1. For the following set of scores, Y 4 5 6 5 3 2 4 3 a. Sketch a scatter plot and estimate the value of the Pearson correlation (ESTIMATE – make a guess!).
1. For the following set of scores, Y 4 5 6 5 3 2 4 3 a. Sketch a scatter plot and estimate the value of the Pearson correlation (ESTIMATE – make a guess!).
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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Transcribed Image Text:**Instruction:**
c. Multiply each of the original X values by 2 and compute the correlation for the modified scores. How does multiplying each score by a constant affect the value of the correlation?
**Educational Explanation:**
Correlation measures the strength and direction of a linear relationship between two variables. When each of the original X values is multiplied by a constant, such as 2, the shape of the data distribution changes (stretched or compressed), but the strength and direction of the linear relationship remain unchanged. Therefore, the correlation coefficient remains unaffected by these scalar transformations. The correlation value will stay the same even after multiplying the X values by 2.
![Certainly! Here is the transcription of the image for educational purposes:
---
1. For the following set of scores,
\[
\begin{array}{c|c}
X & Y \\
\hline
4 & 5 \\
6 & 5 \\
3 & 2 \\
9 & 4 \\
6 & 5 \\
2 & 3 \\
\end{array}
\]
a. Sketch a scatter plot and estimate the value of the Pearson correlation (ESTIMATE – make a guess!).
b. Compute the Pearson correlation.
---
**Explanation for creating a scatter plot:**
To sketch a scatter plot, plot each pair of \(X\) and \(Y\) values on a graph where the horizontal axis (x-axis) represents the values of \(X\) and the vertical axis (y-axis) represents the values of \(Y\). Each pair \((X, Y)\) represents a point on this graph.
**Steps:**
1. Label the x-axis with the possible values of \(X\) (2, 3, 4, 6, 9).
2. Label the y-axis with the possible values of \(Y\) (2, 3, 4, 5).
3. Plot each pair:
- (4, 5)
- (6, 5)
- (3, 2)
- (9, 4)
- (6, 5)
- (2, 3)
**Estimating Pearson Correlation:**
- Observe the direction of the points. If they appear to rise from left to right, the correlation is positive. If they fall, it is negative. If they do not show a clear trend, the correlation may be near zero.
**Compute the Pearson Correlation:**
Use the Pearson correlation coefficient formula to compute the exact value. This measure will indicate the strength and direction of the linear relationship between the variables.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe26ed137-f4d3-48c6-9bbb-9d7bb4efa013%2F3bd1e34f-4dd5-4784-84ec-84c945a256cc%2Fgwk8d7.jpeg&w=3840&q=75)
Transcribed Image Text:Certainly! Here is the transcription of the image for educational purposes:
---
1. For the following set of scores,
\[
\begin{array}{c|c}
X & Y \\
\hline
4 & 5 \\
6 & 5 \\
3 & 2 \\
9 & 4 \\
6 & 5 \\
2 & 3 \\
\end{array}
\]
a. Sketch a scatter plot and estimate the value of the Pearson correlation (ESTIMATE – make a guess!).
b. Compute the Pearson correlation.
---
**Explanation for creating a scatter plot:**
To sketch a scatter plot, plot each pair of \(X\) and \(Y\) values on a graph where the horizontal axis (x-axis) represents the values of \(X\) and the vertical axis (y-axis) represents the values of \(Y\). Each pair \((X, Y)\) represents a point on this graph.
**Steps:**
1. Label the x-axis with the possible values of \(X\) (2, 3, 4, 6, 9).
2. Label the y-axis with the possible values of \(Y\) (2, 3, 4, 5).
3. Plot each pair:
- (4, 5)
- (6, 5)
- (3, 2)
- (9, 4)
- (6, 5)
- (2, 3)
**Estimating Pearson Correlation:**
- Observe the direction of the points. If they appear to rise from left to right, the correlation is positive. If they fall, it is negative. If they do not show a clear trend, the correlation may be near zero.
**Compute the Pearson Correlation:**
Use the Pearson correlation coefficient formula to compute the exact value. This measure will indicate the strength and direction of the linear relationship between the variables.
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