1) Match each of the five scatterplots to the appropriate correlation coefficient and equation of regression line. Explain how you know that you have made a correct match. a. r= 0.83, y= -2.1 + 1.4x d. r= -0.83, y = 11.8 – 1.4x b. r= -0.31, y = 7.8 – 0.5x e. r= 0.41, y=1.4 + 1.4x c. r= 0.96, y= -2.1 + 1.4x Scatterplot 1 Scatterplot 2 Scatterplot 3 Scatterplot 4 Scatterplot 5
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.
![### Correlation and Regression Analysis
**Task:** Match each of the five scatterplots to the appropriate correlation coefficient and equation of the regression line. Explain how you know that you have made a correct match.
#### Provided Correlation Coefficients and Regression Equations:
a. \( r = 0.83 \), \( y = -2.1 + 1.4x \)
b. \( r = -0.31 \), \( y = 7.8 - 0.5x \)
c. \( r = 0.96 \), \( y = -2.1 + 1.4x \)
d. \( r = -0.83 \), \( y = 11.8 - 1.4x \)
e. \( r = 0.41 \), \( y = 1.4 + 1.4x \)
#### Scatterplots:
1. Scatterplot 1: Shows a positive trend with points closely clustered around a line.
2. Scatterplot 2: Shows a negative trend with points closely clustered around a line.
3. Scatterplot 3: Shows a strong positive trend with points very closely clustered around a line.
4. Scatterplot 4: Shows no clear trend, with points scattered widely around a central region.
5. Scatterplot 5: Shows moderate positive trend with points somewhat clustered around a line.
#### Matching:
1. **Scatterplot 1**
- **Match:** a. \( r = 0.83 \), \( y = -2.1 + 1.4x \)
- **Explanation:** The scatterplot shows a strong positive correlation, as \( r = 0.83 \) indicates a strong positive relationship.
2. **Scatterplot 2**
- **Match:** d. \( r = -0.83 \), \( y = 11.8 - 1.4x \)
- **Explanation:** The scatterplot shows a strong negative correlation, which matches the strong negative correlation coefficient \( r = -0.83 \).
3. **Scatterplot 3**
- **Match:** c. \( r = 0.96 \), \( y = -2.1 + 1.4x \)
- **Explanation:** The scatterplot shows a very strong positive correlation, closely matching \( r = 0.96 \).
4. **Scatterplot 4**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F85a16b31-7619-4bbb-b006-067a19fea2d2%2F823858bc-4222-4e93-9622-bbfa796e412a%2Fekwt2l6.png&w=3840&q=75)
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