Solve for the r value for the following data set. Show your work and explain the steps you used to solve. Round your answer to the nearest thousandths. X Y 30 75 60 89 90 88 180 93 150 95 Use the paperclip button below to attach files.
Solve for the r value for the following data set. Show your work and explain the steps you used to solve. Round your answer to the nearest thousandths. X Y 30 75 60 89 90 88 180 93 150 95 Use the paperclip button below to attach files.
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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Question
![## Educational Exercise: Calculating the Correlation Coefficient (r)
### Objective:
Solve for the correlation coefficient \( r \) value for the following data set. Show your work and explain the steps you used to solve. Round your answer to the nearest thousandths.
```
X Y
30 75
60 89
90 88
180 93
150 95
```
### Instructions:
1. **Understand the Data**:
- The data represents pairs of values (X, Y).
2. **Formula for Correlation Coefficient (r)**:
\[
r = \frac{n(\sum{XY}) - (\sum{X})(\sum{Y})}{\sqrt{[n\sum{X^2} - (\sum{X})^2][n\sum{Y^2} - (\sum{Y})^2]}}
\]
where \( n \) is the number of pairs.
3. **Summarize the Data**:
- Calculate the sum of X values: \(\sum{X}\)
- Calculate the sum of Y values: \(\sum{Y}\)
- Calculate the sum of the products of X and Y pairs: \(\sum{XY}\)
- Calculate the sum of the squares of X values: \(\sum{X^2}\)
- Calculate the sum of the squares of Y values: \(\sum{Y^2}\)
4. **Plug in the values**:
- Substitute the calculated summations into the formula and solve for \( r \).
### Graphs and Diagrams Explanation:
- This problem does not include any explicit graphs or diagrams but involves numerical data. It requires the calculation of summations and the final correlation coefficient to understand the linear relationship between the X and Y variables. If a graph were to be plotted, you would see the plotted points (X, Y) on a scatter plot and potentially a line of best fit.
### Example Steps:
1. **Calculate Summations**:
\[
\sum{X} = 30 + 60 + 90 + 180 + 150 = 510
\]
\[
\sum{Y} = 75 + 89 + 88 + 93 + 95 = 440
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc4056cef-3867-489f-a260-f13d42f9bf0e%2F7b5af464-ec30-443b-a078-402d017430ba%2F1xmtjk8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Educational Exercise: Calculating the Correlation Coefficient (r)
### Objective:
Solve for the correlation coefficient \( r \) value for the following data set. Show your work and explain the steps you used to solve. Round your answer to the nearest thousandths.
```
X Y
30 75
60 89
90 88
180 93
150 95
```
### Instructions:
1. **Understand the Data**:
- The data represents pairs of values (X, Y).
2. **Formula for Correlation Coefficient (r)**:
\[
r = \frac{n(\sum{XY}) - (\sum{X})(\sum{Y})}{\sqrt{[n\sum{X^2} - (\sum{X})^2][n\sum{Y^2} - (\sum{Y})^2]}}
\]
where \( n \) is the number of pairs.
3. **Summarize the Data**:
- Calculate the sum of X values: \(\sum{X}\)
- Calculate the sum of Y values: \(\sum{Y}\)
- Calculate the sum of the products of X and Y pairs: \(\sum{XY}\)
- Calculate the sum of the squares of X values: \(\sum{X^2}\)
- Calculate the sum of the squares of Y values: \(\sum{Y^2}\)
4. **Plug in the values**:
- Substitute the calculated summations into the formula and solve for \( r \).
### Graphs and Diagrams Explanation:
- This problem does not include any explicit graphs or diagrams but involves numerical data. It requires the calculation of summations and the final correlation coefficient to understand the linear relationship between the X and Y variables. If a graph were to be plotted, you would see the plotted points (X, Y) on a scatter plot and potentially a line of best fit.
### Example Steps:
1. **Calculate Summations**:
\[
\sum{X} = 30 + 60 + 90 + 180 + 150 = 510
\]
\[
\sum{Y} = 75 + 89 + 88 + 93 + 95 = 440
\]
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