botanist gathered data about the number of pine, oak, and birch trees found in local parks. He used a graphing tool to organize ,
ata in different scatter plots and found the following lines of best fit:

The relationship between the numbers of pine trees, , and oak trees, , is modeled by the equation , and the
comelation coefficient for the data is 0.664 .

The relationship between the numbers of birch trees, , and oak trees, , is modeled by the equation , and the
correlation coefficient for the data is 0.939 .

The relationship between the numbers of birch trees, , and pine trees, , is modeled by the equation , and the
correlation coefficient for the data is 0.813 .
Which line of best fit can the botanist expect to produce the most reliable predictions?
the line modeling the numbers of pine trees and oak trees
the line modeling the numbers of birch trees and oak trees
the line modeling the numbers of birch trees and pine trees
All three lines will give equally reliable predictions.

Ask by Reed Bond. in the United States

Jan 23,2025

Question

botanist gathered data about the number of pine, oak, and birch trees found in local parks. He used a graphing tool to organize ,
ata in different scatter plots and found the following lines of best fit:

The relationship between the numbers of pine trees, , and oak trees, , is modeled by the equation , and the
comelation coefficient for the data is 0.664 .

The relationship between the numbers of birch trees, , and oak trees, , is modeled by the equation , and the
correlation coefficient for the data is 0.939 .

The relationship between the numbers of birch trees, , and pine trees, , is modeled by the equation , and the
correlation coefficient for the data is 0.813 .
Which line of best fit can the botanist expect to produce the most reliable predictions?
the line modeling the numbers of pine trees and oak trees
the line modeling the numbers of birch trees and oak trees
the line modeling the numbers of birch trees and pine trees
All three lines will give equally reliable predictions.

Ask by Reed Bond. in the United States

Jan 23,2025

UpStudy AI · Accepted Answer

To determine which line of best fit provides the most reliable predictions, we can examine the **correlation coefficients** for each relationship. The correlation coefficient ($$ r $$) measures the strength and direction of a linear relationship between two variables, with values ranging from -1 to 1. A value closer to 1 or -1 indicates a stronger linear relationship, while a value near 0 suggests a weak or no linear relationship.

Here are the given correlation coefficients:

1. **Pine vs. Oak Trees:** $$ r = 0.664 $$
2. **Birch vs. Oak Trees:** $$ r = 0.939 $$
3. **Birch vs. Pine Trees:** $$ r = 0.813 $$

**Analysis:**

- **Birch vs. Oak Trees** has the highest correlation coefficient ($$ r = 0.939 $$), indicating a very strong positive linear relationship.
- **Birch vs. Pine Trees** also has a strong correlation ($$ r = 0.813 $$), but it's not as strong as the Birch vs. Oak relationship.
- **Pine vs. Oak Trees** has the lowest correlation ($$ r = 0.664 $$), suggesting a moderate linear relationship.

**Conclusion:**

The higher the correlation coefficient, the more reliable the predictions based on the line of best fit. Therefore, the botanist can expect the most reliable predictions from the line modeling the **number of birch trees and oak trees**.

**Answer:**  
the line modeling the numbers of birch trees and oak trees
The line modeling the number of birch trees and oak trees provides the most reliable predictions.

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