https://file.aiquickdraw.com/mathbot/file/1726854893009e3l8izhr.jpg

The scatter plot in the image shows a clear U-shaped pattern, indicating a nonlinear relationship between the variables. Despite this, the correlation coefficient \( r = 0.845 \) suggests a strong linear relationship, which is misleading in this context due to the nonlinearity of the data.

**Correct Answer: (c) It is affected by nonlinearity.**

The correlation coefficient measures the strength of a linear relationship, and in the presence of nonlinearity, as in this case, it can give a distorted view of the relationship between the variables.

Would you like more details or have any other questions? Here are some related questions to consider:

1. What does a correlation coefficient close to 1 or -1 indicate in a dataset?
2. How can we detect nonlinearity in a dataset using visual methods?
3. What are some statistical tests that can be used to check for nonlinearity?
4. How do influential points affect the correlation coefficient?
5. What alternative methods can be used to measure nonlinear relationships?

**Tip:** Always plot your data before relying solely on statistical measures like the correlation coefficient, especially when assessing linearity or nonlinearity.

Which of the following statements explains how the correlation is affected based on the scatter plot provided?

Analyze the scatter plot with a correlation coefficient of r = 0.845 to understand how nonlinearity affects correlation. Learn about the limitations of correlation in identifying nonlinear relationships and the importance of visual data inspection. Suitable for college-level students.

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