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B A This graph has an r of -0.5. с D

B A This graph has an r of -0.5. с D

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 Correlation Coefficient (r) through Graphs** In this educational section, we explore the concept of the correlation coefficient (denoted as \(r\)) by examining various scatter plots. The correlation coefficient measures the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where: - \(r = 1\): Perfect positive linear relationship. - \(r = -1\): Perfect negative linear relationship. - \(r = 0\): No linear relationship. **Analysis of Scatter Plots:** - **Graph A:** - Description: A scatter plot depicting a downward trend of data points. - Interpretation: It likely has a negative correlation, indicating that as one variable increases, the other decreases. - **Graph B:** - Description: A scatter plot depicting an upward trend of data points. - Interpretation: It likely shows a positive correlation, indicating that as one variable increases, the other also increases. - **Graph C:** - Description: A scatter plot with data points spread without any discernible upward or downward trend. - Interpretation: It likely signifies no or very weak correlation, indicating no clear relationship between the variables. - **Graph D:** - Description: A scatter plot where data points are randomly spread without any visible pattern. - Interpretation: It likely indicates no correlation, suggesting that the variables do not have a linear relationship. **Contextual Information from the Image:** - The text below the graphs states, "This graph has an \(r\) of -0.5." - Given this information, we can identify the graph that matches the correlation coefficient \(r = -0.5\). A correlation of -0.5 indicates a moderate negative linear relationship between two variables. Therefore, this description most closely matches the scatter plot in **Graph A**. Understanding and visually analyzing these graphs helps in grasping how the correlation coefficient quantifies the direction and strength of the linear relationship between variables in statistics.
Transcribed Image Text:**Understanding Correlation Coefficient (r) through Graphs** In this educational section, we explore the concept of the correlation coefficient (denoted as \(r\)) by examining various scatter plots. The correlation coefficient measures the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where: - \(r = 1\): Perfect positive linear relationship. - \(r = -1\): Perfect negative linear relationship. - \(r = 0\): No linear relationship. **Analysis of Scatter Plots:** - **Graph A:** - Description: A scatter plot depicting a downward trend of data points. - Interpretation: It likely has a negative correlation, indicating that as one variable increases, the other decreases. - **Graph B:** - Description: A scatter plot depicting an upward trend of data points. - Interpretation: It likely shows a positive correlation, indicating that as one variable increases, the other also increases. - **Graph C:** - Description: A scatter plot with data points spread without any discernible upward or downward trend. - Interpretation: It likely signifies no or very weak correlation, indicating no clear relationship between the variables. - **Graph D:** - Description: A scatter plot where data points are randomly spread without any visible pattern. - Interpretation: It likely indicates no correlation, suggesting that the variables do not have a linear relationship. **Contextual Information from the Image:** - The text below the graphs states, "This graph has an \(r\) of -0.5." - Given this information, we can identify the graph that matches the correlation coefficient \(r = -0.5\). A correlation of -0.5 indicates a moderate negative linear relationship between two variables. Therefore, this description most closely matches the scatter plot in **Graph A**. Understanding and visually analyzing these graphs helps in grasping how the correlation coefficient quantifies the direction and strength of the linear relationship between variables in statistics.
### Student Absence Data Analysis The table below displays the number of absences (\(x\)) in a class and the corresponding final exam grades (\(y\)) for seven students. | \(x\) | 1 | 0 | 2 | 6 | 4 | 3 | 3 | | :-: | :-: | :-: | :-: | :-: | :-: | :-: | :-: | | \(y\) | 95 | 90 | 90 | 55 | 70 | 80 | 85 | ### Task Use a graphing calculator to determine the correlation coefficient for the data provided. This will help to quantify the relationship between the number of absences and the final exam grades. **Instructions:** 1. Input the data into your graphing calculator. 2. Calculate the correlation coefficient. 3. Round the answer to three decimal places (e.g., 0.123, not .123). **Input Field:** [ ] *Note: Ensure that the rounded answer is accurate to three decimal places.*
Transcribed Image Text:### Student Absence Data Analysis The table below displays the number of absences (\(x\)) in a class and the corresponding final exam grades (\(y\)) for seven students. | \(x\) | 1 | 0 | 2 | 6 | 4 | 3 | 3 | | :-: | :-: | :-: | :-: | :-: | :-: | :-: | :-: | | \(y\) | 95 | 90 | 90 | 55 | 70 | 80 | 85 | ### Task Use a graphing calculator to determine the correlation coefficient for the data provided. This will help to quantify the relationship between the number of absences and the final exam grades. **Instructions:** 1. Input the data into your graphing calculator. 2. Calculate the correlation coefficient. 3. Round the answer to three decimal places (e.g., 0.123, not .123). **Input Field:** [ ] *Note: Ensure that the rounded answer is accurate to three decimal places.*
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