MATLAB: An Introduction with Applications
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.
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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:

r=n∑xy×-∑x∑yn∑x2-∑x2×n∑y2-∑y2

x y x2 y2 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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