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Match each scatterplot shown below with one of the four specified correlations.

Match each scatterplot shown below with one of the four specified correlations.

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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Match each scatterplot shown below with one of the four specified correlations.

**Understanding Scatter Plots: Analysis and Interpretation** The image above represents a scatter plot, a valuable type of data visualization used in various fields including statistics, mathematics, and science to observe and analyze relationships between two sets of data. **Description of the Scatter Plot:** 1. **Axes and Quadrants**: - **Horizontal Axis (X-axis)**: Represents the independent variable. - **Vertical Axis (Y-axis)**: Represents the dependent variable. - The plot is divided into four quadrants by intersecting axes. 2. **Data Points**: - Each yellow circle represents a data point with a corresponding pair of X and Y values. - The scatter plot contains numerous data points spread across all four quadrants. 3. **Distribution Pattern**: - There appears to be a cluster of points in the first quadrant (top-right section) conveying a possible concentration of high values for both variables. - A notable spread of points exists in the third quadrant (bottom-left section), illustrating a distribution of lower values for both variables. - Additionally, some points are scattered in the second (top-left) and fourth (bottom-right) quadrants, indicating a mixture of high and low values for the respective variables. 4. **Zoom and Scale Adjustments**: The plot includes interactive buttons (with "+" and "-" symbols) allowing users to zoom in and out for a detailed view of data points. **Interpretation**: The scatter plot is often used to visually assess: - **Trends**: By observing any clear direction or pattern that data points form. - **Correlation**: To deduce the potential relationship between variables (positive or negative). - **Outliers**: Identifiable as data points that deviate significantly from other observations. Understanding scatter plots aids in making informed data-driven decisions, determining correlations, and identifying trends and anomalies in datasets. This visualization thus acts as a cornerstone in empirical research and statistical analysis. Feel free to utilize the interactive tools provided in the plot for a deeper exploration and analysis of the dataset.
Transcribed Image Text:**Understanding Scatter Plots: Analysis and Interpretation** The image above represents a scatter plot, a valuable type of data visualization used in various fields including statistics, mathematics, and science to observe and analyze relationships between two sets of data. **Description of the Scatter Plot:** 1. **Axes and Quadrants**: - **Horizontal Axis (X-axis)**: Represents the independent variable. - **Vertical Axis (Y-axis)**: Represents the dependent variable. - The plot is divided into four quadrants by intersecting axes. 2. **Data Points**: - Each yellow circle represents a data point with a corresponding pair of X and Y values. - The scatter plot contains numerous data points spread across all four quadrants. 3. **Distribution Pattern**: - There appears to be a cluster of points in the first quadrant (top-right section) conveying a possible concentration of high values for both variables. - A notable spread of points exists in the third quadrant (bottom-left section), illustrating a distribution of lower values for both variables. - Additionally, some points are scattered in the second (top-left) and fourth (bottom-right) quadrants, indicating a mixture of high and low values for the respective variables. 4. **Zoom and Scale Adjustments**: The plot includes interactive buttons (with "+" and "-" symbols) allowing users to zoom in and out for a detailed view of data points. **Interpretation**: The scatter plot is often used to visually assess: - **Trends**: By observing any clear direction or pattern that data points form. - **Correlation**: To deduce the potential relationship between variables (positive or negative). - **Outliers**: Identifiable as data points that deviate significantly from other observations. Understanding scatter plots aids in making informed data-driven decisions, determining correlations, and identifying trends and anomalies in datasets. This visualization thus acts as a cornerstone in empirical research and statistical analysis. Feel free to utilize the interactive tools provided in the plot for a deeper exploration and analysis of the dataset.
### Understanding Correlation in Scatterplots #### Exercise: Match Each Scatterplot with Its Correlation Scatterplots are a graphical representation of the relationship between two variables. In this exercise, you are given two scatterplots and a list of correlation coefficients. Your task is to match each scatterplot with the correct correlation coefficient. **Scatterplots:** 1. **Top Scatterplot:** - The data points trend downward from the top left to the bottom right. - This plot shows a clear negative correlation, though the points do not fit perfectly on a straight line, indicating a somewhat strong negative relationship. 2. **Bottom Scatterplot:** - The data points are scattered with no clear pattern. - This suggests a very weak correlation, likely close to 0, as the points do not form a clear line or trend. **Correlation Coefficients to Match:** a. -0.59 b. 0.94 c. -0.93 d. 0.56 ### Explanation of Correlation Coefficients: - **-0.59:** Indicates a moderate negative correlation. - **0.94:** Indicates a very strong positive correlation. - **-0.93:** Indicates a very strong negative correlation. - **0.56:** Indicates a moderate positive correlation. Using the descriptions of the scatterplots and the definitions of the correlation coefficients, match each scatterplot with its corresponding correlation: - **Top Scatterplot:** Given the downward trend of the data points and the strong negative relationship, this plot most likely corresponds to **c. -0.93.** - **Bottom Scatterplot:** Given the scattered nature of the data points with no clear pattern, this plot most likely corresponds to **a. -0.59.** Understanding these scatterplots and their correlations helps in analyzing the strength and direction of the relationships between variables in your data.
Transcribed Image Text:### Understanding Correlation in Scatterplots #### Exercise: Match Each Scatterplot with Its Correlation Scatterplots are a graphical representation of the relationship between two variables. In this exercise, you are given two scatterplots and a list of correlation coefficients. Your task is to match each scatterplot with the correct correlation coefficient. **Scatterplots:** 1. **Top Scatterplot:** - The data points trend downward from the top left to the bottom right. - This plot shows a clear negative correlation, though the points do not fit perfectly on a straight line, indicating a somewhat strong negative relationship. 2. **Bottom Scatterplot:** - The data points are scattered with no clear pattern. - This suggests a very weak correlation, likely close to 0, as the points do not form a clear line or trend. **Correlation Coefficients to Match:** a. -0.59 b. 0.94 c. -0.93 d. 0.56 ### Explanation of Correlation Coefficients: - **-0.59:** Indicates a moderate negative correlation. - **0.94:** Indicates a very strong positive correlation. - **-0.93:** Indicates a very strong negative correlation. - **0.56:** Indicates a moderate positive correlation. Using the descriptions of the scatterplots and the definitions of the correlation coefficients, match each scatterplot with its corresponding correlation: - **Top Scatterplot:** Given the downward trend of the data points and the strong negative relationship, this plot most likely corresponds to **c. -0.93.** - **Bottom Scatterplot:** Given the scattered nature of the data points with no clear pattern, this plot most likely corresponds to **a. -0.59.** Understanding these scatterplots and their correlations helps in analyzing the strength and direction of the relationships between variables in your data.
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