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The variable ris known as the linear correlation coefficient. Summarize what the rvalue tells you about the scatter plot. What type of correlation will the follow scatter plots have based on the r values? Scatter r Values Plots Graph 1 r=-0.87 Graph 2 r= 0.58 Graph 3 r= 0.09

The variable ris known as the linear correlation coefficient. Summarize what the rvalue tells you about the scatter plot. What type of correlation will the follow scatter plots have based on the r values? Scatter r Values Plots Graph 1 r=-0.87 Graph 2 r= 0.58 Graph 3 r= 0.09

MATLAB: An Introduction with Applications
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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### Understanding the Linear Correlation Coefficient (r) The variable \( r \) is known as the linear correlation coefficient. It quantifies the strength and direction of a linear relationship between two variables in a scatter plot. The \( r \) value ranges from -1 to 1, where: - \( r = 1 \): Perfect positive linear correlation. - \( r = -1 \): Perfect negative linear correlation. - \( r = 0 \): No linear correlation. ### Analysis of Scatter Plots Based on \( r \) Values #### Scatter Plot Data - **Graph 1: \( r = -0.87 \)** - **Graph 2: \( r = 0.58 \)** - **Graph 3: \( r = 0.09 \)** #### Interpretation of \( r \) Values 1. **Graph 1 ( \( r = -0.87 \) )**: - **Correlation Type**: Strong negative correlation. - **Description**: As one variable increases, the other variable tends to decrease significantly. The scatter plot will show data points closely aligned along a downward-sloping line. 2. **Graph 2 ( \( r = 0.58 \) )**: - **Correlation Type**: Moderate positive correlation. - **Description**: As one variable increases, the other variable tends to increase as well, but the correlation is not perfect. The scatter plot will show data points forming a somewhat loose upward-sloping pattern. 3. **Graph 3 ( \( r = 0.09 \) )**: - **Correlation Type**: Very weak positive correlation. - **Description**: There is hardly any noticeable linear relationship between the two variables. The scatter plot will show data points scattered loosely with no discernible pattern. Understanding these \( r \) values helps in interpreting the relationship between the variables and provides insight into how strongly they are associated with each other.
Transcribed Image Text:### Understanding the Linear Correlation Coefficient (r) The variable \( r \) is known as the linear correlation coefficient. It quantifies the strength and direction of a linear relationship between two variables in a scatter plot. The \( r \) value ranges from -1 to 1, where: - \( r = 1 \): Perfect positive linear correlation. - \( r = -1 \): Perfect negative linear correlation. - \( r = 0 \): No linear correlation. ### Analysis of Scatter Plots Based on \( r \) Values #### Scatter Plot Data - **Graph 1: \( r = -0.87 \)** - **Graph 2: \( r = 0.58 \)** - **Graph 3: \( r = 0.09 \)** #### Interpretation of \( r \) Values 1. **Graph 1 ( \( r = -0.87 \) )**: - **Correlation Type**: Strong negative correlation. - **Description**: As one variable increases, the other variable tends to decrease significantly. The scatter plot will show data points closely aligned along a downward-sloping line. 2. **Graph 2 ( \( r = 0.58 \) )**: - **Correlation Type**: Moderate positive correlation. - **Description**: As one variable increases, the other variable tends to increase as well, but the correlation is not perfect. The scatter plot will show data points forming a somewhat loose upward-sloping pattern. 3. **Graph 3 ( \( r = 0.09 \) )**: - **Correlation Type**: Very weak positive correlation. - **Description**: There is hardly any noticeable linear relationship between the two variables. The scatter plot will show data points scattered loosely with no discernible pattern. Understanding these \( r \) values helps in interpreting the relationship between the variables and provides insight into how strongly they are associated with each other.
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