Match each scatterplot shown below with one of the four specified correlations.
MATLAB: An Introduction with Applications
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Chapter1: Starting With Matlab
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Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
Question
Match each
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.
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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