For the plot below the value of r2 is 0.7783.

**Which of the following sets of statements is true?**

About 78% of the variation in ticket price can be explained by the distance flown.

The correlation coefficient, r, is 0.882.

About 78% of the variation in distance flown can be explained by the ticket price.

The correlation coefficient, r, is 0.606.

About 22% of the variation in ticket price can be explained by the distance flown.

The correlation coefficient, r, is 0.606.

About 88% of the variation in ticket price can be explained by the distance flown.

The correlation coefficient, r, is 0.882.

To solve this, we need to use the fact that the coefficient of determination \( r^2 \) is given as 0.7783. The relationship between the correlation coefficient \( r \) and \( r^2 \) is as follows:

\[
r = \pm \sqrt{r^2}
\]

Thus, we can calculate \( r \):

\[
r = \sqrt{0.7783} \approx 0.882
\]

### Interpretation of Statements:

1. **"About 78% of the variation in ticket price can be explained by the distance flown."**
   - This is correct because \( r^2 = 0.7783 \), which means 77.83% of the variation in ticket price is explained by the distance flown.

2. **"The correlation coefficient, r, is 0.882."**
   - This is correct because \( r = \sqrt{0.7783} \approx 0.882 \).

3. **"About 78% of the variation in distance flown can be explained by the ticket price."**
   - This statement is false. \( r^2 \) here refers to the percentage of variation in **ticket price** explained by the **distance flown**, not the other way around.

4. **"The correlation coefficient, r, is 0.606."**
   - This is false. The correlation coefficient is 0.882, not 0.606.

5. **"About 22% of the variation in ticket price can be explained by the distance flown."**
   - This is false. \( 100\% - 77.83\% = 22.17\% \), so 22% of the variation in ticket price **cannot** be explained by the distance flown.

6. **"About 88% of the variation in ticket price can be explained by the distance flown."**
   - This is false because 77.83% of the variation in ticket price can be explained, not 88%.

### Conclusion:
The true set of statements is:
- **"About 78% of the variation in ticket price can be explained by the distance flown."**
- **"The correlation coefficient, r, is 0.882."**

Would you like further details or have any other questions?

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Here are some related questions to consider:

1. How is the \( r^2 \) value interpreted in linear regression?
2. What is the difference between \( r \) and \( r^2 \) in correlation analysis?
3. How would the value of \( r \) change if the variables were inversely related?
4. Can \( r^2 \) be negative in any scenario?
5. How do outliers affect the correlation coefficient \( r \)?

**Tip:** The closer the correlation coefficient \( r \) is to 1 or -1, the stronger the linear relationship between the two variables.

For the plot below the value of r2 is 0.7783. Which of the following sets of statements is true? About 78% of the variation in ticket price can be explained by the distance flown. The correlation coefficient, r, is 0.882. About 78% of the variation in distance flown can be explained by the ticket price. The correlation coefficient, r, is 0.606. About 22% of the variation in ticket price can be explained by the distance flown. The correlation coefficient, r, is 0.606. About 88% of the variation in ticket price can be explained by the distance flown. The correlation coefficient, r, is 0.882.

Learn how to interpret the coefficient of determination (r² = 0.7783) and correlation coefficient (r ≈ 0.882) in a linear regression context. This example explains how 78% of the variation in ticket price is explained by the distance flown. Suitable for Grades 10-12 students studying statistics.

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