https://file.aiquickdraw.com/mathbot/file/1726810203300mvx1m4xq.jpg

The scatterplot shows the ages and net worth of 12 wealthy individuals, with a specific point, \( Q \), marked at age 83. The question asks which of the following is likely **not affected** by the removal of \( Q \) from the dataset.

Let's analyze each option to see what might be least affected:

- **A. The correlation coefficient**: Removing point \( Q \) can affect the correlation, as this point appears to be an outlier compared to the other data points. The correlation depends on all points and measures how closely the points form a linear relationship. Removing \( Q \) could alter this significantly.
  
- **B. The sign of the slope coefficient**: The slope of a line in linear regression indicates the direction of the relationship. Even if point \( Q \) is removed, the remaining points still show a positive linear trend (as age increases, net worth increases). Therefore, the **sign** of the slope (positive or negative) is unlikely to change, though its magnitude might.

- **C. The value of the slope coefficient**: The slope is sensitive to the exact position of the data points. Since \( Q \) is further out, its removal would likely change the actual value of the slope, even if the sign remains the same.

- **D. The sum of the squared residuals**: Removing an outlier like \( Q \) would likely decrease the sum of squared residuals, as outliers generally increase this measure. Hence, this would be affected.

- **E. The net worth intercept**: The intercept could shift as well because it depends on the placement of the regression line, which may change once \( Q \) is removed.

### Conclusion: The correct answer is likely **B** (The sign of the slope coefficient), as removing \( Q \) would not change the fact that the trend is positive.

---

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

Here are 5 related questions for deeper understanding:
1. How does an outlier influence the correlation coefficient?
2. What are residuals, and why do outliers increase them?
3. How is the slope of a regression line calculated?
4. What is the impact of removing a data point on the regression equation?
5. How is the intercept of a regression line affected by data changes?

**Tip:** Outliers can have a large impact on regression analysis, particularly on the slope, intercept, and correlation coefficient, but they often don't change the overall direction (sign) of the relationship.

Suppose point Q is removed from the data set. Which of the following is likely not affected by the removal? (Choices: A) The correlation coefficient, B) The sign of the slope coefficient, C) The value of the slope coefficient, D) The sum of the squared residuals, E) The net worth intercept.)

Explore how removing an outlier (point Q at age 83) affects the correlation coefficient, slope, intercept, and residuals in a linear regression analysis. Learn how the sign of the slope remains unaffected while other metrics may change. 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