vvnat is me correation coemicient it me outier is exciuged, A. -0.97 B. -0.50 D. 0.97 b. How does the outlier affect the correlation coefficient? A. Including the outlier will change the sign of the correlation coefficient. B. Including the outlier will decrease the correlation coefficient. C. Including the outlier will increase the correlation coefficient. D. Including the outlier will have no affect on the correlation coefficient.

To address your problem, let's break it down into two parts: ### Part A: Correlation Coefficient You provided four options for the correlation coefficient: - A. -0.97 - B. -0.50 - D. 0.97 However, it seems like there is a typo in the options since "C" is missing. Assuming you meant to include "C" for one of the options, we will focus on the three provided. The correlation coefficient (denoted as \( r \)) measures the strength and direction of a linear relationship between two variables. The values range from -1 to 1: - \( r = 1 \) indicates a perfect positive correlation. - \( r = -1 \) indicates a perfect negative correlation. - \( r = 0 \) indicates no correlation. Given the options: - A. -0.97 indicates a strong negative correlation. - B. -0.50 indicates a moderate negative correlation. - D. 0.97 indicates a strong positive correlation. Without additional context or data, we cannot definitively determine which correlation coefficient is correct. However, if you have data that shows a strong relationship, you would choose the corresponding coefficient. ### Part B: Effect of Outlier on Correlation Coefficient Now, let's analyze how an outlier affects the correlation coefficient. The options provided are: - A. Including the outlier will change the sign of the correlation coefficient. - B. Including the outlier will decrease the correlation coefficient. - C. Including the outlier will increase the correlation coefficient. - D. Including the outlier will have no effect on the correlation coefficient. **Explanation:** 1. **Outliers can significantly affect the correlation coefficient.** If the outlier is in the opposite direction of the existing data trend, it can change the sign of the correlation coefficient (e.g., from positive to negative or vice versa). 2. **If the outlier is in line with the existing trend,** it can increase the correlation coefficient, making it closer to 1 or -1. 3. **If the outlier is far from the trend,** it can decrease the correlation coefficient, making it closer to 0. ### Conclusion - **For Part A**, without additional context, we cannot determine the correct correlation coefficient. - **For Part B**, the most accurate answer is likely **A**: Including the outlier will change the sign of the correlation coefficient, especially if the outlier is significantly different from the rest of the data points. If you have specific data or further context, please provide it for a more precise analysis!