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

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### 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**
Transcribed Image Text:### 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**
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