Find the Pearson r(correlation coefficient value r) for the correlation between the number of hours student slept the night before a test and their test score. Round your answer up to two decimal places. Hours Test |slept(X) |Score(Y) 8 83 7 86 7 74 8 88 6 76 5 7 4 9 7 63 90 60 89 81 Use the formula :r = ΣΧ2 = 482 ΣΥ N Σ XY-(Σ X)(ΣΥ) [N Σ Χ -(Σ X)][N ΣΥ-(ΣΥ)] and Σ XY = 5, 497 = 63, 432 given Σ X = 68 ΣΥ = 790
Find the Pearson r(correlation coefficient value r) for the correlation between the number of hours student slept the night before a test and their test score. Round your answer up to two decimal places. Hours Test |slept(X) |Score(Y) 8 83 7 86 7 74 8 88 6 76 5 7 4 9 7 63 90 60 89 81 Use the formula :r = ΣΧ2 = 482 ΣΥ N Σ XY-(Σ X)(ΣΥ) [N Σ Χ -(Σ X)][N ΣΥ-(ΣΥ)] and Σ XY = 5, 497 = 63, 432 given Σ X = 68 ΣΥ = 790
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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Problem 1P
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![**Calculation of Pearson Correlation Coefficient**
To find the Pearson correlation coefficient \( r \) for the correlation between the number of hours students slept the night before a test and their test score, follow the formula provided. Round your answer to two decimal places.
### Data Table
| Hours Slept (X) | Test Score (Y) |
|-----------------|----------------|
| 8 | 83 |
| 7 | 86 |
| 7 | 74 |
| 8 | 88 |
| 6 | 76 |
| 5 | 63 |
| 7 | 90 |
| 4 | 60 |
| 9 | 89 |
| 7 | 81 |
### Formula
\[
r = \frac{N \sum XY - (\sum X)(\sum Y)}{\sqrt{[N \sum X^2 - (\sum X)^2][N \sum Y^2 - (\sum Y)^2]}}
\]
### Given Values
- \( \sum X = 68 \)
- \( \sum Y = 790 \)
- \( \sum X^2 = 482 \)
- \( \sum Y^2 = 63,432 \)
- \( \sum XY = 5,497 \)
### Explanation
- \( N \) is the number of data points (students).
- \( \sum X \) and \( \sum Y \) are the sums of the hours slept and test scores respectively.
- \( \sum X^2 \) and \( \sum Y^2 \) are the sums of squares of the hours slept and test scores respectively.
- \( \sum XY \) is the sum of the product of each pair of x and y values.
Use these values to calculate the Pearson correlation coefficient \( r \) using the formula above.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc93f7ec4-1394-4d16-9950-c6e617845ace%2F81de69f8-ec7a-4df3-832b-3ad25f9a5e32%2Fgxxsu2j_processed.png&w=3840&q=75)
Transcribed Image Text:**Calculation of Pearson Correlation Coefficient**
To find the Pearson correlation coefficient \( r \) for the correlation between the number of hours students slept the night before a test and their test score, follow the formula provided. Round your answer to two decimal places.
### Data Table
| Hours Slept (X) | Test Score (Y) |
|-----------------|----------------|
| 8 | 83 |
| 7 | 86 |
| 7 | 74 |
| 8 | 88 |
| 6 | 76 |
| 5 | 63 |
| 7 | 90 |
| 4 | 60 |
| 9 | 89 |
| 7 | 81 |
### Formula
\[
r = \frac{N \sum XY - (\sum X)(\sum Y)}{\sqrt{[N \sum X^2 - (\sum X)^2][N \sum Y^2 - (\sum Y)^2]}}
\]
### Given Values
- \( \sum X = 68 \)
- \( \sum Y = 790 \)
- \( \sum X^2 = 482 \)
- \( \sum Y^2 = 63,432 \)
- \( \sum XY = 5,497 \)
### Explanation
- \( N \) is the number of data points (students).
- \( \sum X \) and \( \sum Y \) are the sums of the hours slept and test scores respectively.
- \( \sum X^2 \) and \( \sum Y^2 \) are the sums of squares of the hours slept and test scores respectively.
- \( \sum XY \) is the sum of the product of each pair of x and y values.
Use these values to calculate the Pearson correlation coefficient \( r \) using the formula above.
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