in which case partial credit can be awarded if an error is made. Please round your answer to 3 decimal places. X Y X² Y² XY 20 16 400 80 15 36 225 90 2 100 4 20 8 225 64 120 6 256 36 96 4 324 16 72 Total 55 957 745 478 -0.779 0.779 -0.798 0.824 -0.824 0.798 OO 4 6 10 15 16 18 69
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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![**Calculating the Correlation Coefficient using Given Data**
To determine the correlation coefficient between two variables X and Y, you will use the following dataset that includes their individual values, squares of these values (X² and Y²), and their products (XY).
### Data Table
| **X** | **Y** | **X²** | **Y²** | **XY** |
|:-----:|:-----:|:------:|:------:|:------:|
| 4 | 20 | 16 | 400 | 80 |
| 6 | 15 | 36 | 225 | 90 |
| 10 | 2 | 100 | 4 | 20 |
| 15 | 8 | 225 | 64 | 120 |
| 16 | 6 | 256 | 36 | 96 |
| 18 | 4 | 324 | 16 | 72 |
**Totals:**
- ΣX = 69
- ΣY = 55
- ΣX² = 957
- ΣY² = 745
- ΣXY = 478
### Calculating the Correlation Coefficient
The formula to calculate the correlation coefficient (r) is:
\[ r = \frac{n(\Sigma XY) - (\Sigma X)(\Sigma Y)}{\sqrt{[n \Sigma X^2 - (\Sigma X)^2][n \Sigma Y^2 - (\Sigma Y)^2]}} \]
Where:
- \( n \) is the number of pairs of scores
- \( \Sigma X \) is the sum of X scores
- \( \Sigma Y \) is the sum of Y scores
- \( \Sigma X^2 \) is the sum of squared X scores
- \( \Sigma Y^2 \) is the sum of squared Y scores
- \( \Sigma XY \) is the sum of the product of X and Y scores
Using the provided totals:
\[ n = 6 \]
\[ \Sigma X = 69 \]
\[ \Sigma Y = 55 \]
\[ \Sigma X^2 = 957 \]
\[ \Sigma Y^2 = 745 \]
\[ \Sigma XY = 478 \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff3c0899a-5c62-4a86-a39c-5b160af6a916%2F62f85f1d-83a7-4379-bf78-58ed2646d04b%2Fjpy7io9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Calculating the Correlation Coefficient using Given Data**
To determine the correlation coefficient between two variables X and Y, you will use the following dataset that includes their individual values, squares of these values (X² and Y²), and their products (XY).
### Data Table
| **X** | **Y** | **X²** | **Y²** | **XY** |
|:-----:|:-----:|:------:|:------:|:------:|
| 4 | 20 | 16 | 400 | 80 |
| 6 | 15 | 36 | 225 | 90 |
| 10 | 2 | 100 | 4 | 20 |
| 15 | 8 | 225 | 64 | 120 |
| 16 | 6 | 256 | 36 | 96 |
| 18 | 4 | 324 | 16 | 72 |
**Totals:**
- ΣX = 69
- ΣY = 55
- ΣX² = 957
- ΣY² = 745
- ΣXY = 478
### Calculating the Correlation Coefficient
The formula to calculate the correlation coefficient (r) is:
\[ r = \frac{n(\Sigma XY) - (\Sigma X)(\Sigma Y)}{\sqrt{[n \Sigma X^2 - (\Sigma X)^2][n \Sigma Y^2 - (\Sigma Y)^2]}} \]
Where:
- \( n \) is the number of pairs of scores
- \( \Sigma X \) is the sum of X scores
- \( \Sigma Y \) is the sum of Y scores
- \( \Sigma X^2 \) is the sum of squared X scores
- \( \Sigma Y^2 \) is the sum of squared Y scores
- \( \Sigma XY \) is the sum of the product of X and Y scores
Using the provided totals:
\[ n = 6 \]
\[ \Sigma X = 69 \]
\[ \Sigma Y = 55 \]
\[ \Sigma X^2 = 957 \]
\[ \Sigma Y^2 = 745 \]
\[ \Sigma XY = 478 \]
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