A data set was graphed using a scatterplot.



The correlation coefficient, r, is 0.845.

**Which of the following statements explains how the correlation is affected?**

A.)

It is affected by inappropriate grouping.

B.)

It is not affected.

C.)

It is affected by nonlinearity.

D.)

It is affected by an influential point.

The correlation coefficient, \( r = 0.845 \), indicates a strong positive linear relationship between the variables in the scatterplot. Based on this value, we can analyze how different factors might affect the correlation:

- **A.) It is affected by inappropriate grouping:** Grouping data could potentially affect correlation, but this option is typically more relevant when the data has been aggregated or categorized in a way that distorts relationships between individual data points. This does not seem applicable here.

- **B.) It is not affected:** The correlation coefficient of \( r = 0.845 \) suggests a relatively strong relationship. If the data has no underlying issues like outliers, nonlinearity, or other influencing factors, this could be the correct choice. However, let's consider the other options.

- **C.) It is affected by nonlinearity:** A correlation coefficient is specifically a measure of *linear* relationships. If the data in the scatterplot follows a nonlinear pattern, the value of \( r \) may still be high, but it wouldn't accurately describe the true nature of the relationship. This doesn't appear to be supported here since \( r = 0.845 \) points to a fairly strong linear relationship.

- **D.) It is affected by an influential point:** An influential point (outlier) can significantly affect the correlation. A single influential data point that is far from the others could artificially increase or decrease the correlation coefficient. Therefore, this option could explain how the correlation might be affected.

### Conclusion:
The correct answer is likely **D.) It is affected by an influential point**, as an influential outlier can have a significant impact on the correlation coefficient.

Would you like further details on this topic or have any questions?

Here are 5 related questions for deeper exploration:
1. How do outliers affect correlation and regression lines in scatterplots?
2. What methods can be used to detect influential points in data analysis?
3. How does grouping data impact the calculation of correlation coefficients?
4. Can nonlinear relationships result in misleadingly high or low correlation coefficients?
5. How do you determine when a correlation coefficient accurately reflects a linear relationship?

**Tip:** Always inspect your data visually with a scatterplot to ensure that the correlation coefficient aligns with the actual data pattern, especially looking for outliers or nonlinearity.

A data set was graphed using a scatterplot. The correlation coefficient, r, is 0.845. Which of the following statements explains how the correlation is affected?
A.) It is affected by inappropriate grouping.
B.) It is not affected.
C.) It is affected by nonlinearity.
D.) It is affected by an influential point.

Explore how an influential point can affect the correlation coefficient in a scatterplot, with a strong positive correlation of r = 0.845. This problem covers key concepts in statistics, including outliers, linear relationships, and scatterplot analysis. Suitable for students in Grades 10-12.

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