https://file.aiquickdraw.com/mathbot/file/1728083201868g9nljoaz.jpg

https://file.aiquickdraw.com/mathbot/file/1728083201868yeuwpktd.jpg

accurately match these values of r with the accompanying 5 scatter plots : 0.767, 1, -1, -0.767, and -0.396. 

To match the correlation coefficients (r-values) \( 0.767 \), \( 1 \), \( -1 \), \( -0.767 \), and \( -0.396 \) with the given scatter plots, let's first understand what the r-values represent:

- **r = 1**: This indicates a perfect positive linear relationship. The points should lie on a straight line with a positive slope.
- **r = -1**: This indicates a perfect negative linear relationship. The points should lie on a straight line with a negative slope.
- **r = 0.767**: This suggests a strong positive correlation, but not perfect. The points should generally follow a positive trend but may have some scatter.
- **r = -0.767**: This suggests a strong negative correlation, but not perfect. The points should generally follow a negative trend but may have some scatter.
- **r = -0.396**: This indicates a weaker negative correlation. There is still a downward trend, but the points will be more scattered.

### Scatterplot Observations:

1. **Scatterplot 1**: The points show a negative linear relationship. This indicates a strong negative correlation, likely **r = -1**.
2. **Scatterplot 2**: The points are scattered with no clear trend, but there appears to be a slight negative correlation. This likely corresponds to **r = -0.396**.
3. **Scatterplot 3**: The points are scattered, but there's a slight positive trend, corresponding to a lower positive correlation. This should correspond to **r = 0.767**.
4. **Scatterplot 4**: The points lie on a straight line with a positive slope, indicating a perfect positive correlation, **r = 1**.
5. **Scatterplot 5**: The points have a general negative trend with some scatter, likely indicating **r = -0.767**.

### Final Matching:
- Scatterplot 1: \( r = -1 \)
- Scatterplot 2: \( r = -0.396 \)
- Scatterplot 3: \( r = 0.767 \)
- Scatterplot 4: \( r = 1 \)
- Scatterplot 5: \( r = -0.767 \)

Would you like further details or have any questions on correlation and scatter plots?

### Relative Questions:
1. What does a correlation coefficient of 0 imply about the scatter plot?
2. How can outliers affect the value of r in a scatter plot?
3. What is the difference between positive and negative correlations?
4. How can we visually identify if a scatter plot has a weak or strong correlation?
5. Can non-linear relationships have a high correlation coefficient?

### Tip:
The closer the r-value is to 1 or -1, the stronger the linear relationship. A value near 0 suggests little to no linear relationship.

accurately match these values of r with the accompanying 5 scatter plots: 0.767, 1, -1, -0.767, and -0.396.

Learn how to match the correlation coefficients (0.767, 1, -1, -0.767, and -0.396) with their respective scatter plots. This problem explores key statistical concepts such as positive and negative linear relationships, the correlation coefficient, and how to visually assess scatter plot trends. Suitable for high school students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation